Search

The trajectory of a ball in air is affected by aerodynamic drag and lift. In general, the trajectory needs to be calculated numerically since the acceleration varies with time in both the horizontal and vertical directions. If the trajectory remains approximately parabolic, then simple analytical solutions can be found, giving useful insights into the behavior of the ball as it travels through the air.

A common procedure when conducting physics experiments is to repeat a measurement several times to calculate the mean and standard deviation. That might be the only instruction we give to students as a means to minimize random errors. However, that technique does not guarantee that the answer will be correct. It might give the same wrong answer every time. How then can we teach students to avoid systematic errors? We don't focus on that problem enough when teaching physics. Part of the problem is that we and the students usually know the correct answers in advance, since student experiments have usually been repeated thousands of times by others.

What happens when a perfectly elastic ball collides with a completely inelastic ball? It is shown that the outcome depends on the stiffness of each ball. A standard textbook problem in mechanics is to calculate the outcome of a head-on collision between two balls using conservation of momentum and kinetic energy. It is easily shown that the outcome depends on the relative mass of the balls and their initial speeds. In practice, there is always a net loss of kinetic energy during a collision, which can be expressed in terms of the coefficient of restitution (COR) for the collision. The COR is defined as the relative speed of the two balls after the collision divided by the relative speed before the collision. In a perfectly elastic collision the COR is unity. In a completely inelastic collision, the COR is zero.

The flow of air around a baseball and over the seam acts to slow the ball and to deflect it sideways. Turbulent flow can be visualized, and sideways deflection of the ball can be observed clearly if the ball is dropped in a glass fish tank and filmed with a high-speed camera. Results are presented for a baseball and also for a billiard ball with a metal ring attached to simulate the effect of the baseball seam.

The transition from sliding (where I v i / I i > I R i ) to rolling (where I v i / I i = I R i ) shown in Fig. By that time, I v i was no longer zero since the ball started to slide just before the finger holding the ball was lifted gently off the ball. If I D i / I R i = 0.1, then the ball will roll to a stop if I i < 6° and if the ball is given a push to get it started, since I a i is then negative.[6] Graph: Fig. In order to determine whether the ball rolls without sliding, it is necessary to measure both I v i and I i and to compare the I v i / I i ratio with I R i . [Extracted from the article]

A well-known physics demonstration is to pull a tablecloth rapidly from under some crockery without disturbing the crockery. An interesting question is whether the same result can be expected if the crockery is replaced by a ball, given that the ball might roll backwards on the tablecloth. Theoretical and experimental results are presented showing that the result depends on the acceleration of the tablecloth. If crockery is at rest on a tablecloth, and if the tablecloth is pulled slowly, then the crockery will move at the same speed as the tablecloth. With a rapid pull, the crockery appears not to move at all. In fact, the crockery will move a small distance horizontally since the coefficient of sliding friction is not zero. The secret of success is to minimize the horizontal impulse, not by reducing the friction force but by reducing the time over which it acts.

The acceleration of a vehicle or a bicycle is commonly used in elementary physics courses to illustrate problems concerning Newton's laws of motion when friction forces are involved. The maximum possible acceleration is rarely discussed, although it is of interest to consumers and racing car enthusiasts, and it is sometimes questioned by students. It is the main focus of the present article and is considered from a basic physics point of view, appropriate for classroom discussion.

An ice hockey player can strike a puck at speeds up to about 45 m/s (100 mph) using a technique known as the slap shot. There is nothing unusual about the speed, since golf balls, tennis balls, and baseballs can also be projected at that speed or even higher. The unusual part is that the player strikes the ice before striking the puck, causing the stick to slow down and to bend. There appears to be a significant advantage in hitting the ice before hitting the puck, otherwise hockey players would have learned from experience not to do that. In order to investigate the physics of the problem, the authors set up a simple experiment using a flexible meterstick to simulate a real hockey stick and mounted it as a pendulum so it could swing about an axis near the top end. The results presented in this paper support the fact that hockey players know what they are doing when they slap the ice, even though the result appears at first sight to violate conservation of energy.

In a recent article in this journal, Shakur described an interesting problem where a bullet of mass "m" strikes a block of wood of mass "M" and projects the block upward. The same problem was considered earlier by Cowley et al. and others. The main question of interest is whether the block rises to a greater height if it is struck in the middle rather than near one end. Conservation of energy or conservation of momentum arguments, on their own, appear to yield very different predictions. Both Shakur and Cowley et al. indicated that the block would rise to the same height, regardless of the impact point, based simply on a conservation of momentum argument.

On July 19, 1969, Senator Edward Kennedy drove his vehicle off a low bridge on Chappaquiddick Island in Massachusetts. The vehicle sank in 2.1 m of water, coming to rest on its roof. According to Kennedy's version of events, he managed to escape from the submerged vehicle without injury, but his female companion, Mary Jo Kopechne, drowned without any sign of injury. He did not report the accident to police until 10 hours later. Kennedy's version of the events was widely disbelieved but was never seriously challenged by the local police or accident investigators or at the subsequent inquest. The accident effectively put an end to Kennedy's bid for the presidency of the United States. At least a dozen books have been written on the subject, offering alternative explanations but the physics of the accident itself has never been properly investigated. In this paper, experiments using a toy vehicle are described where the vehicle was projected into a container of water to investigate how the roof may have been damaged. The trajectory through the water was filmed and is explained in terms of elementary physics. Further investigation could be the subject of student projects and would provide an interesting introduction to forensic physics.

The nature of the drag force on an object moving through a fluid is well documented and many experiments have been described to allow students to measure the force. For low speed flows the drag force is proportional to the velocity of the object, while at high flow speeds the drag force is proportional to the velocity squared. The basic physics depends on whether the flow around the object is laminar or turbulent. It is difficult to observe the flow in a student laboratory, although a dye can be injected into the flow of water for demonstration purposes. An alternative method is described in this paper that allows both the drag force and the initial flow pattern to be measured easily. The technique is simply to film an object when it is dropped into a tank of water. The results can be spectacular when filmed in slow motion, adding to the interest in the experiment itself. The results are directly relevant to the problem of calculating the impact force on an object that falls into water. Water is not as hard as concrete, but it can still exert a large force if the object (or a person) impacts at high speed.

A spinning top or a spinning hard-boiled egg is fascinating to observe since both objects can remain upright for a relatively long time without falling over. If spun at sufficient speed on a horizontal surface, the spin axis rises to a vertical position and the bottom end tends to remain fixed in position on the surface. If the initial spin is insufficient, then the spin axis will not rise all the way to the vertical, in which case a spinning top or a spinning egg will precess slowly around a vertical axis. If the bottom end is rounded, as it is with an egg or with a top having a round rather than a pointed peg, then the vertical precession axis does not necessarily pass through the center of mass. Instead, the precession axis may be located several centimeters away from the center of mass, depending on the radius of the bottom end. As a result, the whole egg or the whole top then rolls along the surface in an approximately circular path, several centimeters in diameter. The essential physics is described in Ref. 1 and the references therein, and in the many more books and papers since the early 1900s quoted in each of the references therein.

The PhiTOP® (or FTOP®) is a physics toy designed not only to act as a spinning top but also to appeal to the eye and to the scientifically curious mind.1 It is currently made in two versions, one from solid aluminum and the other solid brass. Each top is highly polished, and is elliptical in one cross section and circular in another. Its name derives from the ratio of the lengths of the major to minor axes, which is equal to the golden mean F = (1+ v5)/2~1.618. It functions in the same way as a spinning egg or a spinning football in that it rises on one end if it is initially set spinning at sufficient speed with its long axis horizontal. The center of mass rises in an unexpected and somewhat mysterious manner, an effect that it also shares with a tippe top.

(1) and (2) need to be solved numerically to find I y i and I F i vs. time, for given values of I k i SB 1 sb , I k i SB 2 sb , I c i , I m i , and I v i SB 0 sb . An interesting question is whether these and other balls store all the initial impact energy as elastic energy when they compress, or whether they lose some of that elastic energy while they are compressing as well as during the expansion stage. The maximum total elastic energy is 0.82 I E i SB 0 sb , so not all of the initial kinetic energy is stored as elastic energy; 82% of the initial kinetic energy is stored as elastic energy at maximum ball compression, and then 82% of the stored elastic energy is returned as kinetic energy when the ball bounces off the surface. The area under the curve while I y i increases represents the energy required to compress the ball, and the area under the curve while I y i decreases represents the energy recovered while the ball expands. [Extracted from the article]

The effect of the aerodynamic drag force on an object in flight is well known and has been described in this and other journals many times. At speeds less than about 1 m/s, the drag force on a sphere is proportional to the speed and is given by Stokes' law. At higher speeds, the drag force is proportional to the velocity squared and is usually small compared with the gravitational force if the object mass is large and its speed is low. In order to observe a significant effect, or to measure the terminal velocity, experiments are often conducted with very light objects such as a balloon or coffee filter or muffin cup, or are conducted in a liquid rather than in air. The effect of the drag force can also be increased by increasing the surface area of the object.

How would a physicist describe the elastic properties of an apple or a banana? Physics students and teachers are familiar with the elastic properties of metal springs, but are likely to be less familiar with the elastic properties of other common materials. The behavior of a metal spring is commonly examined in the laboratory by adding masses to measure the change in the extension or compression. A banana or an apple or any other relatively soft material could just as easily be examined in the same way, as an additional and entertaining exercise. Even if an apparatus is not readily available to undertake such an experiment, it can easily be constructed. In this article I compare the elastic properties of Plasticine (a brand of modeling clay), Silly Putty, and tennis strings. All three materials behave in the same qualitative manner when stretched or compressed slowly, despite the fact that they are quite different when stretched or compressed rapidly and despite the fact that Plasticine and Silly Putty are both much softer than a tennis string. Typical results for a slow deformation are shown in Fig. 1. (Contains 3 figures.)

When two balls collide multiple times in a simplified Newton's cradle, the impact point gradually moves away from the lowest point of the swing. The effect was examined using two billiard balls, and was traced to the fact that the upper support points were not separated by exactly one ball diameter. [ABSTRACT FROM AUTHOR]

The trajectory of a projectile through the air is affected both by gravity and by aerodynamic forces. The latter forces can conveniently be ignored in many situations, even when they are comparatively large. For example, if a 145-g, 74-mm diameter baseball is pitched at 40 ms[superscript -1] (89.5 mph), it experiences a drag force of about 1.5 N. The gravitational force on the ball 1.42 N. Nevertheless, the trajectory of a baseball pitched without spin is not strongly affected by the drag force. Because the ball is relatively heavy and the flight distance is relatively small (about 60 ft), the drag force reduces the ball speed by only about 10% by the time it reaches the batter. As a result, the time taken for the ball to reach the batter is only about 5% longer than in a vacuum, and the actual trajectory is also very similar. (Contains 4 figures.)

A ball that is projected forward without spin on a horizontal surface will slide for a short distance before it starts rolling. Sliding friction acts to decrease the translation speed v and it acts to increase the rotation speed [omega]. When v = R[omega], where R is the ball radius, the ball will start rolling and the friction force drops almost to zero since the contact point at the bottom of the ball comes to rest on the surface. The coefficient of rolling friction is much smaller than that for sliding friction. A different situation arises if the ball is projected forward while it is spinning about a vertical or near vertical axis. The latter situation arises in many ball sports. It arises if a player attempts to curve a ball down a bowling alley, or when a billiards player imparts sidespin or "English" to a ball, and it can arise in golf if a player strikes a ball with a putter at a point well away from the middle of the putter head. The situation also arises in the game of curling, although in that case the object that is projected is a cylindrical rock rather than a spherical ball, and it arises in tennis when a ball lands on the court spinning about a near vertical axis, as it does in both a slice serve and a kick serve. In a slice serve, the axis is almost vertical. In a kick serve, the axis is tilted about 30 degrees away from the vertical in order to increase the amount of topspin.

In sports such as baseball, softball, golf, and tennis, a common objective is to hit the ball as fast or as far as possible. Another common objective is to hit the ball so that it spins as fast as possible, since the trajectory of the ball through the air is strongly affected by ball spin. In an attempt to enhance both the coefficient of restitution (COR) and the spin of a golf ball, I conducted several experiments to see what would happen when a 45-g, 42.8-mm diameter golf ball bounced on: (a) a 58-mm diameter, 103-g Super Ball[R]; (b) an 8-mm thick, 56-mm diameter circular disk of Super Ball material cut from a large Super Ball and glued to a 3.4-kg lead brick; and (c) a 3-mm thick sheet of rubber glued to a 3.4-kg lead brick.

It is well-known that a party balloon can be made to fly erratically across a room, but it can also be used for quantitative measurements of other aspects of aerodynamics. Since a balloon is light and has a large surface area, even relatively weak aerodynamic forces can be readily demonstrated or measured in the classroom. Accurate measurements can be made of drag and buoyant forces, and reasonable estimates can also be made of the Magnus force on a spinning balloon.

The trajectory of a ball in air is affected by aerodynamic drag and lift. In general, the trajectory needs to be calculated numerically since the acceleration varies with time in both the horizontal and vertical directions. If the trajectory remains approximately parabolic, then simple analytical solutions can be found, giving useful insights into the behavior of the ball as it travels through the air. [ABSTRACT FROM AUTHOR]

This article discusses the concept of the quality factor, Q, in damped oscillatory motion. The quality factor is a measure of the energy loss per cycle and can be calculated by plotting oscillator amplitude vs. time or by counting the number of observed cycles. The article provides examples of simple harmonic motion, such as a pendulum and a mass on a spring, and explains the equation that describes their motion. It also explains how the amplitude of the oscillation decreases exponentially with time due to damping and how the quality factor is related to the energy loss. The article suggests that counting the number of cycles can be a simple and quick method to estimate the quality factor of a damped oscillation. [Extracted from the article]

This article discusses a claim made in a previous journal article about kinetic energy conservation in elastic collisions. The authors of the current article argue that the coefficient of restitution (COR) should be defined in terms of the normal components of the incoming and outgoing speeds of the objects at the point of impact, rather than just the translational motion. They argue that this definition would result in a COR of unity in a perfectly elastic collision, regardless of the point of impact. The issue of impact point dependence is recognized by U.S. Major League Baseball, which specifies the performance of baseball bats in terms of the COR at the point of impact. [Extracted from the article]

A common procedure when conducting physics experiments is to repeat a measurement several times to calculate the mean and standard deviation. That might be the only instruction we give to students as a means to minimize random errors. However, that technique does not guarantee that the answer will be correct. It might give the same wrong answer every time. How then can we teach students to avoid systematic errors? We don't focus on that problem enough when teaching physics. Part of the problem is that we and the students usually know the correct answers in advance, since student experiments have usually been repeated thousands of times by others. [ABSTRACT FROM AUTHOR]

A routine problem in an introductory physics course considers a rectangular block at rest on a plane inclined at angle a to the horizontal. In order for the block not to slide down the incline, the coefficient of sliding friction, µ, must be at least tan a. The situation is similar for the case of a ball rolling down an inclined plane. In order for a solid ball to roll without slipping down the inclined plane, µ must be at least (2/7) tan a. In both cases, static friction is responsible for the observed effects and one can find treatments of these topics in most introductory physics textbooks. Notice that when a = 0, no frictional force is required for the ball to roll at constant speed, just as no frictional force would be required to keep the rectangular block from sliding on a horizontal plane. In the case of a rolling ball that is accelerating, a frictional force acts to produce a torque about the center of mass and, thus, plays an important role in the acceleration of the ball, whether on a horizontal or inclined plane.

It has been the author's experience over many years, no doubt shared by others, that a stick of chalk usually breaks into three pieces when accidentally dropped onto the floor. I rarely gave it any thought, apart from noting that the fundamental mode of vibration of a freely supported, rigid rod has two nodes at an equal distance from each end. For example, a baseball bat has a node in the barrel (the sweet spot) about 15 cm from the end and another node in the handle. However, chalk is not expected to break at the node points, since maximum stress arises at the antinode in the middle of the chalk where bending is a maximum. Richard Feynman described a similar problem with long sticks of spaghetti. He found that they always break into three or more pieces when bent slowly beyond their breaking point, rather than simply breaking in half. He was unable to figure out why, although the problem was solved many years later and is nicely illustrated by Vollmer and Mollmann.

In a recent letter to this journal, Mungan noted that translational energy can be converted into gravitational potential energy when an object is projected vertically, but rotational energy is not usually converted in this manner. As an exception, he gave an example where "a ball initially rolling without slipping will travel higher up a rough ramp than it will up a frictionless ramp." However, such a result is unlikely to be observed in practice. A better example would be a ball spinning rapidly forwards as it slides up the ramp, since the friction force on the ball then acts in a direction up the ramp.

Carl Mungan's article[1] on pulling a spool predicts the directions of the friction force acting on the spool at different pull angles. The friction force, I f i , pointed down the incline since the torque I fR i about the center of mass of the spool was equal and opposite the torque I Tr i . 1(b) and (c), those spools would rotate clockwise on the axle, so the string rotates off each of those spools when the spools rotate clockwise on the horizontal surface. [Extracted from the article]

What happens when a perfectly elastic ball collides with a completely inelastic ball? It is shown that the outcome depends on the stiffness of each ball. A standard textbook problem in mechanics is to calculate the outcome of a head-on collision between two balls using conservation of momentum and kinetic energy. It is easily shown that the outcome depends on the relative mass of the balls and their initial speeds. In practice, there is always a net loss of kinetic energy during a collision, which can be expressed in terms of the coefficient of restitution (COR) for the collision. The COR is defined as the relative speed of the two balls after the collision divided by the relative speed before the collision. In a perfectly elastic collision the COR is unity. In a completely inelastic collision, the COR is zero. [ABSTRACT FROM AUTHOR]

In 1974, Professor Eric Laithwaite demonstrated an unusually heavy gyroscope at a Royal Institution lecture in London. The demonstration was televised and can be viewed on YouTube. A recent version of the same experiment, together with partial explanations, attracted two million YouTube views in the first few months. In both cases, the gyroscope consisted of a 40-lb (18-kg) spinning disk on the end of a 3-ft (0.91-m) long axle. The most remarkable feature of the demonstration was that Laithwaite was able to lift the disk over his head with one hand, holding onto the far end of the axle. The impression was given that the 40-lb disk was almost weightless, or "as light as a feather" according to Laithwaite.

A rattleback is a well-known physics toy that has a preferred direction of rotation. If it is spun about a vertical axis in the "wrong" direction, it will slow down, start rocking from end to end, and then spin in the opposite (i.e. preferred) direction. Many articles have been written about rattlebacks. Some are highly mathematical and others are purely descriptive. It is surprising that there is still no simple physical explanation that can be given to a high school student and one that does not involve an obscure set of complicated equations.

A tippe top (see Fig. 1) is usually constructed as a truncated sphere with a cylindrical peg on top, as indicated in Fig. 2(a). When spun rapidly on a horizontal surface, a tippe top spins about a vertical axis while rotating slowly about a horizontal axis until the peg touches the surface. At that point, weight is transferred to the peg, the truncated sphere rises off the surface, and the top spins on the peg until it is upright. A feature of a tippe top is that its center of mass, labeled G in Fig. 2, is below the geometric center of the sphere, C, when the top is at rest. That is where it will return if the top is tilted sideways and released since that is the stable equilibrium position. The fact that a tippe top turns upside down when it spins is therefore astonishing. The behavior of a tippe top is quite unlike that of a regular top since the spin axis remains closely vertical the whole time. The center of mass of a regular top can also rise, but the spin axis tilts upward as the top rises and enters a "sleeping" position. (Contains 4 figures.)

A ball that rolls on an incline can remain at rest or accelerate up the incline if the incline itself is accelerating upward. A simple experiment is described to demonstrate the effect, and the results are compared with the theoretical model described by De Luca et al. [ABSTRACT FROM AUTHOR]

The first recorded experiments describing the phenomena made popular by Newton's cradle appear to be those conducted by Edme Mariotte around 1670. He was quoted in Newton's "Principia," along with Wren, Wallis, and Huygens, as having conducted pioneering experiments on the collisions of pendulum balls. Each of these authors concluded that momentum (then described as the "quantity of motion") is conserved when one ball collides with another.

A vehicle proceeding up an inclined ramp will become airborne if the ramp comes to a sudden end and if the vehicle fails to stop before it reaches the end of the ramp. A vehicle may also become airborne if it passes over the top of a hill at sufficient speed. In both cases, the vehicle becomes airborne if the point of support underneath the vehicle falls below the trajectory that would be followed by the vehicle in the presence of gravity alone. When the vehicle becomes airborne, the normal reaction force exerted by the ramp or the hill drops to zero, first on the front wheels and then on the rear wheels. Just prior to the vehicle's becoming airborne, the normal reaction force on the rear wheels acts to exert a torque on the vehicle, causing the vehicle to rotate. After the rear wheels become airborne, the vehicle will continue to rotate until it lands some distance from the launch point. (Contains 4 figures.)

The flow of air around a baseball and over the seam acts to slow the ball and to deflect it sideways. Turbulent flow can be visualized, and sideways deflection of the ball can be observed clearly if the ball is dropped in a glass fish tank and filmed with a high-speed camera. Results are presented for a baseball and also for a billiard ball with a metal ring attached to simulate the effect of the baseball seam. [ABSTRACT FROM AUTHOR]

The article describes an experiment involving a solid ball resting in a smooth sheet of paper. Topics discussed include the behavior of the ball being independent on the acceleration of the paper as well several different paper removal speeds being investigated experimentally. Also mentioned are calculations involving ball rolling without slipping and ball rolling with slipping.

The acceleration of a vehicle or a bicycle is commonly used in elementary physics courses to illustrate problems concerning Newton’s laws of motion when friction forces are involved. The maximum possible acceleration is rarely discussed, although it is of interest to consumers and racing car enthusiasts, and it is sometimes questioned by students. It is the main focus of the present article and is considered from a basic physics point of view, appropriate for classroom discussion. [ABSTRACT FROM AUTHOR]

An ice hockey player can strike a puck at speeds up to about 45 m/s (100 mph) using a technique known as the slap shot. There is nothing unusual about the speed, since golf balls, tennis balls, and baseballs can also be projected at that speed or even higher. The unusual part is that the player strikes the ice before striking the puck, causing the stick to slow down and to bend. If a tennis player or a golfer did something like that, by hitting the ground before hitting the ball, it would be classed as a miss-hit and the ball would probably dribble away at low speed. Nevertheless, there appears to be a significant advantage in hitting the ice before hitting the puck, otherwise hockey players would have learned from experience not to do that. [ABSTRACT FROM AUTHOR]

The article focuses on the conservation of energy or conservation of momentum arguments that offers different predictions. It mentions that the conservation of energy depicts that the if the block acquires rotational energy, then less energy will be needed to project the block upwards. It mentions that if block rotates, kinetic energy is transferred from the bullet to the block.

The article presents a science experiment on the physics of Senator Edward Kennedy's driving of his vehicle off a Chappaquiddick bridge in Massachusetts in 1969 that would be suitable as a student project. Topics discussed include using and filming a toy vehicle's projection into a water-filled container to calculate a spinning vehicle's air trajectory, the water's drag force, and the vehicle's trajectory in it. Also noted is the analysis of results via the motion analysis software Tracker.

The article discusses an experiment explaining physics behind vertical impact of a sphere falling into water. Topics discussed include nature of the drag force on the sphere moving through a fluid, complications in calculating the force exerted by the ball on the water due to flow of the water, and relation of cavity formation with separation of the flow of water away from the ball's surface.

The article discusses the study on the forces that act on the bottom end of a spinning top or egg which uses an inclined plane rather than a horizontal plane. Topics mentioned include the measure of the change in orbit radius and precession frequency, the result shows the rolling of eggs and tops across the incline plane, and the sliding down if the surface is slippery but the top rolls if it is spinning.

The article discusses physics education and mentions case of spinning ball sliding down inclined plane. Topics discussed include rolling axis, velocity and torque. Other topics such as kinetic energy, total energy and motion are also discussed. Gyroscopes and rate of rotation of the ball are mentioned.

The PhiTOP® (or ΦTOP®) is a physics toy designed not only to act as a spinning top but also to appeal to the eye and to the scientifically curious mind. It is currently made in two versions, one from solid aluminum and the other solid brass. Each top is highly polished, and is elliptical in one cross section and circular in another. It is therefore a prolate ellipsoid or a spheroid, as indicated in Fig. 1. Its name derives from the ratio of the lengths of the major to minor axes, which is equal to the golden mean Φ = (1+ √5)/2∼1.618. It functions in the same way as a spinning egg or a spinning football in that it rises on one end if it is initially set spinning at sufficient speed with its long axis horizontal. The center of mass rises in an unexpected and somewhat mysterious manner, an effect that it also shares with a tippe top. [ABSTRACT FROM AUTHOR]

The PhiTOP® (or ΦTOP®) is a physics toy designed not only to act as a spinning top but also to appeal to the eye and to the scientifically curious mind. It is currently made in two versions, one from solid aluminum and the other solid brass. Each top is highly polished, and is elliptical in one cross section and circular in another. It is therefore a prolate ellipsoid or a spheroid, as indicated in Fig. 1. Its name derives from the ratio of the lengths of the major to minor axes, which is equal to the golden mean Φ = (1+ √5)/2∼1.618. It functions in the same way as a spinning egg or a spinning football in that it rises on one end if it is initially set spinning at sufficient speed with its long axis horizontal. The center of mass rises in an unexpected and somewhat mysterious manner, an effect that it also shares with a tippe top. [ABSTRACT FROM AUTHOR]

Ivchenko recently provided a simple mathematical description and a nice animation of a ball colliding head-on with two other balls at rest but connected by a spring.[1] He was interested primarily in calculating the amount of energy lost due to vibration of the second pair of balls. In effect, he assumed that the coefficient of restitution was unity to calculate the ball speeds immediately after the initial collision, then found that the coefficient of restitution was less than unity due to the subsequent energy loss. That is, what is the value of the coefficient of restitution I e i for a collision between two balls if energy is lost I after i the collision rather than during the collision?. [Extracted from the article]

The article looks into the elastic properties of the putty-like modelling clay Plasticine, Silly Putty, and tennis strings. The three materials behave in the same qualitative manner when stretched or compressed slowly. When stretched or compressed rapidly, Plasticine is not elastic whereas Silly Putty and tennis strings are highly elastic.