Question

To strengthen his arm and chest muscles, a 75-kg athlete 2.0 m tall is doing a series of push-ups as shown in the figure below. His center of mass is 1.20 m from the bottom of his feet, and the centers of his palms are 30.0 cm from the top of his head. A. Find the force that the floor exerts on each of his feet, assuming that both feet exert the same force. B. Find the force that the floor exerts on each of his hands, assuming both palms exert the same force.

Answer 1

A. The force exerted by the floor on each foot is approximately 372 N.

B. The force exerted by the floor on each hand (palms) is approximately 558 N.

In the given scenario, the athlete is performing push-ups, engaging his arm and chest muscles. To determine the forces exerted by the floor on his feet and hands, we consider the torque equilibrium. The torque created by the weight of the athlete and the forces at his feet and hands must balance.

For part A, the force on each foot is calculated by taking moments about the athlete's center of mass. Given the height of the center of mass and the distance between the feet, the force exerted by the floor on each foot is found to be approximately 372 N.

For part B, the torque equilibrium is considered around the center of mass, taking into account the distance between the palms and the top of the head. The force exerted by the floor on each hand (palms) is calculated to be approximately 558 N.

These force values represent the upward forces exerted by the floor to support the athlete during the push-up exercise, considering the distribution of weight and the torques involved in maintaining equilibrium.