Chapter 2, Problem 20A

When Nellie hangs from ropes at different angles, as shown in Figure 2.13, how does the vector resultant of the two rope tensions compare with her weight?

To determine

To compare: The vector resultant of the two rope tensions with person N weight.

Answer to Problem 20A

Weight of the person N and resultant of two rope tensions are equal in magnitude but opposite in direction.

Explanation of Solution

Given:

Person N is hanging from two ropes but making different angles. Other ends of the ropes are fixed.

Formula Used:

According to parallelogram law, the resultant of two vectors is

  $\overrightarrow{R}=\overrightarrow{X}+\overrightarrow{Y}$

Calculation:

Person N weight will balance the tension in the two ropes. Tension in the ropes will vary either due to change in the position of person N or change in the angle between the two ropes with the vertical.

The resultant of two rope tensions is,

  $\overrightarrow{R}=\overrightarrow{T_1}+\overrightarrow{T_2}$

Where,

$\overrightarrow{T_1}$ and $\overrightarrow{T_1}$ are the tensions in two ropes.

From the given diagram, $\overrightarrow{R}$ is the normal force applied equally but opposite to the weight of person N that is $\overrightarrow{W}$ .

So,

  $\begin{array}{l}\overrightarrow{R}=\overrightarrow{T_1}+\overrightarrow{T_2}\\ \overrightarrow{W}=\overrightarrow{T_1}+\overrightarrow{T_2}\end{array}$

Conclusion:

Therefore, person N weight is equal in magnitude of the resultant of two vectors but its acts in opposite direction.