To strengthen his arm and chest muscles, an 85.0 kg athlete 2.00 m tall is doing

Question

To strengthen his arm and chest muscles, an 85.0 kg athlete 2.00 m tall is doing a series of push-ups as shown in the figure below (Figure 1) . His center of mass is 1.10 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.

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

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

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Explanation / Answer

Apparently, the distance from his palms to his center of mass is

2 -1.1 - 0.3 = 0.6 m

Let Fp and Ff be the force exerted on his both hands and feet respectively,

and W be the weight, then W = mg = 85*9.8 = 833N.

The net torque according to his hands is

W*0.6 - Ff*(0.6+1.1) = 0.

So Ff = W*0.6/(0.6+1.1)

Ff = 833* 0.6/(1.7)

Ff = 294 N

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Thus, the force exerted on each of his feet is Ff/2 = 147 N.

The net torque according to his feet is

W*1.1 - Fp*(0.6+1.1) = 0.

So Fp = 833* 1.1/(1.7)

Fp = 539 N

Thus, the force exerted on each of his hands is Fp/2 = 269.5 N.

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