Final answer:
To determine the distance at which the fulcrum must be located from the 40 lb. weight, we use the principle of moments or torque. By setting the clockwise moment created by the 40 lb. weight equal to the counterclockwise moment created by the unknown weight, we can solve for x, which represents the distance. The equation can be simplified and solved to find the required distance.
Step-by-step explanation:
The distance at which the fulcrum must be located from the 40 lb. weight can be determined by applying the principle of moments or torque. The principle states that for a system to be in equilibrium, the sum of the clockwise moments must be equal to the sum of the counterclockwise moments.
In this case, we have a 40 lb. weight on one side of the fulcrum, and we need to balance it with an unknown weight on the other side. Since the weights are perfectly balanced, the clockwise moment created by the 40 lb. weight must be equal to the counterclockwise moment created by the unknown weight.
To calculate the distances, we can use the equation:
(40 lb.) x (distance from fulcrum to 40 lb. weight) = (unknown weight) x (distance from fulcrum to unknown weight)
Since the bar is 9 feet long, we can write the equation as:
(40 lb.) x (x ft.) = (unknown weight) x ((9 ft.) - (x ft.))
Simplifying the equation, we get:
40 lb. x ft. = unknown weight x (9 ft. - x ft.)
Using algebraic methods, we can solve for x and determine the distance at which the fulcrum must be located.