Chapter 2, Problem 46A

A staging that weighs 300 N supports two painters, one 250 N and the other 300 N. The tension in the left rope is 400 N. What is the tension in the right rope?

To determine

Reading in right rope.

Answer to Problem 46A

The reading in the right rope is $T_2=450\text{N}$

Explanation of Solution

Given:

The given figure is,

  

Weight of left painter, $F_{g1}=250\text{N}$

Weight of right painter, $F_{g2}=300\text{N}$

Reading in left scale, $T_1=400\text{N}$

Weight of staging, $W=300\text{N}$

Staging is in mechanical equilibrium.

Formula Used:

For mechanical equilibrium, summation of all forces is zero, that is

  $\sum F=0$

Calculation:

Since, the staging is in mechanical equilibrium so, $\sum F=0$ or

Upward force = Downward force

So,

  $\begin{array}{l}{T}_1+T_2=F_{g_1}+F_{g2}+W\\ \Rightarrow 400+T_2=250+300+300\\ \Rightarrow T_2=850-400=450\text{N}\end{array}$

Conclusion:

Therefore, the reading in the right rope is $T_2=450\text{N}$