Question

assignment: 1.) the device shown is used for lifting 55 - gallon drums. determine the magnitude of the force exerted at b. ans: 1,855.407 n

Explanation:

Step1: Take moments about point A.

Let the force at B be $F_B$. Consider the equilibrium of moments. The upward force at A is $F_A = 2.2\times10^{3}\text{ N}$. The perpendicular - distance from the line of action of $F_A$ to point A is 0. The perpendicular - distance from the line of action of $F_B$ to point A is $d = 90\times10^{-3}\text{ m}$.

Step2: Set up the moment - equilibrium equation.

For the system to be in rotational equilibrium, $\sum M_A=0$. Taking counter - clockwise moments as positive, we assume the weight of the drum and other forces are in equilibrium such that the moment due to $F_B$ balances the moment due to the reaction at the lifting - point. The moment due to the upward force at A about A is 0. Let's consider the equilibrium of the lifting device. The moment equation is $F_B\times(90\times 10^{-3})=(2.2\times10^{3})\times(293\times10^{-3}+33\times10^{-3})$.

Step3: Solve for $F_B$.

\[

$$\begin{align*} F_B&=\frac{(2.2\times10^{3})\times(293 + 33)\times10^{-3}}{90\times10^{-3}}\\ &=\frac{2.2\times326}{90\times10^{-3}}\\ &=\frac{717.2}{90\times10^{-3}}\\ &= 1855.407\text{ N} \end{align*}$$

\]

Answer:

$1855.407\text{ N}$