# If a robot swings a bat from point A to point B and hits a ball at point B then where does that kinetic energy go if there is no ball at point B?

EDIT: After thinking about this I have concluded that my hypothetical experiment isn't possible, because if the robot stops the bat at exactly point B on each swing, then the ball doesn't move since the bat isn't moving right at point B, so there is no kinetic energy to transfer to the ball.

If a robot swings a bat from point A to B and hits a ball at point B and thus transfers energy to it, then where does that kinetic energy go to if the robot makes the same swing from point A to point B but there is no ball at point B? It seems like the kinetic energy which could have been transferred to the ball has disappeared or been destroyed in some way since you can never recover it.

For the sake of this hypothetical experiment we are assuming we can measure a precise point in space called point B, so that the robot's two swings are identical, meaning, the bat is the same weight, the force of the swing is the same, the distance of the swing is exactly the same, and thus the energy used during the swing is identical on both swings.

How do we explain where the kinetic energy goes to on the swing without a ball based on the law of the conservation of energy?

EDIT: To clarify, when I say the bat travels from point A to point B, I mean the bat completely stops at point B on both swings, not simply that the robot stops exerting a force on the bat at point B.

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• Bats do not stop moving by themselves. They keep going, in accordance with Newton's first law. What is causing the bat to stop moving? Commented Jul 7, 2021 at 9:09
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## 5 Answers

If the robot swings the bat and doesn't hit the ball, the kinetic energy stays in the bat and the bat continues on at the same pace, absent some applied force.

Alternately, perhaps you envision the scenario in which the robot swings the bat and the bat stops suddenly as though its kinetic energy had been transferred to the ball, yet there is no ball or anything else to absorb the energy. This scenario is impossible, it violates the conservation of energy.

Finally, we might consider the scenario in which the robot swings the bat and the bat stops suddenly despite encountering no obstacle. If I observed this scenario, I would conclude that the robot had applied a force to the bat to halt it. In this case, the bat's energy and momentum would transfer to the robot, and probably into the ground, which is a vast reservoir of energy and momentum.

• Comments are not for extended discussion; this conversation has been moved to chat. Commented Jul 7, 2021 at 8:13

If the robot stopped the bat in both cases, it would expend less energy stopping the bat when some of the bat's kinetic energy was transferred to the ball. The law of conservation of energy still holds.

There's actually two scenarios that could be happening here based on the details of the question:

1. The swing is only driven until point B. In this case, if there is no ball, the arm has nowhere to transfer its kinetic energy to. This means that it will retain that energy and continue to move past point B. If the arm is mounted on a wheel, it will go round and round the wheel slowing down as the energy is gradually bled off due to friction.

Or, if the arm isn't mounted on a wheel and is more like a human arm with mechanical limitations, the energy will be dissipated by the entire robot itself as the arm will come to a hard stop once it reaches its mechanical limits. Then the energy in the arm will be dissipated in the ground as the entire robot lurches forward (possibly dragged a bit if the swing was hard enough) as the resistance of the robot's base against the ground which stops the robot from just flying away forever. This will cause the shoulder of the robot, which is attached between the base and arm to pull back on the arm to stop the arm from flying away like an asteroid in space. If the swing is hard enough this will damage the robot similar to a human trying to throw a 10lbs weight plate but holding onto it and not releasing at the end of the throw.

2. The swing actually stops in space at point B In this case, you have to consider how stopping the swing from moving past point B is actually achieved. The arm won't magically stop if you don't remove the energy from it; It will behave as #1.

The only way to stop the arm at point B if the ball was not there is to use a hard stop to get rid of the energy in the arm. This might be a steel post set right behind the contact point of the ball so that the bat hits the post when the ball isn't there. Or it could be mechanical brakes in the robot's joints. Either way, the abrupt dissipation of energy without imparting it to something external to the robot is very much like the robot hitting its mechanical limits in #1 which will cause damage if the swing is hard enough. You can imagine the damage you might incur if you swung a bat at a steel post. The energy in your swing isn't being transferred into the ball; It is being transferred into you and being dissipated in your body. Not good.

The robot has to apply a force to start the bat moving. If it wants the bat to stop at point B, it will also have to apply a force to stop it. When it’s starting, the force is in the direction of motion and does positive work. When it stops the bat, the work is negative, so this balances the energy equation.

If the robot is really going to stop the bat at Point B, then the bat should have essentially no energy there and the ball should move minimally or the bat might recoil in the robot’s hands. (This is why real players are always told to “swing through the ball”.) Alternatively, if the robot is adaptively applying force to stop the bat just after hitting the ball or missing the ball, it will need a bit less force to stop the bat when the ball is present precisely because the ball has some of the energy.

Going one step more realistic, the bat - especially a wood bat - is not really rigid. It bends and vibrates during the swing, on contact with the ball, and on a “check swing”. So even just looking at the case where the ball is struck, some of the energy goes into these vibrational modes and is the dissipated as heat or sound. Those modes will definitely be different in your two cases as abruptly stopping the bat will whip the end while striking the ball will send waves in both directions around the impact point.

Related but different, some discussion of the internal dynamics of the bat as well as the transfer of energy from bat to ball here: How can a player hit a home run with a broken bat?

the robot's two swings are identical, meaning, the bat is the same weight, the force of the swing is the same, the distance of the swing is exactly the same

What you describe here is physically impossible. If the robot’s force is the same then the distance will not be. If the distance is the same then the robot’s force cannot be.

If the force is the same then without the ball the bat will continue moving with the same KE, thus conserving energy.

If the distance is the same then without the ball the robot must exert a force in the opposite direction to stop the bat. Since the force is in the opposite direction of the motion the work will be negative and energy will be transferred back into the robot, thus conserving energy.

• Comments are not for extended discussion; this conversation has been moved to chat. Commented Jul 7, 2021 at 8:13