Question

to strengthen his arm and chest muscles, an 82-kg athlete who is 2.0 m tall is doing push ups. his center of mass is 1.15 m from the bottom of his feet, and the centers of his palms are 30.0cm from the top of his head. find the force that the floor exerts on each of is feet and on each hand, assuming that both feet exert the same force and both palms do likewise.

Answer 1

For the force F on both his palms, which are 1.70 m from his toes, set the total moment about his toes equal to zero.

F *1.70 = M*g*1.15
F = 544 N
Divide F by 2 for the force on each palm.

For the force F' on both feet (together), do a vertical force balance.
F' + F = M*g = 804 N

F' = 260 N
Divide F' by 2 for the force on each foot.

Answer 2

Much detailed solution:
F *1.70 = M*g*1.15
F*1.70 = 82 * 9.8 * 1.15
F= 924.14/1.70
F = 544 N
Divide F by 2 for the force on each palm.
F= 544/2 = 272
For the force F' on both feet (together), do a vertical force balance.
F' + F = M*g = N
F' + F = 82 * 9.8 = 804 N
F' = 804 - 544 = 260 N
F' = 260 N
Divide F' by 2 for the force on each foot.
F' = 260/2 = 130