Question

You have a summer job operating a movable, hand-powered crane in a distribution center for a building supply company. The figure below shows the pulley arrangement of the crane. Using this cranevou find it necessary to exert a force of 122 N to support a load. Determine the following.

Answer 1

ANSWER:

(a) 3

(b) 37.35 kg

(c) 488 N

STEP-BY-STEP EXPLANATION:

Given:

T = 122 N

(a)

We make the balance of force to be able to determine the weight, just like this:

$\begin{gathered} F_y=0 \\ \\ 3T-W=0 \\ \\ W=3T \end{gathered}$

Now, the formula to calculate the mechanical advantage is the following:

$\begin{gathered} MA=\frac{W}{T} \\ \\ \text{ We replacing} \\ \\ MA=\frac{3T}{T} \\ \\ MA=3 \end{gathered}$

(b)

The mass is calculated using the following formula:

$\begin{gathered} W=m\cdot g \\ \\ m=\frac{W}{g} \\ \\ m=\frac{3T}{g} \\ \\ \text{ We replacing} \\ \\ m=\frac{(3)(122)}{9.8} \\ \\ m=\:37.35\text{ kg} \end{gathered}$

(c)

We can calculate this force (tension) by the following force balance:

$\begin{gathered} \text{ The top pulley pulling up the center pulley with the following magnitude:} \\ \\ T_1-2T=0\rightarrow T_1=2T \\ \\ \text{ We have the tension up on the pin T0, this is equal to the force that pulls the crane down} \\ \\ T_0-2T-T_1=0 \\ \\ \text{ We replacing} \\ \\ T_0-2T-2T=0 \\ \\ T_0=4T \\ \\ T_0=(4)(122) \\ \\ T_0=488\text{ N} \end{gathered}$