A 340-pound weight lifter needs to lift a 650-pound stone to win a competition. If he uses a 36-foot bar with the fulcrum placed 6 feet from the stone, will he be able to win the competition?

Question

Quizplus · Accepted Answer

To determine if the weight lifter can win the competition, we need to use the formula for torque: torque = force x distance from fulcrum. 
Since the weight lifter is using a lever with a fulcrum, he will need to apply a force to the other end of the lever to lift the stone. 
Let's call the force he needs to apply F. 
We know that the weight of the stone is 650 pounds, and it acts downward at a distance of 6 feet from the fulcrum. 
To counteract this weight, the weight lifter needs to apply an equal and opposite force at a distance from the fulcrum. 
So we have:
(650 pounds) x (6 feet) = F x (36 feet - 6 feet)
3900 foot-pounds = 30F 
F = 130 pounds 
This means that the weight lifter needs to apply a force of 130 pounds at the end of the bar to lift the stone. 
However, we also know that the weight lifter weighs 340 pounds, which acts downward at a distance of 18 feet from the fulcrum. 
To counteract his own weight, he needs to apply an equal and opposite force upward at a distance from the fulcrum. 
So we have:
(340 pounds) x (18 feet) = F2 x (36 feet - 6 feet) 
6120 foot-pounds = 30F2 
F2 = 204 pounds 
This means that the weight lifter needs to apply a force of 204 pounds upward at the end of the bar. 
Since he is capable of applying a force of 130 pounds, he will not be able to lift the stone and win the competition by himself.

A 340-Pound Weight Lifter Needs to Lift a 650-Pound Stone