Question

Two ice skaters, Paul and Tom, are each holding on to opposite ends of the same rope. Each pulls the other toward him. The magnitude of Paul’s acceleration is 1.25 times greater than the magnitude of Tom’s acceleration. What is the ratio of Paul’s mass to Tom’s mass?

Answer 1

0.80

Explanation:

To solve this problem we need to remember Newton's third law which states that: "For every action, there is an equal and opposite reaction".

In this case, we have two forces (Paul's and Tom's) that are interacting on each other. The third law tells us that the force they apply on each other have the same magnitude.

By Newton's second law we know that mass equals force multiplied by acceleration. (F = ma)

Therefore:

(Paul's mass)(Paul's acceleration) = (Tom's mass)(Tom's acceleration)

Paul's mass/ Tom's mass = Tom's acceleration / Paul's acceleration

But we know that Paul's acceleration is 1.25 times greater than Tom's acceleration. Substituting this we get:

Paul's mass / Tom's mass = 1 / 1.25 = 0.8

Thus, the ratio of Paul's mass to Tom's mass is 0.80