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Chapter 2: Problem 23

Jane and John are both on roller skates and facing each other. First Jane pushes John with her hands and they move apart. They get together again, and John pushes Jane equally hard with his hands and they move apart. Is their subsequent motion any different in the two cases? Why or why not?

Short Answer

Expert verified
Explain your answer. Answer: The subsequent motion of Jane and John is not different in the two cases. Regardless of who pushes whom, once they push each other, they will experience equal and opposite forces according to Newton's third law of motion. They will move in opposite directions, and their total final momentum will be conserved as it was initially (0), according to the conservation of momentum principle.

Step by step solution

01

Identify the principles/rules to apply

We will apply Newton's third law of motion and the conservation of momentum in this exercise. The principle states that "For every action, there is an equal and opposite reaction."
02

Understand the first scenario (Jane pushes John)

When Jane pushes John, she applies a force on John, and John simultaneously applies an equal and opposite force on Jane. Due to this action-reaction pair of forces, both Jane and John move apart in opposite directions.
03

Analyze the momentum in the first scenario

As both skaters are initially at rest, their total initial momentum is 0. After Jane pushes John, they have equal and opposite momenta (momenta = mass × velocity). According to the conservation of momentum principle, the total final momentum of the system should be equal to the initial momentum, which is 0 in this case.
04

Understand the second scenario (John pushes Jane)

In this case, John pushes Jane. Similar to the first scenario, an action-reaction pair of forces is applied, and both skaters move apart in opposite directions.
05

Analyze the momentum in the second scenario

As before, they are initially at rest, and their total initial momentum is 0. After John pushes Jane, they have equal and opposite momenta, and their total final momentum would also be 0, as the conservation of momentum principle still applies.
06

Comparing the two scenarios

In both cases, the total final momentum is the same (0), and both skaters move apart in opposite directions.
07

Conclusion

The subsequent motion of Jane and John is not different in the two cases. This is because regardless of who pushes whom, once they push each other, they will experience equal and opposite forces, move in opposite directions, and their total final momentum will be conserved as it was initially (0).

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