Chapter 4.3, Problem 38SSC

To determine

To Explain: The tension in the rope used in a tug of war between two teams.

Answer to Problem 38SSC

The tension in the rope is $500\text{N}$ for the equilibrium of the rope.

Explanation of Solution

Given:

The rope’s one end is tied to the tree and the other end of the rope is pulled by a team with a force of $500\text{N}$ .

Formula used:

Newton’s Third Law of Motion:

According to Newton’s Third Law, for every action, there is an equal and opposite reaction. When a body $A$ applies a force on the body $B$ then the body $B$ exerts an equal and opposite force on the body $A$ .

  $F_{\text{A on B}}=-F_{\text{B on A}}$

Calculation:

The one end is tied to the tree and the other end of the rope is pulled by a team with a force of $500\text{N}$ .

The team exerted a force of $500\text{N}$ for pulling the rope towards them.

Apply Newton’s Third Law of Motion,

The tree also exerts an equal and opposite force on the team. That is, the tree exerts a force of $500\text{N}$ for pulling the tree towards it.

For equilibrium of the rope, the net force acting on the rope should be zero.

Conclusion:

Thus, the tension in the rope should be $500\text{N}$ for the equilibrium of rope.