Chapter 2, Problem 10A

To determine

The amount of weight supported by each arm of the person when he/she do pull-ups and hang at rest.

Answer to Problem 10A

Each arm supports half of the weight.

Explanation of Solution

Introduction:

If the object is at rest, then the net force on that object is zero and the object is said to be in equilibrium. It is given by,

  ${\displaystyle \sum F}=0$

Now if the person hangs at rest while doing pull-ups, then the weight of the person acts in vertically downward direction, while the force supported by the arms of the person will be same and acts in upward direction. Let it be given by $F\text{'}$ . Then considering the fact that net force on the object in equilibrium is zero,

  $\begin{array}{c}{\displaystyle \sum F}=0\\ W-\left(F\text{'}+F\text{'}\right)=0\\ F\text{'}=\frac{W}{2}\end{array}$

Where, $W=$ weight of the person,

In above, it is considered that the force in upward direction is negative while the force in downward direction is positive.

Conclusion:

Hence, the amount of weight supported by each arm of the person when he/she do pull-ups and hang at rest is half of the weight of person.