Beniamin, who weighs one hundred five pounds, sat eight feet from the center of a seesaw. Dylan sat three feet on the other side of the center to balance the seesaw. How much does Dylan weigh?
To balance the seesaw, the two weights and their distances from the center must be equal:
105 pounds x 8 feet = Dylan's weight x 3 feet
840 = 3D
Dylan weighs 280 pounds.
To determine Dylan's weight, we need to use the principle of lever equilibrium. The principle states that the product of the weight and distance from the center of gravity on one side of a lever must be equal to the product of the weight and distance on the other side.
Given that Beniamin weighs 105 pounds and sits 8 feet from the center, we can calculate his torque using the formula:
Torque_B = weight_B * distance_B
Substituting the given values, we have:
Torque_B = 105 pounds * 8 feet
Torque_B = 840 foot-pounds
To balance the seesaw, Dylan is positioned 3 feet from the other side of the center. We can calculate Dylan's torque using the same formula:
Torque_D = weight_D * distance_D
Since the seesaw is balanced, Dylan's torque must be equal to Beniamin's torque. Hence:
Torque_B = Torque_D
840 foot-pounds = weight_D * 3 feet
To solve for Dylan's weight, we divide both sides of the equation by 3 feet:
weight_D = 840 foot-pounds / 3 feet
weight_D ≈ 280 pounds
Thus, Dylan weighs approximately 280 pounds.