Chapter 7, Problem 54A

Two people attempt a tug-of-war on low-friction ice. One person has four times the mass of the other. Relative to the acceleration of the heavier person, what will be the acceleration of the lighter person?

To determine

The acceleration of lighter person relative to the acceleration of the heavier person.

Explanation of Solution

Given:

Let the mass of the lighter person be m , then mass of heavier person would be $m\text{'}=4m$ .

Formula Used:

Newton’s Second law of motion:

  ${\displaystyle \sum F=ma}$

Where, m is the mass a is the acceleration .

Calculation:

In tug of war, equal and opposite force would be experienced by each person. If acceleration of lighter person is a , then acceleration of the heavier person would be:

  $\begin{array}{l}ma=m\text{'}a\text{'}\\ ma=\left(4m\right)a\text{'}\\ a=4a\text{'}\end{array}$

Conclusion:

The acceleration of the lighter person would be four times the acceleration of the heavier person.