150 kg Max and 120 kg Paul were on a 4-inch wide by 8-inch tall (10 cm x 20 cm)

Question

150 kg Max and 120 kg Paul were on a 4-inch wide by 8-inch tall (10 cm x 20 cm) four-meter long balance beam 1-1/2 meters above the ground. The beam's mass is 36 kg and its center of mass is at the center of the beam. Max is 2 meters from one end of the beam and Paul is one meter from the other end. When the police arrived, they claimed they were practicing the balance beam scene from "Swan Lake", but actually they were trapped on the beam by a pack of dogs.

B. If each end of the beam rests on a 10-cm by 10-cm by 1-1/2 meter tall vertical support column, what is the pressure exerted on each support's top end?

Explanation / Answer

the system is in rest so net torque will be 0

torque about end where max is standing = 150 * 2 + 120 * 3 + 36 * 2 - F1* 4

0 = 150 * 2 + 120 * 3 + 36 * 2 - F1 * 4

F1 = 183 N

torque about end where paul is standing = 150 * 2 + 120 * 1 + 36 * 2 - F2* 4

0 = 150 * 2 + 120 * 1 + 36 * 2 - F2* 4

F2 = 123 N

pressure = force / area

pressure on one end = 183 / (0.1 * 0.1)

pressure on one end = 18300 N/m^2

pressure on another end = 123 / (0.1 * 0.1)

pressure on another end = 12300 N/m^2

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