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Chapter 5: Problem 10

A ball hits a floor and rebounds after an inelastic collision. In this case (A) the momentum of the ball just after the collision is the same as that just before the collision. (B) the mechanical energy of the ball remains the same is the collision. (C) the total momentum of the ball and the earth is conserved. (D) the total energy of the ball and the earth is conserved.

Short Answer

Expert verified
The correct statements for the given inelastic collision are A, C, and D. Momentum is conserved during the collision (statement A), total momentum of the ball and Earth is conserved (statement C), and total energy (mechanical energy, heat energy, etc.) of the ball and Earth is conserved (statement D). However, the mechanical energy of the ball is not conserved (statement B is false) as some kinetic energy is transformed into other forms of energy like heat or sound.

Step by step solution

01

Statement A: Conservation of Momentum

In an inelastic collision, the momentum of the ball will be conserved. This means that, just before and just after the collision, the momentum of the ball should be the same. Therefore, statement A is true.
02

Statement B: Mechanical Energy

In an inelastic collision, some of the kinetic energy of the ball is transformed into other forms of energy like heat or sound. This means that the mechanical energy of the ball will not be conserved, making statement B false.
03

Statement C: Total Momentum

Due to the law of conservation of momentum, the total momentum of the ball and the Earth must be conserved, even in an inelastic collision. The Earth and the ball form an isolated system, so their total momentum cannot change. Thus, statement C is true.
04

Statement D: Total Energy

Energy is always conserved in any type of collision, which means that the total energy of the ball and the Earth before and after the collision must be conserved. However, this does not mean that the mechanical energy (which is only part of the total energy) remains the same. Still, statement D is true, because the total energy (mechanical energy, heat energy, etc.) is conserved. So, the correct answers to this exercise are statements A, C, and D.

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