A 38.3-kg crate rests on a horizontal floor, and a 74.7 kg person is standing on the crate. Determine the magnitude of the normal force that a) the floor exerts on the crate and b) the crate exerts on the person.
W=g(38.3+74.7) one is down, the other is up.
crate on person is weight of person
74.7 * g
a) Floor exert on the crate is weight of the crate (38.3kg) plus weight of person (74.7kg) in Newtons
b) Crate on person is weight of person in Newtons
To determine the magnitude of the normal forces, we need to consider the forces acting on the crate and the person.
a) To find the normal force exerted by the floor on the crate, we need to consider the gravitational force acting on the crate and the person.
The gravitational force can be calculated using the formula:
F = m * g
Where:
F is the force due to gravity,
m is the mass of the object,
g is the acceleration due to gravity (approximately 9.8 m/s^2).
For the crate:
m_crate = 38.3 kg
g = 9.8 m/s^2
F_crate = m_crate * g
F_crate = 38.3 kg * 9.8 m/s^2
F_crate = 375.34 N
The normal force exerted by the floor on the crate is equal in magnitude but opposite in direction to the gravitational force. Therefore, the normal force on the crate is 375.34 N acting upwards.
b) To find the normal force exerted by the crate on the person, we consider Newton's third law, which states that for every action, there is an equal and opposite reaction.
Since the person is standing on the crate, the normal force exerted by the crate on the person is equal in magnitude and opposite in direction to the normal force exerted by the person on the crate. Therefore, the normal force on the person is also 375.34 N, acting downwards.
So, the magnitude of the normal force that:
a) The floor exerts on the crate is 375.34 N upwards.
b) The crate exerts on the person is 375.34 N downwards.