Question

A man uses a crowbar of length 1.5 m to raise a load of 75 kgf by putting a sharp edge below the bar at a distance 1 m from his hand. Calculate the load arm.
A) $0.1m$.
B) $1m$.
C) $5m$.
D) $0.5m$.

Answer 1

Hint: The formula of mechanical advantage can be used to solve this problem. The mechanical advantage is the measure by which the applied force is enlarged by the mechanical device or mechanical system. The mechanical advantage is defined as the ratio of the force created by the machine and the force applied on it. The mechanical advantage is based on the law of lever.

Formula used: The formula of the mechanical advantage is given by${\text{MA}} = \dfrac{{{\text{output force}}}}{{{\text{input force}}}} = \dfrac{{{\text{effort arm}}}}{{{\text{load arm}}}}$.

Complete step-by-step answer:
It is given that the total length of the crowbar is 1.5 m; the effort arm is given as 1 m.
Now the value of mechanical advantage is given by,
${\text{MA}} = \dfrac{{{\text{effort arm}}}}{{{\text{load arm}}}}$
Put value of effort arm=1 m and load arm=1.5-1=0.5 m in the above equation,
$
  {\text{MA}} = \dfrac{{{\text{effort arm}}}}{{{\text{load arm}}}} \\
  {\text{MA}} = \dfrac{1}{{0.5}} \\
  {\text{MA}} = 2 \\
 $
Applying the formula of mechanical advantage again as mechanical advantage can be also written as,
${\text{MA}} = \dfrac{{{\text{output force}}}}{{{\text{input force}}}}$
As the output load required is 75 kgf, so let us calculate the value of the input force.
$
  {\text{MA}} = \dfrac{{{\text{output force}}}}{{{\text{input force}}}} \\
  2 = \dfrac{{75}}{{{\text{input force}}}} \\
  {\text{input force}} = \dfrac{{75}}{2} \\
  {\text{input force}} = 37.5{\text{ kgf}} \\
 $
So the input force required to create an output force of 75 kgf is 37.5 kgf. So the final answer for this problem is load arm is 0.5 m long which is option D

Note: Students should remember the definition and also the formulas involved for mechanical advantage as it can help the students to solve these types of problems. A mechanical advantage is a term which can give us the measure of input load required to get output load for given mechanical advantage of the machine.