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.
To find the force exerted by the floor on the athlete's feet and hands, we can use the principle of torque and equilibrium.
First, let's calculate the torques exerted by the athlete's feet and hands.
The torque is given by the product of the force and its perpendicular distance from the pivot point. In this case, the pivot point is the athlete's center of mass.
Torque exerted by the feet:
Torque_feet = Force_feet * Distance from the center of mass to the feet
Torque exerted by the hands:
Torque_hands = Force_hands * Distance from the center of mass to the hands
Since the athlete is in equilibrium, the sum of the torques acting on him must be zero.
Torque_feet + Torque_hands = 0
Let's find the values of the distances:
Distance from the center of mass to the feet = Height - Distance from the bottom of the feet to the center of mass
Distance from the center of mass to the feet = 2.0 m - 1.15 m
Distance from the center of mass to the feet = 0.85 m
Distance from the center of mass to the hands = Distance from the top of the head to the center of the hands
Distance from the center of mass to the hands = 30.0 cm = 0.30 m
Now, let's find the force exerted by the floor on each foot (Force_feet) and each hand (Force_hands) using the equation:
Torque_feet + Torque_hands = 0
Force_feet * Distance from the center of mass to the feet + Force_hands * Distance from the center of mass to the hands = 0
Force_feet * 0.85 m + Force_hands * 0.30 m = 0
Since both feet exert the same force (Force_feet) and both hands exert the same force (Force_hands), we can rewrite the equation as:
2 * Force_feet * 0.85 m + 2 * Force_hands * 0.30 m = 0
Simplifying the equation further:
Force_feet * 0.85 m + Force_hands * 0.30 m = 0
Now, we have an equation with two unknowns. We need additional information or assumptions to solve the problem, such as the distribution of the athlete's weight between his feet and hands.