Chapter 2, Problem 40A

A monkey hangs by a strand of rope and holds onto the zoo cage as shown. Since her arm holding the cage is horizontal, only the rope supports her weight. How does the tension in the rope compare with her weight?

To determine

To compare: The tension in the rope with the monkey’s weight.

Answer to Problem 40A

Tension in the rope is greater than the weight of the monkey.

Explanation of Solution

Given:

A monkey hanging on the rope as shown below.

Formula Used:

All forces applied on any object must be in equilibrium and constant.

Calculation:

When gravitational force is applied on the weight then it is equal to the opposing force that is vertical component of tension on the rope monkey is holding.

T is the tension in rope. W is the weight of monkey. R is the reaction force.

Horizontal Force:

  $T\cos \theta =f=\mu R$

Vertical Force:

  $T\sin \theta =W-R$

Squaring both equations.

  ${\left(Tsin\theta \right)}^2+{\left(T\cos \theta \right)}^2={\left(W-R\right)}^2+{\left(\mu R\right)}^2$

  $T=\sqrt{{\left(W-R\right)}^2+{\left(\mu R\right)}^2}$

  $$

This suggests that tension in the rope is greater than the weight of the monkey.

Conclusion:

Thus, the tension on the rope is greater than the weight of the monkey holding the cage.