A person whose weight is W=584 N doing push-ups. Find the normal force exerted by the floor on each hand each foot, assuming that the persons holds this person
|=central gravity
foot arm
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.840m .410m
double post
To find the normal force exerted by the floor on each hand and each foot, we first need to calculate the weight of the person. The weight can be calculated using the formula:
Weight (W) = mass (m) * gravitational acceleration (g)
Given that the weight is 584 N, we can rearrange the formula to solve for mass:
m = W / g
Next, we need to determine the distribution of weight between the hands and feet. According to the given diagram, the person's center of gravity is closer to the feet than the hands. Let's assume that the person's weight is distributed evenly among the hands and feet.
To find the normal force exerted by the floor on each hand and foot, we can use the equation:
Normal force (N) = Weight (W) / Number of hands or feet
Since the person is doing push-ups and there are two hands and two feet involved, we divide the weight by 4 to get the normal force on each hand and foot.
Let's calculate the normal force on each hand and foot step by step:
Step 1: Calculate the mass of the person.
m = W / g
m = 584 N / 9.8 m/s^2
m ≈ 59.59 kg
Step 2: Calculate the normal force on each hand and foot.
Normal force on each hand (N_hands) = W / 4
Normal force on each foot (N_feet) = W / 4
N_hands = N_feet = 584 N / 4
N_hands = N_feet ≈ 146 N
So, the normal force exerted by the floor on each hand and foot when the person is doing push-ups is approximately 146 N.