. What forces are involved when hitting the sweet spot of a baseball bat?
If the ball bounces from the sweet spot, the two push on one another hard. The ball slows to a stop and then reverses its direction, rebounding from the bat at high speed. The bat accelerates in the opposite direction, and begins to rotate slightly about its center of mass. This rotation is just right to keep the bat's handle from accelerating either toward or away from the ball. That's why the hit feels so clean and neat. The handle doesn't accelerate. The force from the ball on the bat also doesn't cause the bat to vibrate, because the sweet spot is a vibrational node.
. When a bowling ball hits a wall, is it doing work on the wall?
If the wall doesn't move at all, no. Work requires both a force and a movement in the direction of that force. But in reality, the wall will certainly move at least a short distance. When it does, it moves in the direction of the force on it and the ball is doing work on the wall.
. When the falling ball bounced off the rising board, why did the ball go upward very quickly? Because of your frame of reference?
The frame of reference from which you observe the situation doesn't cause the rebounding ball to move quickly, but it does help you to understand why the ball rebounds so quickly. Instead of describing the ball bounce from the rising board, let's look at the ball bouncing from a horizontally moving bat. That way, we won't have to worry about gravity—we can pretend it doesn't even exist for a moment. Let's begin from the fan's inertial frame of reference as a pitched ball heads toward a bat at home plate. As the ball approaches the bat, the bat approaches the ball. Both objects are moving, which makes things complicated. So we'll now shift to the bat's frame of reference for a while. In this frame of reference, the bat is stationary and the ball is approaching at high speed. (This rapid approach speed reflects the fact that the two objects are each moving toward the one another in the fan's reference frame.) The ball now bounces from the bat. Because it approached the bat at such a high speed, the ball rebounded at a high speed, too—it heads away from the bat at high speed. Now we'll shift back to the fan's reference frame. The ball is still going away from the bat at high speed, but now we must notice that the bat itself is heading toward the outfield at a high speed, too. So the ball must really be heading toward the outfield fast—it's outrunning the bat toward the outfield. And that is the case. The ball heads toward the outfield at a much higher speed than it had when it was heading toward the bat originally. In the fan's frame of reference, there is a large transfer of energy from the bat to the ball
. Why do some objects bounce off the ground (balls) whereas others would break (eggs)?
Some objects can deform elastically, storing energy in the process, while others can't. The surface of a rubber ball is made up of long, flexible molecules called polymers that can bend and stretch without breaking. As the ball's surface dents during an impact, these polymer molecules move about and begin to exert forces on one another (storing energy in the process). As the ball rebounds, these molecules release their stored energy and push the ball back into the air. An egg, on the other hand, is made of hard, crystalline material that shatters during the deformation. Whole rows of atoms and molecules rip apart from one another and are unable to return. The egg doesn't store the impact energy. Instead, it turns that energy into thermal energy. The shell just crumbles.
. Why does a basketball bounce higher than a bowling ball?
When a ball bounces from a rigid surface, the ball's surface distorts inward and then pops back outward. During the inward motion, the ball stores energy—pushing its surface inward takes energy. During the outward motion, the ball releases that stored energy. But not all the energy invested in the ball emerges as useful work. Some of that energy is turned into thermal energy and never reappears. A properly inflated basketball returns a good fraction of the energy it receives while other balls may not. In fact, a bowling ball bounces pretty well from a hard surface such as cement. But when it hits a softer surface such as wood, the wood receives much of its energy and wastes that energy as thermal energy.
. 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.
. Can you explain the term centripetal?
Centripetal means "directed toward a center." A centripetal force is a force that's directed toward a center. For example, a ball swinging around in a circle at the end of a string is experiencing a force toward the center of the circle—a centripetal force. Because the ball accelerates in the direction of the force, it accelerates centripetally. And because it experiences a fictitious force in the direction opposite its acceleration, it experiences an outward fictitious force away from the center of the circle. That fictitious force is called centrifugal "force." However, you should always recognize that this outward "force" is not a force at all, but an effect caused by the ball's inertia—its tendency to travel in a straight line.
. If all the kids on the merry-go-round are clustered around its center while it is spinning at a constant angular velocity, then if all the kids were to "cautiously" move away from its pivot to the outer edges (while still spinning), would that cause the merry-go-round to slow down faster than if they had remained in the center?
Yes. When the kids move away from the center, the merry-go-round will slow down. If they then return to the center, the merry-go-round will speed up!