A 40.6-kg crate rests on a horizontal floor, and a 69.1-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.

total weight on floor = 9.8*(40.6+69.1) Newtonns which is the force up from the floor on the crate.

for the crate to the person, the person's weight which is 9.8*69.1 Newtons

To determine the magnitude of the normal force, we can use Newton's third law which states that for every action, there is an equal and opposite reaction.

(a) The normal force that the floor exerts on the crate can be determined by considering the forces acting on the crate. In this case, the weight of the crate acts vertically downward, while the normal force acts upward to balance out the weight. Since the crate is at rest, the vertical forces must be balanced:

Weight of the crate (W_crate) = mass of the crate (m_crate) * acceleration due to gravity (g)

W_crate = 40.6 kg * 9.8 m/s^2
= 398.68 N

According to Newton's third law, the normal force exerted by the floor on the crate will be equal in magnitude and opposite in direction to the weight of the crate. Therefore:

Magnitude of the normal force (N_floor) = |W_crate| = 398.68 N

(b) The normal force that the crate exerts on the person can be determined by considering the forces acting on the person. The weight of the person acts vertically downward, while the normal force acts upward to balance the weight. Again, the vertical forces must be balanced:

Weight of the person (W_person) = mass of the person (m_person) * acceleration due to gravity (g)

W_person = 69.1 kg * 9.8 m/s^2
= 676.18 N

According to Newton's third law, the normal force exerted by the crate on the person will be equal in magnitude and opposite in direction to the weight of the person. Therefore:

Magnitude of the normal force (N_crate-on-person) = |W_person| = 676.18 N

So, the magnitude of the normal force that the floor exerts on the crate is 398.68 N, and the magnitude of the normal force that the crate exerts on the person is 676.18 N.