Chapter 5.1, Problem 9PP

To determine

To Calculate: The combined force of the two ropes on the swing.

Explanation of Solution

Given:

Tension in each rope, $T=2.28\text{N}$

Vertical angle made by the rope to the swing, $\theta =13°$

Formula Used:

From Newton’s second law of motion:

  $\sum F_i=ma$

Where, m is the mass and a is the acceleration.

Calculations:

Consider the component of tension in horizontal direction:

  $T\sin \theta -T\sin \theta =0$

Consider component of tension in vertical direction:

  $F=2T\cos \theta$

Substitute the values and solve:

  $\begin{array}{c}F=2T\cos \theta \\ =2\left(2.28\text{N}\right)\left(\cos 13°\right)\\ =4.44\text{N}\end{array}$

Conclusion:

Thus, the combined force on the swing due to two ropes is $4.44\text{N}$ in the upward direction.