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Flying circus of physics

Chap 1 (motion) archived stories part A

Thursday, February 12, 2009

For Chapter 1, here is part A of the new stories and also the updates to the items in the book, including many video links and journal citations. If you want all the video links (hundreds) and journal citations (thousands) for this chapter, go to

First a list   (use "Ctrl-F" to search for a key word or just scroll down the screen)

1.1   Rain on the back window
1.6   Spin out during police chase
1.11 Headbanging and detached retinas
1.12  High-speed car crash
1.12  Collisions at high speeds
1.12  Car crashes: shops, walls, and other cars
1.19  Scariest car on a roller coaster
1.19  Vertical roller coaster loops
1.23  Humidying baseballs for the Denver team
1.25  Juggling hammers, hitting a nail on the head
1.33  Basketball free throw
1.36  Golf ball hopping out of a cup
1.37  Curtain of death in a meteor strike, and a hoax
1.38  Camel jumping
1.38  Long jump
1.38  Fosbury flop
1.39  Jumping beans
1.41  Dead lift
1.45 Tae-kwon-do punch
1.46  Punches in boxing
1.46  Cannonball Richards
1.49  Fall of window cleaner
1.51  Feline high-rise syndrome

Reference and difficulty dots
Dots · through · · · indicate level of difficulty
Journal reference style: author, title, journal, volume, pages (date)
Book reference style: author, title, publisher, date, pages

Now the stories

1.1   Rain on the back window
Jearl Walker
July 2007
In the Flying Circus book I talk about the common question: To reduce the amount of rain you intercept as you cross a street in falling rain, should you walk or run? The answer involves the relative motion between you and the rain, especially when the drops move along paths that are slanted from the vertical. In that case, if you run in the direction the drops are falling, you get the least wet if you run just as fast as the drops are moving horizontally during their fall. Then you don’t collect drops on your front or back, just on the top of your head.

In 1997, Pietro Ferraro of Istituto Professionale de Stato Per I’Industria e l’Artigianato “G. L. Bernini” and Istituto di Cibernetica del CNR pointed out a similar effect that he noticed while driving. His car had a rear window that was slanted in the forward direction, and he was driving directly into the oncoming rain. That is, its horizontal motion was directly toward him. As he glanced at his rear-view window, he noticed that he could keep the rear window was relatively dry if he drove at a certain speed.

Consider a raindrop that is just above the top of the rear window and falling straight down. If the car has the correct speed, the falling drop is always just above the window as the window moves forward and finally lands on the back of the car (the trunk or the boot). Assuming that we can neglect the air flow coming over the top of the car and down along the rear window, we can use the car’s speed to calculate the speed at which the drop falls.

If you look for this effect, take care. If you concentrate on watching the rear window via the rear-view mirror, the resulting car crash could end up on YouTube. (Well, I could then put a link to the video here in this website. Would that be of any comfort?)

· Ferraro, P., “Raindrops keep falling on my car, but not on the rear window,” Physics Teacher, 35, 523-524 (December 1997)

Want more references? Use the link at the top of this file.

1.6  Spin out during police chase
Jearl Walker
March 2009    In a high-speed car pursuit, a police officer might attempt to disable the pursued car by forcing it into a spin that reverses the car. But, as you can see in this video, a crafty driver can wait until the car is reversed and then continue the escape.

Notice the technique in the first three attempts to stop the pursued car. The police car is positioned with its front bumper to one side of the rear of the pursued car, and then the police car is pulled sharply into the other car, causing that car to spin until it is moving backward down the road. Normally such reversal convinces the pursued driver to stop and surrender because traveling fast down a road in the reverse direction is sure to erode self confidence. However, the driver in the video simply waits until the car slows and then he guns the engine while steering the car until it is again traveling in the proper direction.

Here’s my question: The first bump turned the car a bit to the driver’s left. Why did the car then start to spin instead of simply straightening out?

The car’s engine is in the front, which means that the rear wheels carry little of the car’s weight. Thus, the rightward bump by the police car causes the rear tires to lose traction and begin to slide. Because the car is moving down the road, the frictional forces on the sliding rear tires are toward the rear. The front tires are still turning and still have traction. However, because they are no longer aligned with the car’s direction of travel down the road, frictional forces now act on them parallel to the axle between them, as shown in this diagram from The Flying Circus of Physics book.
Those frictional forces on the front tires create torques that causes the car to continue rotating in the counterclockwise direction. Thus, those frictional forces on the front tires are the cause of the spin out.

Once the car is reversed and the tires are realigned with the direction of motion down the road, the torques tend to disappear and thus the car tends to stop spinning. In the video, at this moment of relative equilibrium, the driver was skilled enough (or desperate enough) to regain control of the car.

The fourth attempt by the police was more successful because the collision was harder, longer lasting, and located about midway along the pursued car’s length, not at the rear. I think that the collision caused both front and rear wheels to lose traction and start to slide. The car still rotated but was effectively pushed off the road by the police car.

Dots · through ··· indicate level of difficulty
Journal reference style: author, title, journal, volume, pages (date)
Book reference style: author, title, publisher, date, pages
· Jones, A. T., "The skidding automobile," American Journal of Physics, 5, 187 (1937)
· Gottlieb, H. H., "Skidding automobile," Physics Teacher, 4, 45-46 + 133 (1966)
··· Unruh, W. G., "Instability in automobile braking," American Journal of Physics, 52, 903-909 (1984)
· Walker, J., "In an emergency stop, should a car's wheels be locked or should the braking be controlled?" in "The Amateur Scientist," Scientific American, 260, 104-107 (February 1989)
··· Goyal, S., A. Ruina, and J. Papadopoulos, “Planar sliding with dry friction. Part 2. Dynamics of motion,” Wear, 143, 331-352 (1991)
·· Noon, R., Engineering Analysis of Vehicular Accidents, CRC Press, 1994, pages 25-27

1.11  Headbanging and detached retinas
Jearl Walker
May 2009    In the human eye, the focusing of light by the cornea and eye lens places an image on the retina at the back of the eye, triggering nerves that send signals about the image along the optic nerve pathway to the visual cortex at the back of the brain. There, multiple layers of processing quickly bring to consciousness a visual image of what the person is looking at.

As a person ages, the retina can gradually detach from the wall at the back of the eye, interfering with or eliminating vision. Retinal detachment can also occur if the eye (and thus likely the head itself) undergoes trauma. Such damage is fairly common in sports involving hitting or kicking the head, such as in boxing and tae-kwon-do. The problem is that a blow to the head causes rapid acceleration of the eye, increasing the pressure on the retina due to the vitreous humor, the clear gel-like substance that fills the back of the eye. That sudden increase in pressure can tear the retina, separating it from the back wall in the tear region. The gel can then seep into the separation space, extending it and thus gradually peeling the retina off the wall.

Such retinal tearing and detachment can also occur in situations that do not involve an obvious blow to the head. For example, the legendary drag racer Don Garlits, who developed the modern design of a dragster with an engine in the front and a cockpit in the rear, suffered a detached retina because of the rapid deceleration he underwent each time his dragster was stopped at the end of its run by the deployment of a parachute.

Large accelerations (or decelerations) are often measured in terms of g units, where g is the acceleration caused by the gravitational force — it is the acceleration you would have if you fell, say, out of bed. In the sudden stopping of his dragster, Garlits typically would undergo a deceleration of about 4 gs. That is, when the parachute suddenly deployed, it rapidly stopped the dragster, which then (slightly later) stopped the body of Garlits via the harness on him, which then (slightly later) stopped his eyes via the eye sockets. His eyes effectively tried to squeeze outward through the eye sockets, dramatically increasing the pressure in the vitreous humor. At some point in his drag racing career, that pressure increase ripped the retina, initiating retinal detachment.

Another situation that seemingly would result in retinal tearing and detachment is bungee jumping.

In the early days of this activity (I hate to call it a sport --- it is more of a flirtation with death), some doctors warned that bungee jumping might cause retinal detachment. Indeed, the jumper is usually head down when the descent is arrested and then reversed, with a typical acceleration of about 2 or 3 gs. Injuries due to the acceleration include hemorrhages of the blood supply system in the retina, but I have not found any report of retinal detachment. I think the acceleration is not quite enough to rip the retina.

Retinal detachment sometimes occurs in the rapid whiplash of a victim in a rear-end car collision. Suppose that the front car is stopped at a red light when a rear car slams into it. The torso of the person in the front car is rapidly accelerated forward by the collision and then (slightly later) so is the head, with the head being whipped around the neck, first in the forward direction and then back toward the rear. (This is the whip in the phrase whiplash.) The acceleration of the head can be 10 gs or much greater.

The most extreme example of rapid acceleration and then even more rapid deceleration occurred in the early testing of human endurance using a rocket sled. John Stapp became famous for his rides on the sled, where he was attached to a rocket that was shot along a track. Then he would be brought to a very abrupt halt when the sled ran through a water trough. In this video about rocket sled runs, Stapp is the one with the bloody eyes being unstrapped from the sled:
He typically underwent accelerations and decelerations of 46 gs! A detached retina was only one of many injuries he endured in this program to determine how much acceleration an astronaut could withstand when shot into space.

My last example of activity involving retinal detachment caught me by surprise. After he finished a gig sometime in 2008, the bass player for the Scottish band The Day I Vanished noticed that he had blurry vision. When he sought medical help, he learned that he had retinal detachment that had been caused by his headbanging during his gig. In the following video, watch how vigorously he and the other band members throw their heads forward and then abruptly reverse the motion, as if they are slinging water off their hair.

The abrupt reversal can dramatically increase the pressure on the retina just as occurred with Garlits when his dragster abruptly slowed. Normally headbanging by members of a band or audience results in neck injuries, but in this one case the action was severe enough to separate the retina from the back wall of the eye.

Headbanging has several distinct styles and is often used to toss long hair in a whip-like fashion in time with the music. In one style, the abrupt reversal occurs in both the forward and rearward motions, which presumably increases the chance of injury. Still, in spite of the danger, headbanging is an essential part of hard rock, especially metal, as you can see in the following video in which Judas Priest plays their classic “Judas Rising.” Watch how the guitarists slam their heads forward in unison.

Physics is everywhere, even in a Judas Priest concert.

More stuff: news item about the headbanging injury another news item the various styles of headbanging headbanging to Judas Priest side-to-side and forward-and-backward, whipping hair in time to death metal Don Garlits site



Dots · through ··· indicate level of difficulty

Journal reference style: author, title, journal, volume, pages (date)

Book reference style: author, title, publisher, date, pages

· Johnson, I., and E. Johnson, “South seas incredible land divers,” National Geographic, 107, 77-92 (1955)
· Russell, A., editor, Guinness Book of World Records, Bantam Books, 1988, page 43
·· Dozorov, A. A., "Taking a flying leap: applying Hooke's law on a South Seas isle," Quantum, 1, 10-11 (September/October 1990)
·· Whineray, S., "Bungi jumping, maglev trains, and misaligned computer monitors," Physics Teacher, 29, 39-42 (1991)
· Vetter, C., "The fabulous, bouncing Kockelman brothers," Outside, 16, no. 7, 46-51 + 104-107 (July 1991)
·· Halliday, D., R. Resnick, and J. Walker, Fundamentals of Physics, John Wiley & Sons, 4th edition, 1993, pages 187, 196-197
··· Palffy-Muhoray, P., "Problem: acceleration during bungee-cord jumping," American Journal of Physics, 61, 379 and 381 (1993)
··· Menz, P. G., “The physics of bungee jumping,” Physics Teacher, 31, 483-487 (November 1993)
· Hite, P. R., K. A. Greene, D. I. Levy, and K. Jackimczyk, “Injuries resulting from bungee-cord jumping,” Annals of Emergency Medicine, 22, No. 6, 1060-1063 (June 1993)
·· Martin, T., and J. Martin, "The physics of bungee jumping," Physics Education, 29, 247-248 (1994)
· David, D. B., T. Mears, and M. P. Quinlan, “Ocular complications associated with bungee jumping,” British Journal of Ophthalmology, 78, No. 3, 234-235 (March 1994)
· Jain, B. K., “Bungee jumping and intraocular haemorrhage,” British Journal of Ophthalmology, 78, No. 3, 236-237 (March 1994)
· Chan, J., (letter) “Ophthalmic complications after bungee jumping,” British Journal of Ophthalmology, 78, No. 3, 239 (March 1994)
· Rens, E., (letter) “Traumatic ocular haemorrhage related to bungee jumping,” British Journal of Ophthalmology, 78, No. 12, 948 (December 1994)
· Innocenti, E., and T. A. G. Bell, (letter) “Ocular injury resulting from bungee-cord jumping,” Eye, 8, No. 6, 710-711 (1994)
· Habib, N. E., and T. Y. Malik, “Visual loss from bungee jumping,” Lancet, 343, No. 8895, 487 (19 February 1994)
· Simons, R., J. Krol, “Visual loss from bungee jumping,” Lancet, 343, No. 8901, 853 (2 April 1994)
· Vanderford, L., and M. Meyers, “Injuries and bungee jumping,” Sports Medicine, 20, No. 6, 369-374 (December 1995)
· Filipe, J. A. C., A. M. Pinto, V. Rosas, and J. Castro-Correia, “Retinal complications after bungee jumping,” International Opththalmology, 18, 359-360 (1995)
· Shapiro, M. J., B. Marts, A. Berni, and M. J. Keegan, “The perils of bungee jumping,” The Journal of Emergency Medicine, 13, No. 5, 629-631 (1995)
· Omololu, A. B., and J. Travlos, “Bungee jumping causing a comminuted proximal femoral fracture,” Injury, 26, No. 6, 413-414 (1995)
· Krott, R., H. Mietz, and G. K. Krieglstein, “Orbital emphysema as a complication of bungee jumping,” Medicine & Science in Sports & Exercise, 29, No. 7, 850-852 (July 1997)
··· Strnad, J., “A simple theoretical model of a bungee jump,” European Journal of Physics, 18, 388-391 (1997)
· Young, C. C., W. G. Raasch, and M. D. Boynton, “After the fall: symptoms in bungee jumpers,” The Physician and Sportsmedicine, 26, No. 5, 75-78 (May 1998)
· Louw, D, K. K. V. Reddy, C. Lauryssen, and G. Louw, “Pitfalls of bungee jumping,” Journal Neurosurgery, 89, 1040-1042 (December 1998)
· Fitzgerald, J. J., S. Bassi, and B. D. White, “A subdural haematoma following ‘reverse’ bungee jumping,” British Journal of Neurosurgery, 16, No. 3, 307-308 (June 2002)
··· Theron, W. F. D., “The dynamics of a bungee rocket,” European Journal of Physics, 23, 643-650 (2002)
·· Biezeveld, H., “The bungee jumper: a comparison of predicted and measured values,” Physics Teacher, 41, 238-241 (April 2003)

1.12  High-speed car crash
Jearl Walker
July 2008
   First, watch this video of a Corvette being chased by police at a reported 165 miles per hour. As the Corvette weaves its way through stationary or slowly moving trucks, the driver turns the front wheels a bit too much and slides into the back end of the next truck. The driver was being stupid --- not only was he endangering himself and others on the highway but he was also not even wearing a seat belt.

My question here is simple: Why wasn’t he killed or seriously injured? same video same video

The role of a seatbelt is probably obvious --- it is to keep you from hitting the dashboard and flying through the windshield in a front-end collision, or hitting the side window in a side collision. In either type of collision, the car rapidly stops. If you are not strapped down, you continue to move until you hit part of the car or go through a window. Rather than go through such an uncontrolled collision, you have a better survival chance if you are slowed along with the car via the seatbelt strapping you to the car seat. The slowing can still be fatal, especially in a collision at over 100 miles per hour as with the Corvette.

So, why did the driver survive without the use of seatbelt? Note that when the car slid into the next truck, the rear of the car hit first and then the car rotated around the far edge of the truck. The impact on the rear of the car was severe because not only did the rear momentarily stop but it also had to bounce backward off the truck. However, the front of the car and the driver did not come to an immediate stop and certainly did not bounce backward. Instead, the front and the driver continued down the road along the far side of the truck. Oh, to be sure, the collision on the side of the car was very damaging, but the driver was not brought to a stop in a very short amount of time like the rear of the car. Instead, the collision on the front of the car was prolonged over a greater amount of time. That decreased the force acting on the front end and also on the driver.

If the driver had hit the back of the truck head on, the driver would have gone through the front windshield and then hit the truck himself. If he had hit the back of the truck more squarely along the side of his car, he would have gone through the side window and hit the truck himself. By sheer luck he hit the truck just right so that he could survive.

The physics lesson here is short: Wear a seat belt. And, oh, maybe also you should never race from the police at over 100 miles per hour (unless you just really need to, you know).

1.12 Collisions at high speeds
Jearl Walker

Oct 2009  Collisions at slow to moderate speeds are commonplace, but collisions at high speeds can be fascinating because the destruction can be extensive, all in less than a blink of an eye. Here is an example.

A few years ago, the Sandia National Laboratories in the United States arranged for an F4 Phantom jet to be attached to a rocket sled that took it from rest to a speed of about 215 meters per second (about 480 miles per hour) before it crashed into a heavy, thick concrete wall.

The wall was not secured to the ground and thus was free to move, and although it yielded in the collision, the airplane was reduced to dust. Well, everything became dust except for the wing tips which extended beyond the wall to the either side. In the video you can see that the tips were sheared off from the rest of wing and continued to move forward as though the collision had not occurred.

Sandia had filled the fuel tanks with water to keep the mass of the airplane at about its normal value, and the crash was conducted in order to study what would happen to an airplane in a high-speed impact. In the video and the photographs, notice how the motion of the debris resembles the splash of water that is produces when a stone falls into the water. The trajectories of such debris forms what is called a granular splash. A common example is the granular splash that occurs when a meteorite hits the ground, throwing up soil and pulverized rock. Here is a video that shows a laboratory study of a granular splash produced when an iron ball is dropped into sand.

In the video you see not only a sand crown (the splash ring), but also the Rayleigh jet (the central fountain that momentarily extends upward).

Here is another example of a high-speed collision. In the video, which is taken from the very popular American television show MythBusters, battering rams are mounted on a rocket sled. Then the rockets are fired so that the sled is moving at about 940 meters per second (650 miles per hour) when it slams into a small car waiting in front of a solid concrete wall.

The collision is not as easy to see as the Sandia collision, and the car is not fully reduced to dust, but still we get another example of granular splash. The television show was trying to demonstrate what would happen to a small car if it were hit simultaneously at both ends by identical large trucks moving at the same high speed. I think we could have guessed the results, but the television hosts could not resist the chance of demolishing that small car. (Well, I could not have either. Life is often full of hardships but if you have a chance of destroying a small car with a high-speed battering ram, things just seem so much better.)

Other copies of the Sandia video voice, overhead included


1.12  Car crashes: shops, walls, and other cars
Jearl Walker
Nov 2009

The evening news often carries videos, such as the following, that show a car crashing into a shop. Is such a crash more dangerous than, say, a car crashing into a wall or a second car that is stationary or moving directly toward the first car for a head-on collision?

Shop crash

First, take a look a few of these shop crashes (more are linked below this story):

These shop crashes make great video, with lots of shop items flying about and people dodging out of the way of moving walls and shelves, and there is a very real danger of someone in the shop being crushed, but the driver is usually not hurt and the car may not be extensively damaged. Why not?

The danger to the car and driver is, of course, the force slowing them to a stop. The size of the force depends on two quantities, the car’s momentum and the rate at which that momentum changes during the collision. Momentum is a common English word that suggests something (such as a football team) has forward motion, but technically it is the product of mass and velocity. When a car crashes into something, a force acts on it to change its momentum (usually to zero).

In the shop-crash videos, the car usually comes off a parking lot, is not traveling very fast, and thus has a relatively small momentum. Further, the crash is not abrupt but is prolonged as the car is gradually slowed, first by the wall of the shop and then by items (counters, desks, shelves, etc.) inside the shop.

Wall crash

Use the following link to see tests in which a car is driven into a solid (non-yielding) wall to rate the safety features of the car.

(A more severe example was featured last month. To see it, click here.) A wall crash is usually more devastating because the speed is probably large and the duration of the collision is sure to be short, especially if the wall is solid and fixed to the ground (and thus non-yielding). Whereas in a shop crash, the car moves through several meters (or even several times of meters) until it stops, in a wall crash, the front bumper stops moving as soon as it hits the wall and then the car moves forward only because the front end is gradually crushed. The combination of a high initial momentum and a very short stopping time means that the force on the car and driver can be severe. Of course, if the driver is not wearing a seat belt or seat harness or if the car lacks an air bag, the driver continues to move into the steering wheel or window after the car frame begins to slow. Then the collision that reduces the driver’s momentum to zero can last only a millisecond or so, which means that the force in the collision can be fatal.

Head-on crash

Now use this link to see a video showing two remote controlled cars that are driven into each other at high speeds in an almost head-on collision.

If two cars are identical (same mass, same speed and thus same momentum), a head-on crash is very similar to each undergoing a crash with a non-yielding wall. The front bumper stops and the car moves forward as the front end is crushed.

However, if the cars are not identical, the situation is more difficult to analyze because the cars may still be moving after the collision. The car with the larger momentum dominates in the collision and, although its front end is crushed, it continues to move in its original direction shortly after the collision.

Studies of head-on collisions have shown that the danger to the occupants of the cars depends on their change in velocity during the collision. The velocity change for the dominant car can be large but because it continues to move in its original direction, the velocity change is not as large as if the car hit a solid wall. However, the velocity change for the second car can be very large because not only is the car brought to a momentary stop but then the car’s motion is reversed.

Here is result that surprised me: Suppose two cars are initially identical but we add an adult passenger to one of them, increasing the mass of that car by 80 kilograms or so. Then that car becomes the dominant one in a head-on collision and the risk of fatality in the car is reduced by about 9%. However, in the other car, because it will be reversed because of the collision and thus will undergo a larger change in velocity, the risk of fatality is increased by about 9%. A single person can make a statistical difference in the risk of fatality.

I guess the outcome of the research is this: When you go driving, take someone with you, just to increase the mass. Well, maybe that is also a good idea because you will talk with the person instead of talking on a cell phone (or worse, texting), which can increase the risk of a fatal crash by a lot more than just 9%. crash into shop crash into shop crash into tattoo shop crash into shop crash into shop crash into Sprint Store crash into Dollar Store car crashes into shop almost head on crash head on crash, race car, one stationary Scenes from a head-on collision and x ray images showing some of the consequences. photo photos and news story

Dots · through ··· indicate level of difficulty
Journal reference style: author, title, journal, volume, pages (date)
Book reference style: author, title, publisher, date, pages
··· Evans, L, “Mass ratio and relative driver fatality risk in two-vehicle crashes,” Accident Analysis and Preventation, 25, No. 2, 213-224 (1993)
·· Evans, L., “Driver injury and fatality risk in 2-car crashes versus mass-ratio inferred using Newtonian mechanics,” Accident Analysis and Prevention, 26, No. 5, 609-616 (1994)
··· Smith, R., “The formula commonly used to calculate velocity change in vehicle collisions,” Proceedings of the Institution of Mechanical Engineers, 212, 73-78 (1998)
·· Evans, L., “Causal influence of car mass and size on driver fatality risk,” American Journal of Public Health, 91, No. 7, 1076-1081 (July 2001)
· Evans, L, “Traffic crashes,” American Scientist, 90, 244-253 (May-June 2002)
·· Halliday, D., R. Resnick, and J. Walker, Fundamentals of Physics, John Wiley & Sons, 7th edition, 2005, pages 201, 219-220, 8th edition, 2008, pages 220-221

1.19 Scariest car on a roller coaster

Jearl Walker
June 2014   Roller coasters are, of course, designed to scare you, to dramatically and unexpectedly upset your sense of balance by accelerating you in surprising ways. Modern roller coasters may turn you upside down or run backwards (or both). In fact, these rides can be so frightening that you pray that the mechanical engineers who designed and built them did not pass their courses simply on partial credit.

Here, in an essay that I wrote for the Halliday and Resnick textbook before I became the book’s author, let’s consider a more conventional roller coaster.

To have the most thrilling ride (well, I really mean the most frightening ride), should you sit in the front or rear car? Both positions offer thrills, especially if the hilltop is greatly curved so that when passing over the crest the force on you from the chair is reduced and you feel as though you are being thrown from the chair. However, even when the hilltop is flat, sitting in the front car is frightening because you experience the illusion that you are falling over a cliff when the car begins its descent. Because your view of the track is limited, you do not anticipate the drop. Suddenly, the supporting force you feel from the chair is reduced. The abrupt change creates the illusion that you have fallen out of control. The illusion is weaker when you sit in the rear car because the disappearance of the front cars as they begin to descend alerts you that your descent is imminent.

The rear car offers a different type of thrill when the coaster descends from a flat hill such as the first one. In the rear car, you begin your descent while the rest of the coaster is already headed downward. Passengers in the front car begin their descent with a slow speed. You begin yours with a larger speed because by then an appreciable part of the coaster’s energy is in the form of kinetic energy. When your car begins to descend, it falls away from you momentarily as you continue to move horizontally. You have the illusion of being thrown from your chair, prevented from flying out of the car altogether by the restraining bar and strap. Some riders enjoy raising their arms as a sign of bravado when beginning their descent at high speed, trusting that the restraining device on them will keep them within the car.

The rapid pace of the car and the illusion of begin thrown from it are two reasons why a ride in the last car is frightening. However, much of the fear comes from a much more subtle factor. When you near the descending track, the force on your back from the chair rapidly increases. You suddenly fear that the chair is going to hurl you free of the car.

Why does the force on you increase in such a dramatic manner? Suppose that the coaster travels from a flat-top hill onto descending track that is at a constant angle θ with the horizontal. Before the first car begins to descend, the coaster’s acceleration is zero because there is no net force on it. When the first cars begin to descend, they are pulled along the track by a force F that is equal to the product of their mass m and the acceleration of gravity (g sin θ) along the track:

F = mg sin θ

Since the first cars are attached to the rest of the coaster, this force accelerates the entire coaster:

F = Ma,

where M is the coaster’s mass and a is the acceleration of the coaster and you. Equating the two expressions and solving for the acceleration, we find

a = (mg sin θ)/M.

As more cars begin to descend, the mass m on the slanted track grows larger, increasing your acceleration.

Assume that the mass of the passengers is uniformly distributed along the length of the coaster. Let x be the length of the coaster on the descending track and L be the total length of the coaster. Then,

m/M = x/L.

Substitute this ratio into the equation for the acceleration:

a = x (g sin θ)/L.

The acceleration of you and the coaster increases as x increases, until x = L.

The equation may appear to be tame but it is responsible for the sudden, wrenching fear you undergo when you ride the last car. You accelerate because the back of your chair pushes on you. The acceleration and the force form the chair depend on the value of x. As x increases, the acceleration increases, but that means that x increases even faster, which makes the acceleration even larger, which makes x increase faster still.

Your mind races with the changes you experience. The force on your back is initially small but as you near the descending track it rapidly increases.

You feel as though some unseen agent is behind you, attempting to propel you over the edge of the hill. Suddenly, just when the force on your back has shot up to its peak value, it abruptly disappears as you begin your descent, enhancing the illusion that you have been thrown from the chair.

Dots · through ··· indicate level of difficulty
Journal reference style: author, title, journal, volume, pages (date)
Book reference style: author, title, publisher, date, pages
·· Roeder, J. L., "Physics and the amusement park," Physics Teacher, 13, 327-332 (1975)
··· Prato, D., and R. J. Gleiser, "Another look at the uniform rope sliding over the edge of a smooth table," American Journal of Physics, 50, 536-539 (1982)
· Walker, J., "Thinking about physics while scared to death (on a falling roller coaster)" in "The Amateur Scientist," Scientific American, 249, 162-170 (October 1983); reprinted with added notes in J. Walker, Roundabout: The Physics of Rotation in the Everyday World, Freeman, 1985, pages 1-7
·· Roeder, J., and J. Walker, "Fear and trembling at the amusement park," Essay 2 in Fundamentals of Physics, 3rd edition by D. Halliday and R. Resnick, John Wiley & Sons, 1988, pages E2-1 - E2-8
·· Halliday, D., R. Resnick, and J. Walker, Fundamentals of Physics, John Wiley & Sons, 7th edition, 2005, pages 127, 250-251
··· Pendrill, A-M., “Rollercoaster loop shapes,” Physics Education 40, No. 6, 517-521 (November 2005)
1.19  Vertical roller coaster loops
Jearl Walker
September 2006
   Vertical roller coaster loops are often tear-shaped (as in this photo by TingyWende) instead of circular in order to maintain a large acceleration of the passenger during the upward climb. The problem is that the roller coaster slows as it climbs, as kinetic energy is traded in for gravitational potential energy. So the acceleration (the centripetal acceleration, or "toward the center" acceleration, which depends on the speed) decreases. That's no fun for rabid coaster fans. To offset this effect, modern tracks are tear shaped so that the curvature increases with height. The passenger's speed still decreases with height, but the ever sharper curvature maintains the acceleration and thus also the thrill. On some tracks, the curvature increases even more, so that the acceleration increases near the top of the loop. Then the acceleration is greatest where the passenger might be upside down. Just lovely for the coaster fans.

Want references? Use the link at the top of this file.

1.23  Humidifying baseballs for the Denver team
Jearl Walker
July 2008 
 American baseball is chock full of strange procedures, both personal and institutional. Here is a prime example: The baseballs used in Denver, Colorado, in a game with the Colorado Rockies team are humidified by being stored for many days in a room-size humidor with a fixed temperature and a relative humidity of about 50%, that is, with a humidity that is 50% of the saturation humidity at which water would begin to condense out of the air to form drops. Why would anyone want to play with a humid baseball?
Here is part of the reasoning:

1. The low humidity of Denver can dry out a baseball so much that the ball is then too light and too small to meet regulations.
2. Denver, being at high altitude, has such thin air that baseballs can be hit farther than in the other Major League Baseball ballparks, which are at lower altitudes. The prevailing winds can also produce longer flights.
3. The thin air also means that pitchers are less able to throw pitches that involve tricky aerodynamics, and that means more hits by the batters.

Thus, scoring is seemingly easier in Denver than in the other ballparks, being a delight for hitters who want to improve their hitting records but being dreadful for pitchers who want to decrease the number of hits they give up. To compensate for the unusual playing conditions, the baseballs used in Denver are allowed to absorb water in the humidor. Since 2002, the argument has been that a wetter ball does not bounce from a bat as well as a dry ball and thus will not travel as far over the playing field. However, does the treatment actually make any difference?

In 2004, David Kagan of California State University at Chico and David Atkinson of Napa High School in Napa, California, published a study of how the bounce of a baseball from a bat is affected by humidifying the baseball. They arranged for a pitching machine to hurl baseballs through a device that could measure the speed of the balls, both before and after the balls hit a wood wall. They found that the more humid balls (stored in more humid conditions) bounced more poorly from the wall. This meant that, as baseball officials had thought, humidifying the baseballs decreased the range of the balls. However, the researchers concluded that the effect was too small to actually affect the outcome of a game.

In 2008, Edmund R. Meyer and John L. Bohn of JILA, NIST, and the University of Colorado further considered whether humidifying the baseballs made any difference. In particular they considered the effect of the water on the flight of a baseball. The air drag on the ball depends in part on the cross-sectional area of the ball. The greater that area is, the more air the ball runs into and thus the more air drag it experiences. Because humidifying the ball increases the ball’s diameter slightly, the air drag tends to increase slightly, thus decreasing the flight distance slightly. However, the increase in mass due to the water allows the ball to go slightly farther because the extra mass means that the ball has extra amounts of momentum and energy that must be removed by the air drag. Still, this effect is also small.

So, humidifying the baseballs seems to have little or no effect on the playing conditions in Denver. Nevertheless, the procedure is great for building the lore of the game and has probably provoked countless sports conversations in the Denver pubs. USA Today article with photo of lots of baseballs in the Coors Field humidor Another shot of the humidor

· Adair, R., The Physics of Baseball, Harper & Row, 1990, pages 18-23 (this first edition was written before Major League Baseball was established in Denver)
· · · Kagan, D., and D. Atkinson, “The coefficients of restitution of baseballs as a function of relative humidity,” Physics Teacher, 42, 330-333 (September 2004)
· · · Meyer, E. R., and J. L. Bohn, “Influence of a humidor on the aerodynamics of baseballs,” arXiv:0712.0380v2 (29 Feb 2008) Available at

Want more references? Use the link at the top of this file.

1.25 Juggling hammers, hitting a nail on the head
Jearl Walker
October 2015  Juggling takes great skill and timing, of course, and most jugglers are content with continually tossing objects into the air. However, sometimes those objects could hurt or even kill the jugglers if the timing is off. Here is a juggler who not only wants to throw something dangerous into the air (hammers with points) but also wants to put them to work by driving a nail into an overhead wood beam.

The act is impressive but it also looked strange to me. When something is thrown into the air, it slows as it ascends. So, how can a hammer hit the nail with enough force to drive it into the wood? Ah, then I realized, he throws each hammer up with a strong rotation. Although the upward speed decreases as the hammer rises, the rotational speed does not change. He has timed the rotation and toss so that the hammer hits squarely on the nail head during its strong rotation.


1.33  Basketball free throw
Jearl Walker
Jan 2008
   In his book The Physics of Basketball, John Fontanella explains the proper form for a free throw in basketball. As you push the ball to release it when your arm is fully upward, you should also flip your hand forward about the wrist, so that your fingers are pointed forward as the ball leaves your hand. The technique is undoubtedly correct, but why is the wrist snap needed? Can’t you simply throw the ball to the basket as a shot putter hurls a shot?

The idea is to put back spin on the ball, so that the top rotates toward you and the bottom rotates away from you. You produce such a rotation when you snap your hand forward about your wrist because the frictional force from your hand on the bottom of the ball is in the forward direction.

Good players know that back spin increases the chance of the ball going into the basket. It can somewhat affect the flight of the ball but the primary advantage of the spin is to help slow the ball if the ball hits the rim. When the ball reaches the rim, you want it moving slowly so that it does bounce away from the basket. However, by then the ball has gone past the high point in its trajectory and is picking up speed.

The backspin can reduce that speed via the frictional force on the ball from the rim. The speed of the ball’s center is typically 5 meter per second, and the speed of the bottom of the ball relative to the center is about 1.5 meters per second in the forward direction. When the ball hits the rim, the colliding surface tends to slide forward, and the frictional force, which opposes the sliding, is in the backward direction (back toward the player). That backward force slows the ball, so that it might then fall into the basket.

The legendary basketball player Michael Jordan argued that the release of the ball should be so automatic and well practiced that it can be done with the eyes closed. Indeed, one of the video links here shows Jordan shooting a free throw with his eyes closed (and a mischievous smile on his face). Watch the wrist snap Michael Jordan free throw Jordan makes free throw with his eyes closed Jeff Liles makes a free throw world record

· · Fontanella, J. J., The Physics of Basketball, Johns Hopkins University Press, 2006. (You can order this from through the Store button at the left side of this screen.)
· · · Silverberg, L., C. Tran, and K. Adcock, “Numberical analysis of the basketball shot,” Journal of Dynamic Systems Measurement and Control. Transactions of the ASME, 125, No. 4, 531-540 (December 2003)
· · · Gablonsky, J. M., and A. S. I. D. Lang, “Modeling basketball free throws,” SIAM Review, 47, No. 4, 775-798 (2005)
· · Okubo, H., and M. Hubbard, “Dynamics of the basketball shot with application to the free throw,” Journal of Sports Sciences, 24, No. 12, 1303-1314
· · · Liu, C. Q., and R. L. Huston, “Dynamics of a basketball rolling around the rim,” Journal of Dynamic Systems Measurement and Control. Transactions of the ASME, 128, No. 2, 359-364 (June 2006)

Want more references? Use the link at the top of this file.

1.36  Golf ball hopping out of a cup
Jearl Walker
July 2006 
  As discussed in the book, a golf ball might hop out of a cup if its forward rotation causes it to climb the cup wall up to the lip. However, an escape is also possible if the ball's center initially has a downward component of motion. Then the ball rolls around the interior of the cup while it also oscillates up and down, and it can escape the cup during the up phase.
· · ·  Gualtieri, M., T. Tokieda, L.A.-G., B. Carry, E. Reffet, and C. Guthmann, “Golfer’s dilemma,” American Journal of Physics, 74, No. 6, 497-501 (June 2006)
· ·  Gualtieri, M., T. Tokieda, L.A.-G., B. Carry, E. Reffet, and C. Guthmann, “Golfer’s dilemma [Am. J. Phys. 74, (6), 497-501 (2006),” American Journal of Physics, 74, No. 12, 1149 (December 2006)
· · ·  Pujol, O., and J. Ph. Perez, “On a simple formulation of the golf ball paradox,” European Journal of Physics, 28, 379-384 (2007)

Want more references? Use the link at the top of this page.

1.37  Curtain of death in a meteor strike, and a hoax
Jearl Walker 
Nov 2009   Whenever a metallic asteroid reaches the ground (instead of burning up in the atmosphere), it digs a crater by throwing rock into the air. However, the ejecta material, as it is called, does not come out haphazardly. Rather, the faster moving rocks tend to be ejected at steeper angles to the ground. If you were to witness this ejecta fly toward you, you would see that at any instant it forms a thin, curved curtain --- a curtain of death. The drawing here is from The Flying Circus of Physics book, and here also is a link to a lab simulation of an impact. 

Particles higher in the curtain are ejected at greater speeds and angles than the particles lower in the curtain. The slower rocks hit the ground earlier than the higher rocks; thus you see and hear a steady pounding of the ground as the curtain moves toward you. Being anywhere near the crash of even a moderate size meteor would be very frightening. First you would hear a loud noise as it flew through the air, then a large boom as it hit, and then the steady pounding of the rocks hitting the ground, working their way out toward you.

This ejection of material is similar to the splash of water when you drop a stone into, say, a pond. As the stone pushes down into the water, the displaced water rises around the sides of the stone, forming a crown and throwing off water drops.

Last month reports raced around the world about a fairly large meteor that had crashed in a field in Latvia during the night, leaving a smoldering crater. Photos were issued to support the claim and a video was taken by someone walking up to the crater soon after the crash, with fire and smoke at the bottom. A photo can be found here: 

The event was quickly labeled a hoax. (1) No one in the nearby region heard any extra noise that night. (2) The crater was way too neat, with no ejected material in the surrounding field. Someone had simply used an earth-moving machine to dig a round hole in the ground and then had lit some flammable material at the bottom to give the impression of a hot impact. There was no curtain of death

Well, I suppose someone was hoping to charge spectators a fee to see the crater. Now that the crater is known to be a hoax, that’s not going to happen, but maybe the owner could fill the hole with water and charge people to swim in it. hoax footage simulation (drawings) lab simulation Video of meteor in Australia Video of meteor in Mexico Video of meteor over Madrid Video of meteor Video of meteor over football game Video meteor over Washington Video of meteor in Portland Video of meteor flight Multiple-exposure photo of ball hit granular material and digging a crater. Look at the “curtain” of debris. Photos, sketches, and discussion of cratering NASA’s report to congress on near-Earth objects, March 2007. Click on the “final report.”

Dots · through ··· indicate level of difficulty
Journal reference style: author, title, journal, volume, pages (date)
Book reference style: author, title, publisher, date, pages
· Rampino, M. R., “Tillites, diamictites, and ballistic ejecta of large impacts,” Journal of Geology, 102, 439-456 (1994)
· Oberbeck, V. R., “The role of ballistic erosion and sedimentation in lunar stratigraphy,” Reviews of Geophysics and Space Physics, Reviews of Geophysics and Space Physics, 13, 337-362 (1975)
··· Barnouin-Jha, O. S., and P. H. Schultz, “Interactions between an impact generated ejecta curtain and an atmosphere,” International Journal of Impact Engineering, 23, 51-62 (1999)
·· Walsh, A. M., K. E. Holloway, P. Habdas, and J. R., de Bruyn, “Morphology and scaling of impact craters in granular media,” Physical Review Lettters, 91, No. 10, # 104301 (4 pages) (5 September 2003)
·· Uehara, J. S., M. A. Ambroso, R. P. Ojha, and D. J. Durian, “Low-speed impact craters in loose granular media,” Physical Review Letters, 90, 19, #194301 (4 pages) (16 May 2003)
· Perkins, S., “A century later, scientists still study Tunguska,” Science News, 173, 5-6 (21 June 2008)
· Steel, D., “Tunguska at 100,” Nature, 453, 1157-1159 (26 June 2008)

1.38 Camel jumping
Jearl Walker

Dec 2010 Camel jumping is a sport practiced by a tribe in Yemen, where manhood can established by jumping over several camels that stand quietly side-by-side. (Well, they stand quietly if the men hold their tails.)

As you can see, clearing the camels is usually accomplished by bringing the legs up and forward, to avoid them catching on a camel and to allow the jumper to land feet first. (Vaulting by pushing off from a camel with a hand is not fair, and landing on a camel eliminates the jumper from the contest.) A similar need to bring the legs up and forward is also characteristic of the common running long jump, where an athlete attempts to maximize the horizontal distance of the jump. Here is a jump by Irving Saladino from Panama:

A camel jumper leaps from a small mound of dirt or sand. A long jumper attempts to leap from a small board level with the path. (Leaping from any point beyond the board disqualifies the jump.) In both types of jumps, the final launching force on the jumper is upward and forward. That force produces rotation around the jumper’s center of mass, that is, the launch creates a torque about the center of mass.

Assume the jump occurs as shown here in the figure from my textbook. The launching torque tends to rotate the jumper clockwise around the center of mass, bringing legs toward the rear. The jumper must somehow counter that rotation and bring the legs toward the front.

Straight-line motion of an object has an associated momentum that can be changed only by a force from outside the body, not inside. Similarly, rotational motion has an associated angular momentum that can be changed only by a torque from outside the body (due to a force outside the body). We say that, without any such outside torque, the angular momentum of the object is conserved. So, once airborne, the jumper is stuck with the clockwise angular momentum produced by the launch, until contact with the ground (or camel) provides an external torque to change it.

However, the jumper can stop the rearward rotation of the legs and bring them forward by rapidly bending forward with the top half of the body. Such rapid clockwise rotation of the top half of the body involves so much clockwise angular momentum that there is too much. But the total angular momentum cannot change from what the launch produced. So, the legs automatically rotate counterclockwise to keep the total constant. Thus the jumper manages to move the legs forward without changing the total angular momentum. This technique appears to be adequate for a camel jumper in order to clear the camels.

A long jumper, however, usually wants to bring the legs even farther toward the front. So, in addition to bending over at the waist, the arms are rapidly rotated clockwise in a windmill fashion. That adds even more to the clockwise angular momentum, requiring that the legs rotate even farther counterclockwise.

Elite long jumpers study this physics in order to maximize their jumps, but the rest of us simply learn how to jump as a child by trial and error, with not a single thought given to things such the conservation of angular momentum. Do you think that if someone studied the physics of jumping that they could clear seven? Eight camels? Dwight Phillips long jump camel jumping jump over 6 camels camel jumping


Dots · through ··· indicate level of difficulty
Journal reference style: author, title, journal, volume, pages (date)
··· Ramey, M. R., "Significance of angular momentum in long jumping," Research Quarterly, 44, 488-497 (1973)
··· Bedi, J. F., and J. M. Cooper, "Take off in the long jump -- angular momentum considerations," Journal of Biomechanics, 10, 541-548 (1977)
· Herzog, W., "Maintenance of body orientation in the flight phase of long jumping," Medicine and Science in Sports and Exercise, 18, 231-241 (1986)
· Koh, T. J., and J. G. Hay, "Landing leg motion and performance in the horizontal jumps I: the long jump," International Journal of Sport Biomechanics, 6, 343-360 (1990)
··· Alexander R. McN., "Optimum take-off techniques for high and long jumps," Philosophical Transactions of the Royal Society of London B, 329, 3-10 (1990)
··· Seyfarth, A., A. Friedrichs, V. Wank, and R. Blickhan, “Dynamics of the long jump,” Journal of Biomechanics, 32, 1259-1267 (1999)
··· Graham-Smith, P., and A. Lees, “A three-dimensional kinematic analysis of the long jump take-off,” Journal of Sports Sciences, 23, No. 9, 891-903 (2005)
··· Ashby, B. M., and S. L. Delp, “Optimal control simulations reveal mechanisms by which arm movement improves standing long jump performance,” Journal of Biomechanics, 39, 1726-1734 (2006)
· Bridgett, L. A., and N. P. Linthorne, “Changes in long jump take-off technique with increasing run-up speed,” Journal of Sports Sciences, 24, No. 8, 889-897 (2006)

More references are listed in the pdf files. Go to
and scroll down to item 1.38.

1.38 Long jump

Jearl Walker

July 2012 At London’s summer Olympics, some of the best athletes in the world will attempt to break the world record long jump of 8.95 meters set by Mike Powell in the 1991 World Track and Field Championship in Tokyo. Here is an image of Powell during the jump

and a video showing the full jump.

Making a world-class jump certainly takes much athletic skill but a great deal of physics is also involved. Can the location of the jump make a difference in that physics? I’ll use some of the material in The Flying Circus of Physics to fill out that physics, starting with the man whose record was beaten by Powell.

Bob Beamon 1968 Olympics

One of the most stunning events in the history of track and field sports occurred at the Mexico City 1968 Olympics. In mid-afternoon on October 18, Bob Beamon prepared for the first of three allowed attempts at the long jump by measuring off his steps along the approach path. Then he turned, ran back along the path, hit the takeoff board, and soared through the air. The jump was so long that the optical sighting equipment for measuring the jumps could not handle it, and a measuring tape had to be brought out. One judge said to Beamon, who then sat dazed off to one side, “Fantastic, fantastic.” The jump was an astounding 8.90 meters, easily beating the previous record of 8.10 meters (a difference of nearly two feet!).

Beamon was certainly aided somewhat by the wind at his back, because it was just at its allowed upper limit of 2.0 meters per second. Did he also benefit from the high altitude and low latitude of Mexico City; that is, did matters of air density and the strength of gravity account for his astonishing jump?

The length of a long jump is measured to where the jumper’s heels dig out sand upon landing, unless the jumper’s buttocks then land on and erase the heel marks. If those marks are erased, the length of the jump is only to the near edge of the hole left in the sand by the buttocks. Thus, landing in the proper orientation is important in the long jump.

When a long jumper takes off, with the final footfall on a takeoff board, the torso is approximately vertical, the launching leg is behind the torso, and the other leg is extended forward. When the long jumper lands, the legs should be together and extended forward at an angle so that the heels will mark the sand at the greatest distance but still disallow the buttocks from erasing that mark. How does the jumper manage to go from the launching orientation to the landing orientation during the flight?

Beamon’s long jump was aided only slightly by the wind and the location. Mexico City is at an altitude of 2300 meters, which is considerably higher than the altitudes of many other locations for the Olympics. The high altitude meant that the air density was low, and so the air drag retarding the jump was smaller than if the jump at been at a lower altitude. The high altitude also meant that the gravitational acceleration was smaller, and so the gravitational pull that opposed Beamon’s launch and that eventually pulled him back to the ground was smaller. The acceleration and pull were further reduced because of the effective centrifugal force on Beamon due to Earth’s rotation. That effective force is larger at lower latitudes, because such places travel faster during the ­rotation.

However, all of these factors played only a small role in the jump. So, why then did Beamon travel so far? The primary reason is that he hit the launch board while running rapidly. Most long jumpers approach more slowly so as to avoid placing their last step just past the board, which would disqualify the jump. They also want to avoid taking off before the board and losing the solid support it gives during the launch while also losing distance in the jump since the jump is measured from the board. Because the board is only 20 centimeters long, the final step must be planned.

Beamon, who was known for disqualified jumps, apparently decided to gamble on his first try and sprinted to the board. His last step barely avoided extending beyond the board. Had he gone beyond the board, he presumably would have made his next two jumps with more concern about the board and less speed.

Reorienting the body

To consider the reorientation of a long jumper during flight, suppose that the jump is to the right in your perspective as in this figure from my textbook (Fundamentals of Physics, by Halliday, Resnick, and Walker). During the launch from the board, the force on the launching foot from the board produces a clockwise rotation of the body, which tends to bring the trunk of the body forward and the forward leg rearward. This tendency of clockwise rotation is increased as the trailing leg is brought forward to ready for the landing. The reason is that the jumper is then free of the ground, and so the angular momentum of the body must remain constant. So, when the trailing leg is rotated counterclockwise to be forward, the rest of the body tends to rotate clockwise.

To decrease the clockwise rotation, so that the jumper is in the proper orientation for landing, the arms are rapidly swung clockwise about the shoulders. In addition, the legs might continue to move as in running, with a leg outstretched when rotated clockwise to the rear and pulled in when rotated counterclockwise to the front. (None of this motion alters how far the jumper goes; it only alters the orientation of the body.) Novice jumpers often fail to swing the arms sufficiently or, worse, they swing one or both arms in the wrong direction. The trunk and legs are then not in the best orientation, and the jump is short because the heel marks are short or the buttocks erase the heel marks.

Mike Powell

No one jumped as far as Beamon, including Beamon himself, for the next 23 years. Then, finally, at the 1991 World Track and Field Championship, Mike Powell jumped 8.95 meters—2.0 inches farther than Beamon. He did it in Tokyo and thus without any benefit of higher altitude, and he did it with only a mild wind of 0.3 meter per second at his back. Powell stunningly demonstrated that the effects of altitude and wind are secondary to athletic ability. Carl Lewis and Mike Powell compete

I have many references on the physics of long jumps. Go to

and scroll down to item 1.38

1.38  The Fosbury flop
Jearl Walker
December 2012 When Dick Fosbury won the high-jump contest in the 1968 Olympics in Mexico City, he introduced what appeared to be a bizarre way to jump. The technique is now known as the Fosbury flop and is used almost universally by high jumpers. To flop, a competitor runs with a measured pace up to the bar and then twists at the last moment, going over the bar backwards and face up. What advantage does such a style have? Here is a video from that Olympics that shows his jumps:

The height that is recorded in high jumping is, of course, the height of the bar, not the maximum height of the head or some other part of the jumper. Suppose that during a jump, the athlete can raise the center of mass (com) to a height L. If the athlete hurdles over the bar, the bar must be considerably lower than L if the body is not to touch it, and so the height of the jump is not very much. Here is Fig. 1-13a from The Flying Circus of Physics. In a straddle (or barrel roll) jump, the body is laid out horizontally and can pass over the bar with the bar much closer to the center of mass, and so the bar can be higher (Fig. 1-13b). In a flop, the curvature of the body around the bar lowers the center of mass to a point below the body, and the athlete can pass over an even higher bar than with a straddle jump (Fig. 1-13c). The last-moment twist and backward leap in a flop also gives a stronger launch.

Here is a longer video of the Olympics high jump, showing the classic straddle used by all the other high jumpers. interview with Dick Fosbury

Dots · through ··· indicate level of difficulty
Journal reference style: author, title, journal, volume, pages (date)
Book reference style: author, title, publisher, date, pages
··· Offenbacher, E. L., "Physics and the vertical jump," American Journal of Physics, 38, 829-836 (1970)
· Dapena, J. A., "Mechanics of translation in the Fosbury-flop," Medicine and Science in Sports and Exercise, 12, 37-44 (1980)
· Dapena, J. A., "Mechanics of rotation in the Fosbury-flop," Medicine and Science in Sports and Exercise, 12, 45-53 (1980)
··· Hubbard, M., and J. C. Trinkle, "Clearing maximum height with constrained kinetic energy," Journal of Applied Mechanics ASME, 52, 179-184 (1985)
· Frohlich, C., "Resource letter PS-1: physics of sports," American Journal of Physics, 54, 590-593 (1986)
· Dapena, J., and C. S. Chung, "Vertical and radial motions of the body during the take-off phase of high jumping," Medicine and science in Sports and Exercise, 20, 290-302 (1988)
· Dapena, J., C. McDonald,and J. Cappaert, "A regression analysis of high jumping technique," International Journal of Sport Biomechanics, 6, 246-261 (1990)
··· Alexander R. McN., "Optimum take-off techniques for high and long jumps," Philosophical Transactions of the Royal Society of London B, 329, 3-10 (1990)
· McGeer, T., "Fosbury floppers: safe enough for now?" Physics World, 3, 24-25 (September 1990)
· Harman, E. A., M. T. Rosenstein, P. N. Frykman, and R. M. Rosenstein, “The effects of arms and countermovement on vertical jumping,” Medicine and Science in Sports and Exercise, 22, No. 6, 825-833 (1990)
· Dapena, J., “Contributions of angular momentum and catting to the twist rotation in high jumping, Journal of Applied Biomechanics, 13, 239-253 (1997)
··· Seyfarth, A., A. Friedrichs, V. Wank, and R. Blickhan, “Dynamics of the long jump,” Journal of Biomechanics, 32, 1259-1267 (1999)
·· Lees, A., J. Rojas, M. Cepero, V. Soto, and M. Gutierrez, “How the free limbs are used by elite high jumpers in generating vertical velocity,” Ergonomics, 43, No. 10, 1622-1636 (2000)
··· Tan, J. C. C. and M. R. Yeadon, “Why do high jumpers use a curved approach?” Journal of Sports Sciences, 23, No. 8, 775-780 (August 2005)
1.39  Jumping beans
Jearl Walker
July 2007 One of the strangest things I saw as a child at the Texas State Fair was a Mexican jumping bean, which moved or even jumped when I held it in my hand. Although I did not know much about the world and certainly knew nothing about Newton’s laws of motion, I realized that seeds are not supposed to jump.

Here’s the story behind the apparent violation of Newton’s laws: After the moth Laspeyresia solitans lays its eggs in the flowers of the shrub Sebastiana pavoniana and a larva hatches inside one of the seeds produced by the flower, the larva consumes the interior of the seed. Once rain knocks the remaining seed shell to the ground, the larva can make the shell move over the ground until it reaches a point of relative safety, such as a crack or under leaves. Eventually, the larva cuts a hole in the shell, escapes, and then transforms to become an adult moth.

Before that final stage, however, the shell may be sold as a toy or novelty because if you hold it in your hand, it can move seemingly of its own accord. Other seeds (indeed, most other common objects) cannot move themselves. As you can see at the URL link given below, the shell can roll or turn over, but it might even hop up off your hand by a short distance. To make the shell move, the larva presses its rear section on the bottom of the seed and the head against the top of the shell. Then the larva snaps the rear section upward, slamming it against the top of the shell. The collision throws the shell upward and may also rotate it. To see how the larva moves the shell, one researcher suggests that it be carefully removed from the shell and then placed in a transparent gelatin capsule that normally might contain medicine.

A jumping gall is similar to a jumping bean except it is smaller, being only a millimeter wide. When a jumping gall reaches the ground, the enclosed larva can make the shell jump up by as much as a centimeter. One of the links below provides a graph comparing the jumps of the galls and the beans. There, that is something you can do on a lazy summer day. Buy some jumping beans and jumping galls and then, with a glass of lemonade (or whatever is your favorite beverage), monitor their jumps. But be careful: The excitement might be too much for you. Video of the seeds (or rather, seed shells) that seemingly move themselves Jumping beans plus some good salsa music Jumping bean race. Just the thing to watch with a good beverage on a lazy summer afternoon. Wayne’s Word: An on-line textbook of natural history, which has many fine pages to explore. Details about the larvae, the seeds, and the plants. Also, click to read about the jumping galls.

· Heckrotte, C., “The influence of temperature on the behaviour of the Mexican jumping bean,” Journal of Thermal Biology, 8, No. 4, 333-335 (1983)

1.41  Deadlift
Jearl Walker
September 2014   In weight lifting, a deadlift requires that the weighted bar be lifted from the floor until the athlete’s legs and back are straight and then lowered back to the floor (not dropped). In March 2014, Lithuanian powerlifter Zydrunas Savickas set a new record with deadlift of 1155 pounds (corresponding to 524 kilograms and 5138 newtons) at the 2014 Arnold Strongman classic.

Instead of the conventional weight plates, he used wheels produced for Hummer vehicles.

Although that deadlift was stunning, the record for the greatest lift of any kind by anyone was reportedly set in 1957 by Paul Anderson. He employed a back lift in which he stooped beneath a reinforced wood platform that was supported by sturdy trestles. In front of him was a short stool against which he could both steady himself and push downward. On the platform were auto parts and a safe filled with lead. With an astonishing effort of both arms and legs, he lifted the platform by about a centimeter—the composite weight was 6270 pounds (2844 kilograms and 27 900 newtons)!

Comparisons of such powerful lifts is usually done in terms of force (pounds or newtons) or the corresponding mass (kilograms), but another way is to calculate the amount of work done in the lift. In physics, work done on an object is defined to be the product of the force applied to the object and the distance that the object is moved. The calculation does not include any of the other energy transfers that might be involved, especially when the force is produced by a person. For example, the thermal energy released in the muscles is not included.

Let’s approximate the lift distance for Savickas to be about 0.25 meter (because the bar sags, the weights are not lifted as far as the middle of the bar). Then the amount of work he did was

(5138 newtons)(0.25 meter) = 1280 newton-meter = 1280 joules.

Anderson, with the greatest lift in recorded history, surely exceed this work, but let’s check:

(27 900 newtons)(0.010 meter) = 280 joules.

Anderson certainly applied a far larger force, but work also depends on the distance an object is moved, and for him it was only a centimeter.

1016 pounds, deadlift Benedikt “Benni” Magnusson from Hanarfjordur, Iceland

documentary about Paul Anderson: part 2 part 3 part 4

1.45 Tae-kwon-do punch

Jearl Walker

May 2010   In the Korean martial art of tae-kwon-do, you are trained to control a forward punch in three ways, one of which surprised me. (1) Starting with your fist positioned at your belt, you strike forward until the arm is fully extended, and there you stop. (2) You do not continue by bending your body forward like cowboys fighting in the movies. Instead you maintain your posture so that you can rapidly deliver a second punch or a kick.

(3) Those first two points were obvious to me but this third was not. You punch so that the stopping point is buried inside your opponent’s body or somewhat beyond it. Here Patrick Walker demonstrates the several points: 

When I trained in tae-kwon-do, I did not understand the third point until I made a movie of my forward punch, found the distance my fist moved from frame to frame, divided the distances by the time between frames, and thus calculated the speed of my fist as it moved outward. My fist began and ended with zero speed, and it had its maximum speed when it was about 80% of the way out to the full extension of my arm.

After making a graph of my fist speed versus fist position, I finally understood that third point of throwing a punch. The force of my fist on my opponent depends on the momentum of the fist just as I make first contact with him. Momentum is the product of mass and speed. Thus, my fist had its greatest momentum at the 80% point, where it had the greatest speed. (The graph and my simple calculation are available as a video at the Flying Circus of Physics site at Facebook. Either Goggle “Flying Circus of Physics Facebook” or click on!/pages/Cleveland-OH/Flying-Circus-of-Physics/339329532602?ref=ts .)

To make first contact at that optimum point, so that I deliver the greatest force, I must adjust the punch so that the stopping point is (mentally) inside the opponent’s body or slightly beyond it. In the jargon, I “punch through the target.” Here is a video example where someone punches through a board.


Short punch (jabs)

For maximum force, I need to accelerate the fist as much as possible to the point of maximum speed. The acceleration is due to my muscles and also the way in which I snap my hips to rotate my torso as I throw my fist outward. If I shorten the distance in which I accelerate the fist, the maximum speed is necessarily less and I hit with a weaker force. Still, such a jab is advantageous because it is so rapid that an opponent may not be able to defend against it. Here is a video that shows lots of jabs, each with a short accelerations, smaller fist speeds, and weaker forces on the opponent. However, note how confusing and hurtful the barrage of jabs would be to the face, where they would water the eyes and rapidly decrease vision.


One-inch punch

In the following video you see a type of punch in which the fist is accelerated through only a few inches or centimeters. The punch became legend when the movie star Bruce Lee demonstrated it, as seen in the videos:

Here are videos showing short punches into boards:

In English, this type of punch is known as the one-inch punch. The punch can hurt the opponent, especially if delivered to the solar plexus. It can also cause the opponent to fall backward if he cooperates by squarely facing the master instead of standing with feet separated both front-to-back and left-to-right (the proper stance). However, this punch is very theatrical because the acceleration distance is so short so that the force on the opponent is much less than if the punch is thrown from the usual starting point at the belt.


Breaking stacks of boards or bricks

People practicing tae-kwon-do take great efforts to not hurt one another. So, to demonstrate technique and power, they often strike boards or bricks to break them, instead of breaking each other. If only a few boards or bricks are in place, the rule about punching through the target still applies.

However, in some demonstrations, a stack of objects may be too deep for the stopping point to be below the stack. In that case, the person strikes through only the first several objects. They bend and then break, and then the pieces crash into and break the next lower object. Then those pieces crash into and break the next lower object, and so on, as a chain reaction is sent down through the stack. In the following videos, you can see the successive breaking move down through the stack. This first one involves four bricks:

And this one involves 35 bricks. You can hear the wave of breaking traveling down through the stack.

Note that such a chain reaction of bending and breaking is possible because the objects are separated by spacers. In the following video, the demonstrator leaves out the spacers in what I think is a marvelous demonstration of force.

Note that he did not use a single object with the depth of his stack. That would have been impossible. These breaking demonstrations depend on the ability of the fist to make an object bend to the breaking point. That is possible with a stack of separated individual objects, where you need to bend and break only the first several to set up the chain reaction. It is marginally possible with a stack of non-separated objects, where you can bend them in layers that slide over each other. However, a single object of the same thickness as the stack is dramatically harder to bend because the “layers” are now bonded to each other.


Dots · through ··· indicate level of difficulty
Journal reference style: author, title, journal, volume, pages (date)
Book reference style: author, title, publisher, date, pages
· Vos, J. A., and R. A. Binkhorst, "Velocity and force of some karate arm-movements," Nature, 211, 89-90 (1966)
·· Walker, J., "Karate strikes," American Journal of Physics, 43, 845-849 (1975); reprinted in The Physics of Sports, Volume One, A. Armenti Jr., editor, American Institute of Physics, 1992, ISBN 0-88318-946-1, pages 210-214
··· Blum, H., "Physics and the art of kicking and punching," American Journal of Physics, 45, 61-64 (1977)
· Feld, M. S., R. E. McNair, and S. R. Wilk, "The physics of karate," Scientific American, 240, 150-158 + 190 (April 1979)
··· Wilk, S. R., R. E. McNair, and M. S. Feld, "The physics of karate," American Journal of Physics, 51, 783-790 (1983); reprinted in The Physics of Sports, Volume One, A. Armenti Jr., editor, American Institute of Physics, 1992, ISBN 0-88318-946-1, pages 215-222
·· Halliday, D., R. Resnick, and J. Walker, Fundamentals of Physics, John Wiley & Sons, 6th edition, 2003, pages 372-373
· Landry, S. G., and G. R. Denn, “Classroom use of martial arts exhibitions,” Physics Teacher, 44, 430-431 (October 2006)

For the full list of references, go to
and scroll down to item 1.45 Karate.
1.46  Punches in boxing
Jearl Walker
September 2006    In a recent study, Olympic boxers (in the categories of flyweight, light welterweight, middle-weight, and super heavyweight) threw forward punches into a laboratory dummy's face, so that the force of a punch could be measured. Not surprisingly, the size of the force correlated with the weight of the boxer. (I don't know about you, but I have spent a lifetime in avoiding fights with a heavy opponent. Well, actually, any opponent, but especially anyone twice my size and wearing a motorcycle jacket.)
      The size of the force in a collision (here, between the fist and the face) depends on the fist's change in momentum (the product of mass and speed) during the collision. A greater initial momentum means a greater change in momentum and thus a greater force. This is the reason why both boxers and karate fighters are taught to aim a punch "through" the opponent, so that the collision begins when the fist has the greatest momentum.
      Surprisingly (at least to me), the recent study showed that all boxers (light weight to heavy weight) have about the same fist speed. Thus, the force size is greater for a heavier boxer primarily because the fist has more mass.

· ·   Walilko, T. J., D. C. Viano, and C. A. Bir, “Biomechanics of the head for Olympic boxer punches to the face,” British Journal of Sports Medicine, 39, No. 10, 710-719 (2005)

Want more references? Use the link at the top of this file.

1.46 Cannonball Richards
Jearl Walker
Oct 2008    Frank “Cannonball” Richards made a living by standing in front of a cannon and taking a cannonball shot to the stomach, as you can see in the following video. The obvious question is, how can someone take a cannonball shot to the stomach? Well, to begin with, the cannonball was shot with a spring and an explosive and thus came out with far less speed than a traditional cannonball shot. The smoke you see in the video is just to give the illusion of an explosion.

Still, there is no way that I would take a spring-launched cannonball to the stomach.

Second, Richards may have had a large stomach, but he also had very strong stomach muscles. Normally I would argue that a flabby stomach would offer protection because it would act like an airbag, prolonging any collision with it and thereby decreasing the size of the force in the collision. That is certainly the idea behind a car airbag --- prolong the collision that stops the occupant rather than having the occupant stop suddenly, such as on the steering wheel or dashboard.

However, with the human body, the argument can be wrong because of the rather delicate organs near the stomach. Harry Houdini, the legendary magician and escape artist, would also demonstrate how he could take punches to the stomach without apparent consequences. However, he always said he needed to “prepare” himself, which I think meant he needed to tighten the stomach muscles.

After a performance in Montreal in 1926, a student tested Houdini’s ability to take a punch but without first warning Houdini. Houdini was already suffering from appendicitis. The punches from the student apparently traumatized the appendix and Houdini died a few days later from peritonitis after the appendix burst.

There is one more factor that worked to protect Cannonball Richard --- he fell backward. The motion prolonged the collision, reducing the force. To be sure, the fall was almost uncontrolled and he could have broken a hand in landing but the greater danger probably came from having that very heavy cannonball fall down on the mat between his feet and then bounce onto a foot.

So, the repeated success of the Richards’ performance depended on (1) the relative slow launch of the cannonball and (2) prolonging the collision. Still, the stunt must have hurt, and that is probably why he never did it more than twice a day.

Here is one more question, but it is the really big question. When Richards first did the stunt, why did he do the stunt? Was it that one day, sitting at the breakfast table over a bowl of cold cereal, he said, “You know, my life is really not going anywhere, so I think today I’ll stand in front of a cannon and be shot in the stomach.” And then after being shot that day, over dinner and a beer, he said, “Well, that was ok. Maybe I could make a career out of being shot in the stomach by a cannon.” Is that how it all started?

For those of you who are physics instructors, you know that the most depressing student question is, “Why do I need to know this? I’ll never use it.”

I suggest that whenever a student asks that question that you respond, “Learning physics is about learning how to think. Of course, there are careers in which thinking is not required. Here is an example.” Then play the Richards video. another video of Frank Cannonball Richards

1.49 Fall of window cleaner
Jearl Walker
Dec 2009   Here is a video from a surveillance camera that shows the end of an eight-story fall by a window cleaner. Don’t worry --- not only did he survive but he suffered only a broken finger.

He survived what should have been a fatal fall because of two features.

(1) During the fall the rope that was attached to him caught on a projection, and the rope length from the projection extended down to just above the alley pavement. Otherwise he would have hit the pavement at high speed. The impact would have then been “hard,” which is one way of saying that the collision would have lasted only a short amount of time. So, he would have begun the collision with a large momentum (mass times speed) and a very short time later would have had zero momentum. The force he would have felt is equal to the change in his momentum divided by the duration of the collision. With a large change in the momentum occurring in a short amount of time, the force would have been large and lethal.

(2) He bounced at the end of the rope, with the yield in the rope allowing him to just barely miss hitting the pavement. When a rock climber falls while on belay, the rope is designed to have a certain yield because when the rope begins to slow and stop the climber, the process is effectively a collision. If the rope were stiff with no yield, the duration of the collision would small. So, by the argument above, the force stopping the climber could be very large. However, with a rope that yields, the slowing process takes longer and the force is smaller. The rope on the window cleaner apparently had a good deal of yield, as we can see from his bounce at the end of the rope.

In short, the window cleaner was very lucky. His fall is the stuff in my nightmares --- I fall from a building, bridge, or some other structure that is high enough that I have time to think during the fall. In the nightmare, I start running numbers through my head about my impending change in momentum, the duration of the impact, and the force that I am going to experience. Physics is everywhere, even in my nightmares.

Dots · through ··· indicate level of difficulty
Journal reference style: author, title, journal, volume, pages (date)
Book reference style: author, title, publisher, date, pages
· De Haven, H., “Mechanical analysis of survival in falls from heights of fifty to one hundred and fifty feet,” War Medicine, 2, 586-596 (1942)
· Snyder, R. G., “Human tolerances to extreme impacts in free-fall,” Aerospace Medicine, 34, No. 8, 695-709 (August 1963)
· Snyder, R. G., and C. C. Snow, “Fatal injuries resulting from extreme water impact,” Aerospace Medicine, 38, 779-783 (August 1967)
··· Benedek, G. B., and F. M. H. Villars, Physics with Illustrative Examples from Medicine and Biology, vol. 1, Addison-Wesley, 1974, pages 4-58 through 4-71
· Hoagland, E., "Big frog in a small pond," Sports Illustrated, 42, 36-43 (3 March 1975)
· Maull, K. I., R. E. Whitley, and J. A. Cardea, “Vertical deceleration injuries,” Surgery, Gynecology & Obstetrics, 153, 233-236 (1981)
· Harvey, P. M., and B. J. Solomons, “Survival after free falls of 59 metres into water from the Sydney Harbour Bridge, 1930-1982,” Medical Journal of Australia, 1, No. 11, 504-511 (28 May 1983)
· Warner, K. G., and R. H. Demling, “The pathophysiology of free-fall injury,” Annals of Emergency Medicine, 15, 141-146 (9 September 1986)
· Scalea, T., A. Goldstein, T. Phillips, S. J. A. Sclafani, T. Panetta, J. McAuley, and G. Shaftan, “An analysis of 161 falls from a height: the ‘jumper syndrome’,” Journal of Trauma, 26, No. 8, 706-712 (1986)
· Katz, K., N. Gonen, I. Goldberg, J. Mizrahi, M. Radwan, and Z. Yosipovitch, “Injuries in attempted suicide by jumping from a height,” Injury, 19, 371-374 (November 1988)
· Copeland, A. R., “Suicide by jumping from buildings,” American Journal of Forensic Medicine and Pathology, 10, No. 4, 295-298 (December 1989)
· Hanzlick, R., K. Masterson, and B. Walker, American Journal of Forensic Medicine and Pathology, 11, No. 4, 294-297 (December 1990)
· Buckman Jr, R. F., and P. D. Buckman, “Vertical deceleration trauma,” Surgical Clinics of North America, 71, No. 2, 331-344 (April 1991)
· Isbister, E. S., and J. A. Roberts, “Autokabalesis: a study of intentional vertical deceleration injuries,” Injury, 23, No. 2, 119-122 (1992)
· Mathis, R. D., S. H. Levine, and S. Phifer, “An analysis of accidental free falls from a height---the spring break syndrome,” Journal of Trauma, 34, No. 1, 123-126 (January 1993)
· Teh, J., M. Firth, A. Sharma, A. Wilson, R. Reznek, and O. Chan, “Jumpers and fallers: a comparison of the distribution of skeletal injury,” Clinical Radiology, 58, 482-486 (2003)
· Lee, B. S., S. R. Eachempati, M. D. Bacchetta, M. R. Levine, and P. S. Barie, “Survival after a documented 19-story fall: a case report,” The Journal of Trauma, 55, No. 5, 869-872 (November 2003)
·· Cross, R., “Forensic Physics 101: Falls from a height,” American Journal of Physics, 76, No. 9, 833-837 (September 2008)

1.51  Feline high-rise syndrome
Jearl Walker
May 2007 
    In the Flying Circus book I describe data collected by veterinarians on the severity of injury to cats falling from high places, such as a windowsill in an apartment building. Such injuries are collectively known as the feline high-rise syndrome. In one early study, the severity of injury appeared to increase with the height of the fall up to the seventh floor and then decrease with height for greater falls. The result was counterintuitive because the severity of the injury to you or me would surely increase with height until the lethal limit is reached.

Here is the explanation: As a cat begins to fall, it quickly rotates its body until its feet are downward. As it then falls, two forces act on it: The gravitational force pulls downward and air drag pushes upward. But the air drag depends on the cat’s speed. Thus, the air drag starts out small and then increases as the cat’s speed increases.

If the fall is less than seven floors, the air drag does not build up enough to match the gravitational force, and so the cat continues to accelerate downward throughout the fall. The acceleration affects the balance sensing mechanism in the cat’s inner ear, scaring the animal, and so the cat maintains its feet below its body in preparation for landing. That way, when it hits, it can flex its legs to cushion the impact.

However, if the fall is greater than seven floors, the upward air drag increases until it matches the downward gravitational force, and so there is then no net force on the cat through the rest of the fall. That means there is no sensation of acceleration to scare the cat. As it cat relaxes, it extends its legs sideways, to increase the air drag. In sports language, it is “catching air,” which slows it to a smaller speed. Hitting with a smaller speed means that the severity of injury might be less than for a shorter fall.

Well, that’s the going explanation, but I do not believe that we have any movies of cats falling for more than seven floors so that we can actually see what a cat does. (Don’t you dare think that thought! That would be very cruel! Cats may be aloof, but don’t you dare put them aloft.) So, the going explanation is only a theory.

However, in 2004, veterinarians of the University of Zagreb in Zagreb, Croatia, published a study of 119 cases of feline high-rise syndrome. They found that the probability of leg fracture increased for falls up to the third floor and then decreased for greater falls, but the probability for thoracic (throat) injury increased dramatically for falls greater than six floors. This data suggest that the going explanation is basically correct. For falls from less than seven floors, the cat lands legs first and thus the legs can be fractured. For greater falls, with the legs extended sideways, the chest hits first and then the throat, and so the throat can be injured.

So the going explanation is still the best one, but I cannot guarantee its validity. What I really need is an interview with one of the cats falling from a great height. “Did you manipulate the air drag by extending your legs out sideways? Where did you learn about air drag and how to “catch the air”? Did you take a physics class just in case you fell from a great height or just for fun? Was it for a grade or just pass/fail?” Alas, so far, all cats that fallen from great heights have refused all interviews. They just don’t want to talk about it. Maybe they are holding out for the book rights. Or maybe their throats just hurt too much.

 Vnuk, D., B. Pirkic, D. Maticic, B. Radisic, M. Stegskal, T. Babic, M. Kreszinger, and N. Lemo, “Feline high-rise syndrome: 119 cases (1998–2001),” Journal of Feline Medicine and Surgery, 6, 305-312 (2004)

Want more references? Use the link at the top of this file.


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