Chapter 6.6, Problem 13FP

Determine the force P needed to hold the 60-lb weight in equilibrium.

Prob. F6-13

To determine

The force P needed to hold the 60 lb weight in equilibrium.

Answer to Problem 13FP

The force P needed to hold the 60 lb weight in equilibrium is $\underset{\_}{20\text{lb}}$.

Explanation of Solution

Given information:

The weight in equilibrium (w) is 60 lb.

Assumptions:

• Consider the state of member as tension where the force is pulling the member, and as compression where the force is pushing the member.
• Consider the force indicating the right side as positive, and the left side as negative in horizontal components of forces.
• Consider the force indicating the upside is taken as positive, and the downside as negative in vertical components of forces.
• Consider the clockwise moment as negative and the anti-clock wise moment as positive wherever applicable.
• Apply the equation of equilibrium wherever applicable.

Explanation:

Show the free body diagram of a pulley as in Figure (1).

Using Figure (1),

Along vertical direction:

Determine the force P by resolving the vertical component of forces.

$\begin{array}{l}{\displaystyle \sum F_y=0}\\ P+P+P-w=0\\ 3P=w\end{array}$ (I)

Conclusion:

Substitute 60 lb for w in Equation (I).

$\begin{array}{l}3P=60\\ P=\frac{60}{3}\\ P=20\text{lb}\end{array}$

Thus, the force P needed to hold the 60 lb weight in equilibrium is $\underset{\_}{20\text{lb}}$.