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A loop-the-loop experiment usually involves a ball rolling around a vertical loop. A different version of the experiment is described where a nut was allowed to slide around a vertical loop. In both experiments there is a large decrease in kinetic energy when the ball or the nut first enters the loop.

A loop-the-loop experiment is described to show how sliding friction affects motion of the ball. Conservation of energy can be used to explain the basic physics, but significant energy loss is observed in practice and expands the usefulness of this apparatus as a teaching tool.

A simple experiment is described to compare the descent time between two vertically separated points when an object slides down tracks of varying shape. A surprising result is that the descent time is shortest when it follows a circular track rather than a cycloidal track. Cycloidal tracks are usually predicted to result in the shortest descent time, but only if friction is negligible.

Experimental results are presented concerning the motion of a ball that bounces up an incline a few times then bounces back down again. The number of bounces up the incline is typically small since the speed of the ball in a direction parallel to the incline decreases rapidly, not only during each bounce but also while the ball is in the air. The ball heads back down the incline when it is incident at right angles to the incline.

An experiment is described where a pendulum bob was allowed to roll back and forth across an inclined plane. The period of oscillation is larger than that for oscillation in a vertical plane, in part because the effective value of "g" is reduced on an inclined plane. The experiment highlights the differences between all three common forms of friction, namely sliding, rolling and static friction.

A collision of one object with two or more objects is relatively complicated in general, but a simple example is provided by Newton's cradle since all the objects are identical and in line. In the present paper, an experiment is described where a heavy mallet collides head-on with two billiard balls. The two conservation equations indicate that many different outcomes are possible. The experimental results are surprising but can be explained in terms of the relative mass and stiffness of the mallet and the balls.

A 2.7 m long stringless pendulum was set up to measure the coefficient of rolling friction of various balls, at higher rolling speeds than usually observed with a short stringless pendulum. The arrangement is easy to set up and makes an impressive classroom demonstration as well as an interesting laboratory experiment.

The trajectory of a ball rolling across an inclined plane was recorded on video film to determine if it followed a parabolic path as others have suggested. The challenges in this case were (a) to determine the magnitude and direction of the friction force on the ball, (b) to determine the effect of the friction force on the trajectory and (c) to explain why the rotation axis of the ball rotates as it rolls up and down the incline. The experiment is a simple extension of standard inclined plane experiments but with the extra pedagogical feature that angular velocity sometimes needs to be treated as a vector quantity.

Measurements and calculations are presented showing how the trajectory of an object sliding across an inclined plane varies with the launch and incline angles. The trajectory depends on the magnitude and direction of the sliding friction force. The experiment is easy to set up, can be analysed using a video camera, and would be suitable for a student experiment or demonstration.

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.

If a ball rolls in a circular path on a horizontal surface at constant speed then its horizontal rotation axis changes direction with time. A simple experiment is presented showing that the torque applied to the ball is equal to the rate of change of its angular momentum, even though the magnitudes of its angular velocity and angular momentum remain constant in time.

Calculations are presented showing that the usual 'faster than g' demonstration has a surprising property. That is, a rod hinged at its bottom end rotates at an exponentially increasing rate until it falls with maximum vertical acceleration, unlike an object that falls freely by gravity alone. If the rod is hinged at its top end and released from a horizontal position, then the vertical acceleration is a maximum at the instant it is released.

Oblique angle collisions of two penny coins on a smooth, horizontal surface were filmed with a video camera to investigate the physics of the collision process. If one of the coins is initially at rest, then the two coins emerge approximately at right angles, as commonly observed in billiard ball collisions and in puck collisions on an air table. The coins actually emerged at an angle less than 90 degrees due to friction between the coins, which also resulted in both coins rotating after the collision. At glancing angles, the friction force was due to sliding friction. At other angles of incidence the coins gripped each other and the friction force was then due to static friction.

If an empty coffee cup is spun on a horizontal surface about a vertical axis in an anti-clockwise direction, then the whole cup rotates slowly backwards, in a clockwise direction, about a vertical axis located outside the cup. Clues to this curious behaviour are presented by comparing it with other spinning objects.

A solid ball placed on a rotating turntable is known to roll slowly around a circular path, at a speed 3.5 times slower than the turnable itself. If the ball is located in a straight track across a diameter of the turntable, then it accelerates rapidly to the edge. Both effects were filmed in slow motion using a video camera and a cake decoration turntable, and are presented as supplementary videos. The results agree well with calculations based on rolling motion of the ball.

The coefficient of restitution (COR) for a collision is usually a number between 0 and 1 depending on whether the collision is completely inelastic, or perfectly elastic or something in between. That is the usual situation for colliding spheres or a ball dropped on a horizontal surface. A different situation arises when a bat collides with a ball. A simple experiment is described where a rod is dropped on another rod at right angles. In that case, two different values of the COR can be defined.

Experimental results are presented on the collision of a superball with two different wood blocks. The results are in reasonable agreement with a simple collision model where kinetic energy is conserved, but better agreement is obtained if a small loss of kinetic energy is assumed, as observed. The physics is slightly more complicated than the standard head-on collision of two balls studied in elementary mechanics since it involves rotation as well as translation of one or both of the colliding objects.

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.

If a smooth ball is dropped vertically without spin on a smooth horizontal surface then one might expect the ball to bounce vertically without spin. If it does not then the centre of mass of the ball does not coincide with its geometric centre. An experiment is described where a billiard ball and a superball are deliberately biassed by adding a small steel ball on one side. The results agree well with theoretical calculations.

Points near the top end of a falling rod hinged at its bottom end can fall faster than g. If a rod falls on a frictionless surface then the bottom end slides backwards and the centre of mass falls vertically with acceleration less than g. The effect was simulated by mounting a rod on wheels and filming the result with a video camera. The experiment provides an example of accelerated motion where the acceleration increases with time.

Experimental results are presented concerning a bead sliding on a rotating, horizontal rod. If the rod rotates at constant angular velocity then the sliding speed in the radial direction increases exponentially with time, provided that the rotation speed is sufficient to overcome friction. Otherwise the bead rotates in a circular path of constant radius.

An experiment is described where a billiard ball and a golf ball were projected with backspin on a horizontal surface to measure the transition from sliding to rolling. During both phases, the torque on the ball is affected by an offset in the line of action of the normal reaction force.

A standard problem for physics students is to calculate or measure the acceleration of an object down an inclined plane. Additional information can be obtained by measuring the angular acceleration as well as the linear acceleration. An experiment is described where a billiard ball was filmed as it rolled down an inclined plane at different inclination angles. The transition from rolling without slipping to rolling with slipping was identified, and the relevant friction coefficients were measured independently from the linear and angular accelerations.

The vertical bounce of a plastic egg was investigated by dropping the egg on a horizontal surface and filming the result with a video camera. If the egg is dropped on one end then it bounces just like a spherical ball. If the top end of the egg is pointing forwards or backwards when it lands on the surface, or if the egg is spinning when it lands, then the bounce is very different. The egg can bounce forwards or backwards and it can bounce to a large height or only a very small height. The experiment would be suitable for a student project. It involves both translational and rotational motion of an object subject to an impact force and a torque.

A hula hoop rotating around a person's waist is an example of circular motion where the centripetal force on the hoop is directed towards the centre of the circle rather than the centre of the hoop. The friction force on the hoop is relatively small by comparison since the hoop rolls around the waist. A slight complication is that the hoop rotates in an elliptical path if the waist rotates back and forth in a straight line or if the waist rotates in an elliptical path. Three simple experiments are described to illustrate the physics involved.

Newton's cradle is a well-known physics toy that is commonly used by teachers to demonstrate conservation laws in mechanics. It can also be used to investigate the physics of colliding objects, by recording motion of the balls on video film. Various experiments are described using 3-ball and 5-ball cradles, showing how different types of collision can be investigated depending on whether the balls are touching or separated. The sequence of collisions was examined as a function of time, with the surprising observation that very small gaps between the balls, invisible on video film, make a significant difference to the collision dynamics. Additional experiments illustrate the effects of changes in ball stiffness and the mass of the middle ball and provide an introduction for students and teachers into possible research projects. Each experiment is illustrated with a supplementary video. [For "Understanding Newton's Cradle. I: Modelling the Ideal Cradle," see EJ1286997.]

Newton's cradle is often discussed in science classrooms as a clear example of the laws of conservation of momentum and energy although it has been shown that this use is somewhat misleading. Approaches to understanding the behaviour of this apparatus are often over-simplified and deficient or over-complex and with little impact among teachers. In this paper, basic principles of mechanics are used to explain the behaviour of ideal cradles of various lengths and to use a simple model by which to simulate its operation. The purpose is to demonstrate that the real behaviour of Newton's cradle provides a rich source of application of those principles in coming to terms with how the apparatus behaves and experiencing the process of modelling in physics. [For "Understanding Newton's Cradle. II: Exploring a Real Cradle," see EJ1286996.]

A simple experiment for students is to measure the coefficient of restitution (COR) for a vertical bounce on a horizontal surface. In this paper, measurements are presented of the COR for a tennis ball bouncing at an oblique angle on a horizontal surface. Changes in the horizontal and rotation speeds were also measured, by filming the bounce with a video camera. A measurement of this type involves a more extensive examination of basic mechanics, since the friction force acting at the bottom of the ball acts to change both the horizontal speed of the ball and its rotational velocity. The COR for an oblique bounce was found to be larger than that for a vertical bounce and was also found to depend on the incident spin of the ball.

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 impact force and duration when one billiard ball collides head-on with another is estimated by assuming that the balls are connected by a spring. The results are compared with a measurement when a billiard ball collides with a heavy, rigid surface.

A standard physics experiment for students is to measure the terminal velocity of an object in air or in glycerine. A more difficult challenge is to measure the terminal velocity in water since the depth of the water needs to be large or the object needs to be dropped in the water at a speed close to its terminal velocity. Results obtained by filming the fall in a fish tank are presented for a range of different spheres, showing how the terminal velocity depends on the density of the sphere and its radius. The results provide a useful measurement of the drag force and the drag coefficient for a sphere in water. An additional experiment to measure the Magnus force is described where a ball was spinning when it entered the water.

A well known physics problem is to calculate the friction forces required to support a ladder against a wall. A more tractable problem is to calculate the friction forces needed to support an inclined beam on a ball or a cylinder. In the latter case there are three rather than two points of sliding support. Measurements and calculations are presented to show that a ball can support an inclined beam without slipping, provided the incline angle is not too large.

Two balls on an incline can remain at rest if friction between the balls prevents them rolling down the incline. Results with various balls are presented to show how ball mass, diameter and friction affects the outcome. A stack of four identical balls is also examined.

If a ball is incident obliquely on a horizontal surface and is allowed to bounce more than once, then it is likely to bounce many times before it starts rolling along the surface. The number of bounces before rolling commences depends on the initial vertical speed and the normal coefficient of restitution. The transition from bouncing to rolling is examined using a simple theoretical model and is compared with experimental data obtained by filming the process with a video camera. We find that the final rolling speed is proportional to the initial horizontal speed of the ball and depends on the initial ball spin, but is independent of the tangential coefficient of restitution. Representative videos for different balls are included as supplementary material, including a superball thrown with a backspin that creates a back and forth motion. Instructors could use the experiment and/or analysis for an advanced undergraduate lab or use a simplified observational exercise for non-majors. Editor's Note: When a ball is dropped on a horizontal surface with no initial spin, previous studies have found that its bouncing behavior can be simply described using a coefficient of restitution, which gives the ratio of the velocity after the bounce to before the bounce. The value of this coefficient is −1 for a perfectly elastic ball/surface, with a smaller magnitude for any real ball. In many sports, like golf, basketball, or bowling, balls are thrown at an angle and are often given some initial spin by the player. Depending on initial conditions, these balls can bounce, roll, or start by bouncing and then transition to rolling. Here, the transition from bouncing to rolling is shown to be described by using both a vertical and horizontal coefficient of restitution, with the horizontal velocity defined at the spinning edge of the ball rather than its center. Videos of undergraduate level experiments are included, with results used to validate the model. [ABSTRACT FROM AUTHOR]

A ball at rest on a surface can be made to bounce up by pushing it down then releasing the downward force as fast as possible. Measurements and calculations are presented to show how it can best be done.

A method is described to measure the coefficient of restitution (COR) by dropping a ball on a piezoelectric disk. Multiple bounces can be observed at small drop heights, so the average COR over say ten bounces can be obtained from just one ball drop, without having to measure the bounce height or the bounce speed. The results show directly that the maximum impact force on the ball during each bounce decreases linearly with time until the ball stops bouncing.

If a ball rolls at constant speed on a horizontal surface about a horizontal axis then the angular velocity is easily measured. If the ball is projected with additional spin about the vertical axis, then the rotation axis is tilted and it is more difficult to measure the rotation speed. A few examples are presented to show how the separate topspin and sidespin components can be measured.

A spinning top with a spherical bottom end was constructed to examine its behaviour. Experimental results were consistent with theoretical predictions.

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.

When a ball bounces obliquely on a horizontal surface, the bottom of the ball stretches horizontally and then vibrates backward. The resulting ball spin depends sensitively on the transverse vibration frequency. A simple model is presented to describe the effect, showing how the stored elastic energy can result in additional spin.

An experiment is described where a metal nut was allowed to slide from the top to the bottom of a vertical wire loop. An interesting feature is that the normal reaction force on the nut decreases to zero and reverses direction before the nut reaches the bottom of the loop. [ABSTRACT FROM AUTHOR]