A weight of 120 pounds is placed five feet from the fulcrum of a lever. How far from the fulcrum should a 100 pounds weight be placed in order to balance the lever?
To balance the lever, the torques on both sides of the fulcrum must be equal. Torque is calculated by multiplying the weight by its distance from the fulcrum.
Given:
Weight 1 = 120 pounds
Distance 1 = 5 feet (from Weight 1 to fulcrum)
Unknowns:
Weight 2 = ?
Distance 2 = ?
Using the formula for torque, we have:
Torque 1 = Torque 2
Weight 1 * Distance 1 = Weight 2 * Distance 2
Plugging in the given values:
120 pounds * 5 feet = Weight 2 * Distance 2
600 ft-lb = Weight 2 * Distance 2
We need to solve for Weight 2. Since we know that Weight 2 is 100 pounds, we can substitute that value into the equation:
600 ft-lb = 100 pounds * Distance 2
To find Distance 2, we can rearrange the equation:
Distance 2 = (600 ft-lb) / (100 pounds)
Distance 2 = 6 feet
Therefore, a 100 pounds weight should be placed 6 feet from the fulcrum in order to balance the lever.
To balance the lever, the torques on both sides of the fulcrum must be equal. The torque of an object is calculated by multiplying its weight by the distance from the fulcrum.
Let's denote the unknown distance from the fulcrum to the 100 pounds weight as "x."
The torque of the 120 pounds weight is 120 pounds multiplied by 5 feet (since it is placed 5 feet from the fulcrum). This gives us a torque of 600 pound-feet.
The torque of the 100 pounds weight is 100 pounds multiplied by "x" feet (since it is placed "x" feet from the fulcrum). This gives us a torque of 100x pound-feet.
Since the lever is balanced, the torques on both sides of the fulcrum are equal. Therefore, we can set up the equation:
600 pound-feet = 100x pound-feet
To find the value of "x," we can divide both sides of the equation by 100:
600 pound-feet / 100 = 100x pound-feet / 100
6 feet = x
Therefore, the 100 pounds weight should be placed 6 feet from the fulcrum in order to balance the lever.
5/6 the weight, so 6/5 the distance
or, if you insist,
100x = 120*5