The drawing shows a person (weight W = 580 N, L1 = 0.849 m, L2 = 0.410 m) doing push-ups. Find the normal force exerted by the floor on each hand and each foot, assuming that the person holds this position.
To find the normal force exerted by the floor on each hand and each foot, we need to consider the forces acting on the person during the push-up exercise.
Let's draw a free-body diagram of the person during a push-up:
H
F_NH <===[person]===
F_NF
F_NF
F_NH <====[floor]====
In this diagram, F_NH represents the normal force exerted by the floor on each hand, F_NF represents the normal force exerted by the floor on each foot, and H represents the location where the hands are in contact with the floor.
From the free-body diagram, we can see that the vertical forces acting on the person are the weight of the person (580 N) and the normal forces exerted by the floor on each hand and each foot. According to Newton's third law, the magnitudes of these normal forces are equal to the weight of the person since the person is not accelerating vertically.
Therefore, the normal force exerted by the floor on each hand and each foot is 580 N.
Note: The horizontal distance (L1 and L2) provided doesn't affect the calculation of the normal force in this case, as the person is not accelerating horizontally.