Consider a beam of length feet with a fulcrum x feet from one end as shown in the figure. Two objects weighing 36 pounds and 108 pounds are placed at opposite ends of the beam. Find x (the distance between the fulcrum and the object weighing 36 pounds) such that the system is equilibrium.
A) 10 feet
B) 11 feet
C) 8 feet
D) 9 feet
E) 7 feet

Question

Consider a beam of length  feet with a fulcrum x feet from one end as shown in the figure. Two objects weighing 36 pounds and 108 pounds are placed at opposite ends of the beam. Find x (the distance between the fulcrum and the object weighing 36 pounds) such that the system is equilibrium. 
A) 10 feet 
B) 11 feet 
C) 8 feet 
D) 9 feet 
E) 7 feet

Quizplus · Accepted Answer

For the system to be in equilibrium, the sum of the moments on both sides of the fulcrum should be equal.
Taking moments about the fulcrum:
$$36(x) = 108(11 - x)$$
$$\Rightarrow 36x = 1188 - 108x$$
$$\Rightarrow 144x = 1188$$
$$\Rightarrow x = \frac{1188}{144} = 9$$
Therefore, the distance between the fulcrum and the object weighing 36 pounds is 9 feet, which is choice D.

Consider a Beam of Length Feet with a Fulcrum