A man doing push-ups pauses. His mass is 80-kg. Determine the normal force exerted by the floor on each hand and on each foot.
a = 40 cm
b = 95 cm
c = 30 cm
W = mg = 784 N
see later post.
Sorry coudnt get this one
To determine the normal force exerted by the floor on each hand and each foot, we can use Newton's second law, which states that the net force acting on an object is equal to the mass of the object multiplied by its acceleration. In this case, the man is not accelerating vertically, so the net force in the vertical direction is zero. This means that the normal force exerted by the floor on the man's hands and feet must balance the force of gravity acting on him.
Let's first calculate the force of gravity acting on the man:
Force of gravity (W) = mass (m) x acceleration due to gravity (g)
Given that the mass (m) is 80 kg and the acceleration due to gravity (g) is approximately 9.8 m/s^2, we can calculate the force of gravity:
W = 80 kg x 9.8 m/s^2
W = 784 N
Now, let's consider the forces acting on the man when he is doing push-ups. There are four contact points: two hands and two feet. The normal force exerted by the floor on each of these points balances the force of gravity.
Since the man's arms and legs are not evenly distributed, we'll need to consider the distribution of his weight. Given that:
a = 40 cm (distance from the center of gravity to each hand)
b = 95 cm (distance from the center of gravity to each foot)
c = 30 cm (distance between each foot)
We can use these distances to calculate the normal forces:
Normal force on hands = (2b x W) / (a + b)
Normal force on feet = W - Normal force on hands
Plugging in the values:
Normal force on hands = (2 x 95 cm x 784 N) / (40 cm + 95 cm)
Normal force on feet = 784 N - Normal force on hands
Converting cm to meters:
(2 x 0.95 m x 784 N) / (0.4 m + 0.95 m) = 652.2 N
784 N - 652.2 N = 131.8 N
Therefore, the normal force exerted by the floor on each hand is approximately 652.2 N, and the normal force exerted by the floor on each foot is approximately 131.8 N.