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When one hard steel ball collides with another, kinetic energy is conserved, even if the balls have different diameters. Why is kinetic energy conserved in such a collision, given that kinetic energy is not conserved when two unequal length steel springs or rods collide? Experimental results with bouncing balls, springs, and rods are presented, which reveal the answer. For colliding springs and rods a significant fraction of the initial kinetic energy is retained after the collision as vibrational energy in the longer spring and rod. When two hard balls collide, a negligible fraction of the initial energy is converted to vibrational energy because the collision time is much longer than the transit time of an acoustic wave across each ball due to the fact that the contact region of a hard spherical ball is much softer than the rest of the ball. [DOI: 10.1119/1.2948778]

The physics of falling from a height, a topic that could be included in a course on forensic physics or in an undergraduate class as an example of Newton's laws, is applied to a common forensic problem. [DOI: 10.1119/1.2919736]

A billiard ball struck by a cue travels in the same direction as the cue unless the ball is struck toward one side in order to impart sidespin. In that case the ball deflects or 'squirts' away from the line of approach of the cue, typically by a few degrees. Measurements and calculations are presented showing how a cue tip slides across the ball if it is unchalked, resulting in a large squirt angle, and how it grips the ball when it is chalked, resulting in a smaller squirt angle. [DOI: 10.1119/1.2825392]

When a tennis ball rests on top of a basketball and both drop to the floor together, the tennis ball is projected vertically at high speed. A mass-spring model of the impact, as well as air track data, suggest that the tennis ball should be projected at relatively low speed. Measurements of the forces on each ball and the bounce of vertically aligned superballs are used to resolve the discrepancy. [DOI: 10.1119/1.2772286]

The gear effect arises when a ball collides with an object and the object recoils with a component of its acceleration in a direction parallel to the two contacting surfaces. Two experiments are described that show how the surfaces of the ball and the object can engage without slip similar to two gears. The effect is used in golf to correct for off-center impacts and it plays a minor role in baseball. [DOI: 10.1119/1.2713788]

(Received 23 May 2005; accepted 16 September 2005) If an inclined pencil is released from rest with its bottom end resting on a table, the bottom end will slide forward or backward or it will remain at rest at the start of the fall, then slide backward for a short period before sliding forward. The magnitude and direction of the displacement of the bottom end of the pencil depends on the initial angle of inclination, the coefficient of friction, and on the length and mass distribution of the pencil. The same ground reaction forces play a similar role in the fall of trees and chimneys, the bounce of a football and any other elongated object, and in activities such as walking and running. When an elongated object is thrown obliquely to the ground, the object can bounce either forward or backward depending on the angle of inclination at impact. Spherical objects bounce away from the thrower. The difference arises because the horizontal friction force is determined not only by the normal reaction force, but also by the line of action of the normal reaction force relative to the center of mass.

A spinning ball incident at right angles to a surface bounces at an oblique angle and with reduced spin. Consequently, a spinning ball struck head-on does not rebound along its incident path, which presents a control problem in bat and racquet sports. The rebound angle and spin depend in a nontrivial manner on the coefficient of friction between the ball and the surface and on the elastic properties of the ball and the surface. Values of the normal and tangential coefficients of restitution coefficients are presented for a tennis ball impacting a smooth and a rough surface and on strings of a tennis racquet. The implications for spin generation in tennis are briefly described. [DOI: 10.1119/1.2008299]

A block sliding down an inclined plane normally accelerates. However, if the friction force increases with speed, then the block can slide at a constant terminal speed in a manner similar to the fall of an object through a fluid. Measurements of the increase in the coefficient of friction for tennis ball cloth sliding on a smooth surface are described over speeds varying by a factor of 9000. For the low speed measurements, the ball cloth was attached to the bottom of a weighted box and pulled along a horizontal surface by a constant horizontal force. Results at higher speeds were obtained by bouncing a tennis ball off the surface. (c) 2005 American Association of Physics Teachers. [DOI: 10.1119/1.1891174]

Experimental results on the large-amplitude motion of a double pendulum are presented, with emphasis on the first half cycle. The initial part of the swing is reproducible and is of interest in modeling various human movement activities such as running, throwing, kicking, and the swing of a bat or racquet. Beyond this time, the motion is chaotic. The forces and torques acting on each pendulum segment are analyzed to explain its motion. The results show how a 'perfect' bat could be designed where all the kinetic energy from the player's arms is transferred to the ball and none is retained in the arms or the bat after the impact.

If a small object is placed under the front leg of a chair, the chair tilts backwards. If the object is placed under a rear leg, the chair tilts sideways. The effect is surprising but can be analysed in terms of elementary physics.

The center of percussion is commonly regarded as a sweet spot when referring to a baseball bat or a tennis racquet because it is assumed that there will be no sudden motion of the handle with respect to the hand if the corresponding axis of rotation passes through the hand. A problem with this interpretation is that the hand extends over a finite length of the handle and exerts an opposing reaction force on the handle. The hand also changes the total mass and moment of inertia of the system, while the arm restricts free motion of the hand. Experimental results are presented showing that the axis of rotation passes through the hand or the wrist for all the usual impact points on a hand-held implement. As a result, the impact point that feels best is usually the node of the fundamental vibration mode, not the center of percussion.

Measurements are presented of the speed at which objects of different mass can be projected by an overarm throw. Light objects can be thrown faster than heavy objects, although the difference in speed is not as large as one might expect. For a factor of 60 increase in the thrown mass, there was a decrease of only 2.4 in the throw speed. The relatively small change in throw speed is due to the fact that the force that can be applied to a thrown object increases with object mass. Estimates of the muscle forces involved indicate that the increase in force with mass is primarily an inertial rather than a physiological effect. The total kinetic energy of the mass, hand, and the forearm was found to be almost independent of the object mass, and the throw speed is almost independent of the mass of the upper arm.

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]

Measurements of the normal reaction force and the friction force acting on an obliquely bouncing ball were made to determine whether the friction force acting on the ball is due to sliding, rolling, or static friction. At low angles of incidence to the horizontal, a ball incident without spin will slide throughout the bounce. At higher angles of incidence, elementary bounce models predict that the ball will start to slide, but will then commence to roll if the point of contact on the circumference of the ball momentarily comes to rest on the surface. Measurements of the friction force and ball spin show that real balls do not roll when they bounce. Instead, the deformation of the contact region allows a ball to grip the surface when the bottom of the ball comes to rest on the surface. As a result the ball vibrates in the horizontal direction causing the friction force to reverse direction during the bounce. The spin of the ball was found to be larger than that due to the friction force alone, a result that can be explained if the normal reaction force acts vertically through a point behind the center of the ball.

When a ball is incident obliquely on a flat surface, the rebound spin, speed, and angle generally differ from the corresponding incident values. Measurements of all three quantities were made using a digital video camera to film the bounce of a tennis ball incident with zero spin at various angles on several different surfaces. The maximum spin rate of a spherical ball is determined by the condition that the ball commences to roll at the end of the impact. Under some conditions, the ball was found to spin faster than this limit. This result can be explained if the ball or the surface stores energy elastically due to deformation in a direction parallel to the surface. The latter effect was investigated by comparing the bounce of a tennis ball with that of a superball. Ideally, the coefficient of restitution (COR) of a superball is 1.0 in both the vertical and horizontal directions. The COR for the superball studied was found to be 0.76 in the horizontal direction, and the corresponding COR for a tennis ball was found to vary from -0.51 to + 0.24 depending on the incident angle and the coefficient of sliding friction. [DOI: 10.1119/1.1450571] (Received 9 July 2001; accepted 20 December 2001)