Category: bouncing balls

The earth’s surface is moving at something like 950 mph as it rotates. Why don’t we notice this when we are in an airplane? — DT, Nicosia, Cyprus

It’s true that the earth’s surface is moving eastward rapidly relative to the earth’s center of mass. However, that motion is very difficult to detect. When you are standing on the ground, you move with it and so does everything around you, including the air. While you are actually traveling around in a huge circle once a day, for all practical purposes we can imagine that you are traveling eastward in a straight line at a constant speed of 950 mph relative to the earth’s center of mass. Ignoring the slight curvature of your motion, you are in what is known as an inertial frame of reference, meaning a viewpoint that is not accelerating but is simply coasting steadily through space.

You’ll notice that I keep saying “relative to the earth’s center of mass” when I discuss motion. I do that because there is no special “absolute” frame of reference. Any inertial frame is as good as any other frame and your current inertial frame is just as good as anyone else’s. In fact, you are quite justified in declaring that your frame of reference is stationary and that everyone else’s frames of reference are moving. After all, you don’t detect any motion around you so why not declare that your frame is officially stationary. Since the air is also stationary in that frame of reference, flying about in the air doesn’t make things any more complicated. You are flying through stationary air in your old stationary frame of reference. The only way in which the 950 mph speed appears now is in comparing your frame of reference to the rest of the earth: in your frame of reference, the earth’s center of mass is moving westward at 950 mph.

I’m doing a science experiment of what factors affect the distance a golf ball travels. One of my factors is the bounciness of the ball. Does this have any effect on the distance the ball will go? — EG, North Salem, NY

Yes. The bouncier the golf ball, the farther it will go after being struck by a golf club. While we normally think of a bounce as occurring when a ball hits a stationary object, it’s also a bounce when a moving object hits a stationary ball. The golf ball bounces from the golf club and the more bouncy the golf ball is, the faster and farther it will travel.

What is the difference in distance that a soccer ball will travel if the air pressure in the ball changes? — AB

A properly inflated soccer ball bounces well when you drop it on a hard floor because the ball stores energy by compressing the air during the bounce and the air returns this energy quite efficiently during the rebound. An under inflated soccer ball doesn’t bounce so well because it stores energy by bending its leather surface during the bounce and the leather doesn’t return energy very efficiently during the rebound. The same result holds true when you kick a ball rather than dropping it on the floor. Whether a moving ball hits a stationary surface or a stationary ball hits a moving surface, the ball is still bouncing from a surface. When you kick a ball with your foot, the ball is bouncing from your foot and a properly inflated ball will bounce more efficiently from your foot than an under inflated ball. The properly inflated ball will rebound at a higher speed and will travel farther.

What causes a dropped ball to bounce? – MK

When you lift a ball off the floor, you transfer energy to it. This energy is stored in the gravitational force between the ball and the earth and is called gravitational potential energy. When you release the ball, its weight makes it accelerate downward and its gravitational potential energy gradually becomes kinetic energy, the energy of motion. When the ball hits the floor, both the ball’s bottom surface and the floor’s upper surface begin to distort and the ball’s kinetic energy becomes elastic potential energy in these two distorted surfaces. The ball accelerates upward during this process and eventually comes to a complete stop. When it does, most of the energy that was initially gravitational potential energy and later kinetic energy has become elastic potential energy in the surfaces. However, some of the original energy has been converted into thermal energy by internal frictional forces in the ball and floor. The distorted ball and floor then push apart and the ball rebounds into the air. Some or most of the elastic potential energy becomes kinetic energy in the ball, and the rising ball then converts this kinetic energy into gravitational potential energy. But the ball doesn’t reach its original height because some of its original gravitational potential energy has been converted into thermal energy during the bounce.

Does the air pressure of a basketball and the hardness of the floor surface have an effect on the height of the bounce? — BB, West Unity, OH

Yes to both questions. When a basketball collides with the floor, the ball’s kinetic energy—its energy of motion—is temporarily stored as elastic potential energy in two objects: the ball and the floor. The fractions of the collision energy stored in the basketball and the floor depend on how far each of them dents—the more one dents, the larger the fraction of the collision energy it receives. How well the basketball rebounds from the floor depends on how much of the collision energy returns to the ball during the rebound. Some of the stored energy in each dented surfaces is converted to thermal energy and is lost from the bouncing process. A hardwood floor is very springy and returns its share of the collision energy efficiently. A properly inflated basketball is also very springy. Thus when a firm basketball bounces on a good hardwood floor, it bounces well. But if the basketball is underinflated, its surface bends too far so that it receives most of the collision energy and internal friction in the ball’s skin wastes most of that energy. The ball bounces weakly. And if you try to bounce the ball on a soft carpet, the carpet dents easily, receives most of the collision energy, and wastes most of it as thermal energy. Again, a weak bounce.

What effects, if any, does storage temperature have on the height of a tennis ball’s bounce?

I suspect that cool storage will prolong the life of a tennis ball in an opened can. That’s because the ball’s bounciness depends on its retaining air inside its rubber shell. As the ball loses air by diffusion through the rubber, it loses its ability to bounce high. Diffusion is a thermally activated process in which the individual air molecules move between the rubber molecules and migrate through the material. At lower temperatures, the air molecules will move much more slowly through the rubber and the pressure inside the ball will stay high for a longer time.

Why does a rubber ball transfer more forward momentum as the ball rebounds off an object?

As the ball hits a wall and stops, it transfers its forward momentum to the wall. The ball pushes the wall forward for a certain time and thus provides a forward impulse to the wall. As the ball rebounds from the wall, it also pushes the wall forward for a certain time and thus provides an additional forward impulse to the wall. The ball ends up traveling in the opposite direction from that which it had initially, so its momentum points in the opposite direction. This reversal of momentum required an enormous transfer of forward momentum to the wall; so large that the ball actually ended up with a negative amount of forward momentum (which is equivalent to a positive amount of backward momentum).

Why when you play baseball is it easier to hit a home run off a fast ball than off a slow ball?

The speed of the ball’s rebound from the stationary bat (let’s adopt the bat’s inertial frame of reference for the moment) depends on the speed at which the ball and bat approach one another. The faster the ball approaches the bat, the higher the ball’s rebound speed will be. Since a fastball approaches the bat faster than a slow ball, the fastball also leaves the bat at a higher speed and is more likely to fly out of the outfield for a home run. You can even consider the case in which the batter tries to bunt and holds the bat stationary. A fastball will approach the bat faster and will bounce back faster than a slow ball will. If the pitch is fast enough, the rebounding ball could conceivably fly past the outfield for a home run, too.

Would a baseball bat do more damage on a person if the point of contact was the very end of the bat (torque=force x lever arm) or at the sweet spot? (assuming the bat was swung with a constant angular momentum)

The sweet spot. Hitting someone with the bat is very similar to hitting a ball. When you hit a ball with the sweet spot of the bat, the bat slows down and begins to rotate slowly. The slowing is good because it means that some of its kinetic energy has been transferred to the ball. The rotation is bad, because it means that the bat has put energy into rotation (spinning objects have kinetic energy). If the ball hit the bat’s center of mass, the bat wouldn’t rotate and the transfer of energy would be better; except for one new problem: the bat would begin to vibrate and that vibration would use energy. By hitting the ball on the sweet spot, you keep the bat from vibrating and wasting some of its energy. The transfer of energy and momentum to the ball is maximized. The same occurs when hitting any other object, including a person.

How do rubber bouncing balls work? Does the table exert more force than is applied, causing an upward acceleration?

The table never pushes up on the ball harder than the ball pushes down on the table. That would violate Newton’s third law and is just not the way our universe works. As the ball strikes the table, the two objects dent. The ball dents most and has work done on its surface—the table pushes the surface inward and work is force times distance in the direction of that force. The ball stores this work/energy as a deformation of its elastic surface and a compression of the air inside the ball. The ball then rebounds from the table as this stored energy reemerges as kinetic energy in the ball. Throughout the bounce, the upward force that the table exerts on the ball is much larger than the ball’s downward weight. As a result, the ball accelerates upward the whole time. It starts the bounce heading downward and finishes the bounce heading upward.