Search

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.

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 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.

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.

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 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.

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.

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.

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.

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

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.

A simple throwing task is described to illustrate various aspects of projectile motion. The task was to throw a tennis ball in a waste paper bin about 2 m away. Success depends on skill, but it also depends on the physics of the problem. If the ball is thrown underarm, then success depends primarily on the throw speed, which must be controlled to within about 2%. The launch angle can be chosen within a wide range. If the ball is thrown overarm, then the launch angle is just as important as the throw speed.

When a hard object rolls on a soft surface, or vice versa, rolling friction arises from deformation of the soft object or the soft surface. The friction force can be described in terms of an offset in the normal reaction force or in terms of energy loss arising from the deformation. The origin of the friction force itself is not entirely clear. It is investigated qualitatively in this paper by rolling a steel ball on soft foam and by rolling a foam cylinder on a hard surface. The deformation of the foam was observed visually, providing simple insights into the origin of the friction force.

A ball that rolls without sliding down an inclined plane requires a small static friction force to prevent the ball sliding down the incline. The magnitude of that force is investigated by considering the force needed to prevent the contact point from slipping.

Three simple experiments are described using a small water bottle with two holes in the side of the bottle. The main challenge is to predict and then explain the observations, but the arrangements can also be used for quantitative measurements concerning hydrostatic pressure, Bernoulli's equation, surface tension and bubble formation.

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.

A simple experiment is described to measure the coefficient of rolling friction for a low bounce ball rolling on a horizontal surface. As observed previously by others, the coefficient increased with rolling speed. The energy loss due to rolling friction can be explained in terms of the measured coefficient of restitution for the ball, meaning that low bounce balls have a higher coefficient of rolling friction than high bounce balls.

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.

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.

The bounce of a ball is a seemingly innocuous event that can be used to illustrate many aspects of elementary and even advanced mechanics. Both normal and oblique bounces on a rigid surface are considered in this article, emphasizing qualitative features of the bounce process. If the ball bounces at an oblique angle then it can slide throughout the bounce, or just at the start of the bounce, and may even slide backwards at the end of the bounce. A ball can also grip the surface after a short sliding phase, or it can grip right from the start. When the ball grips, static friction rather than sliding friction determines the rebound speed, spin and angle.

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.

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.

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.

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.

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.

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.

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.)

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.)