$\text { Consider a beam of length } L = 12 \text { feet with a fulcrum } x \text { feet from one end as shown }$ 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

$\text { Consider a beam of length } L = 12 \text { feet with a fulcrum } x \text { feet from one end as shown }$ 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

To keep the system in equilibrium, the sum of the moments on both sides of the fulcrum should be equal. Taking moments about the fulcrum:

$36(x) = 108 (12 - x)$

$36x = 1296 - 108x$

$144x = 1296$

$x = 9$

Therefore, the distance between the fulcrum and the object weighing 36 pounds is 9 feet. Answer choice D is the correct choice.

Consider a beam of length L=12 feet with a fulcrum x feet from one end as shown \text { Consider a beam of length } L = 12 \text { feet with a fulcrum } x \text { feet from one end as shown } Consider a beam of length L=12 feet with a fulcrum x feet from one end as shown

$\text { Consider a beam of length } L = 12 \text { feet with a fulcrum } x \text { feet from one end as shown }$