It seems like conservation of momentum and conservation of energy can helps us describe any and all observations that you have. Indeed, both of these principles are quite powerful and can be used in many situations. However, there are some where a new idea must be brought to bear to be able to predict or explain the motion of the system. In these notes, you will read about a puzzle where linear momentum and energy are insufficient to explain the motion.

Consider a person sitting on a still that is free to rotate. Another person throws a heavy ball (like a medicine ball) directly at the sitting person and “nothing happens”. The sitting person catches the ball but there's no observable motion.

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This is an inelastic collision. You have learned how to deal with this this kind of collision and you can explain this observation relatively well with conservation of momentum and energy.

• The frictional force by the floor is large enough to keep the stool and the sitting person from sliding away. That is, for the system of the sitting person, the ball, and the stool, there is an external force by the floor that changes the momentum of that system.

$$\Delta \vec{p}_{sys} = \vec{F}_{ext}\Delta t$$ $$\vec{F}_{floor} = \dfrac{\Delta \vec{p}_{sys}}{\Delta t}$$

With estimates of the velocity and mass of the ball as well as the collision time, you can determine the frictional force that the floor exerts on the stool.

• The collision is inelastic, so the kinetic energy of this system is not conserved, which is fairly obvious. Initially the system has kinetic energy (the ball is moving) and in the final state it does not. The system's internal energy has increased as a result. Because there is no displacement, the floor does no work. We can further assume (as we have in other collisions) that there is no exchange of energy due to a temperature difference.

$$\Delta E_{sys} = W_{surr} + Q$$ $$\Delta E_{sys} = \Delta K_{ball} + \Delta E_{internal} = 0$$ $$\Delta E_{internal} = -\Delta K_{ball}$$