A man doing push-ups pauses in the position shown in the figure . His mass m = 80 kg.
In push up position:
From hands to waist = 40 cm
From waist to feet = 95 cm
height - heel of foot to ground = 30 cm
Determine the normal force exerted by the floor on each hand.
Determine the normal force exerted by the floor on each foot.
ignore that partial post.
To determine the normal force exerted by the floor on each hand, we need to find the weight of the man and then divide it equally between his two hands.
1. Calculate the weight of the man:
Weight (W) = mass (m) x gravitational acceleration (g)
W = 80 kg x 9.8 m/s^2
W = 784 N
2. Divide the weight equally between his two hands:
Normal force exerted by the floor on each hand = Weight / 2
Normal force on each hand = 784 N / 2
Normal force on each hand = 392 N
Therefore, the normal force exerted by the floor on each hand is 392 N.
To determine the normal force exerted by the floor on each foot, we first need to find the weight of the lower part of the man's body (from the waist to the feet) and then divide it equally between his two feet.
1. Calculate the weight of the lower part of the man's body:
Weight of the lower part = mass x gravitational acceleration
Weight of the lower part = 80 kg x 9.8 m/s^2
Weight of the lower part = 784 N
2. Divide the weight of the lower part equally between his two feet:
Normal force exerted by the floor on each foot = Weight of the lower part / 2
Normal force on each foot = 784 N / 2
Normal force on each foot = 392 N
Therefore, the normal force exerted by the floor on each foot is 392 N.
To determine the normal force exerted by the floor on each hand and foot, we need to first understand what normal force is. The normal force is the force exerted by a surface to support the weight of an object resting on it. In this case, the floor is exerting a normal force on the hands and feet to counteract the force of gravity.
To find the normal force exerted by the floor on each hand, we can consider the forces acting on the person in the vertical direction. We have the person's weight acting downward, and the normal force exerted by the floor acting upward. Since the person is in equilibrium, these two forces must be equal in magnitude.
The weight of the person can be calculated using the formula:
Weight = mass * gravity
Given that the mass (m) is 80 kg and gravity (g) is approximately 9.8 m/s^2, we can calculate the weight:
Weight = 80 kg * 9.8 m/s^2 = 784 N
Since there are two hands, each hand is supporting half the weight of the person. Therefore, the normal force exerted by the floor on each hand is half the weight:
Normal force on each hand = Weight / 2 = 784 N / 2 = 392 N
To find the normal force exerted by the floor on each foot, we need to consider the horizontal and vertical components of the weight. The vertical component of the weight is the same as the weight calculated earlier (784 N), while the horizontal component is negligible in this case.
Since there are two feet, each foot is supporting half the vertical component of the weight:
Normal force on each foot = (Weight * vertical component) / 2 = (784 N * 30 cm / (40 cm + 95 cm)) / 2
First, we need to convert the heights to meters:
Vertical component = 30 cm = 0.30 m
From hands to waist = 40 cm = 0.40 m
From waist to feet = 95 cm = 0.95 m
Therefore, the normal force on each foot is:
Normal force on each foot = (784 N * 0.30 m) / (0.40 m + 0.95 m) / 2 = 290.37 N
So, the normal force exerted by the floor on each hand is 392 N and the normal force exerted by the floor on each foot is approximately 290.37 N.