If someone catches a moving ball with some velocity, then there must be some energy conversion as the ball looses its a kinetic energy. But the ball doesn't move while being caught, and thus does not move in the direction of the force applied by the person's hands. So is the person doing any work?
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3$\begingroup$ Re, "the ball doesn't move while being caught." If that actually was true, then the ball would experience infinite acceleration. In reality, there is no such thing as a perfectly rigid object. The ball will be compressed, different parts of it will experience different accelerations. The "hand" that catches the ball will be compressed. Work will be done. $\endgroup$– Solomon SlowCommented Feb 12, 2020 at 17:19
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$\begingroup$ Some of the ball's kinetic energy is converted into heat and acoustic energy upon catching, but I'm not sure the energy is converted to other forms as well. $\endgroup$– electronpusherCommented Feb 12, 2020 at 17:19
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$\begingroup$ P.S., If you do the math, you'll find that when you stop a moving object by exerting force on it, the amount of work that you did on the object will be a negative number. That means that the object did work on you. $\endgroup$– Solomon SlowCommented Feb 12, 2020 at 17:20
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3 Answers
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You can model a catch in 2 ways, in the first you catch the ball and immediately grab it to not let the ball escape. In this case some part of the kinetic energy will dissipate due to the distorsion of the ball (potencial energy) and some part of the energy will dissipate due the sound of the collision.
In the second way you catch the ball while move your arm backwards so you can damp the impact. In this case you done working while you move your arm.
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The person is exerting a force on the ball and if you assume the ball to be perfectly rigid,then the centre of mass of the ball should undergo some displacement before coming to rest even if the force exerted by the person is highly impulsive.In a rigid system the displacement of the centre of mass is same as the displacement of the point of application of force(pure translatory motion) and hence the ball is doing work against the external force at the expense of its kinetic energy..
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The person does work taking away the kinetic energy of the ball bringing the ball to a stop. Per the work energy theorem the net work on the ball equals its change in kinetic energy or
$$W_{net}=F_{ave}d=-\frac{mv^2}{2}$$
Where $F_{ave}$ is the average impact force on the person, $d$ is the stopping distance of the ball from the instant of impact to when the person brings it to a stop, $v$ Is the velocity of the ball on impact, and $m$ is the mass of the ball.
The negative sign means a loss of kinetic energy and that the person has done negative work taking the energy away from the ball and absorbing it in the body increasing its internal energy. Some energy is also absorbed by the ball
Hope this helps
