To strengthen his arm and chest muscles, an 75.0 kgathlete 2.00 m tall is doing

Question

To strengthen his arm and chest muscles, an 75.0 kgathlete 2.00 m tall is doing a series of push-ups as shown in the figure below (Figure 1) . His center of mass is 1.15 m from the bottom of his feet, and the centers of his palms are 30.0 cm from the top of his head. Find the force that the floor exerts on each of his feet and on each hand, assuming that both feet exert the same force and both palms do likewise.

Part A

Find the force that the floor exerts on each of his feet, assuming that both feet exert the same force.

Part B

Find the force that the floor exerts on each of his hand, both palms exert the same force.

Explanation / Answer

since the boy is stationary

net torque about the feet will be 0

torque about feet = weight of athlete * 1.15 - force floor exerts on hands * (2 - 0.3)

0 = weight of athlete * 1.15 - force floor exerts on hands * (2 - 0.3)

weight of athlete * 1.15 = force floor exerts on hands * (2 - 0.3)

75 * 9.8 * 1.15 = force floor exerts on hands * (2 - 0.3)

force floor exerts on hands = 497.2058 N

force floor exerts on each hand = 497.2058 / 2

force floor exerts on each hand = 248.6029 N

also torque about hands will also be 0

torque about hands = weight of athlete * (2 - 1.15 - 0.3) - force floor exerts on feet * (2 - 0.3)

0 = weight of athlete * (2 - 1.15 - 0.3) - force floor exerts on feet * (2 - 0.3)

75 * 9.8 * (2 - 1.15 - 0.3) = force floor exerts on feet * (2 - 0.3)

force floor exerts on feet = 237.794 N

force floor exerts on each foot = 237.794 / 2

force floor exerts on each foot = 118.897 N

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