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.

a. F = (m1+m2)g,

F = (40.6+69.1)*9.8 = 1075N.

b. F = -1075N.

A 110- crate, starting from rest, is pulled across a floor with a constant horizontal force of 380 . For the first 11 the floor is frictionless, and for the next 11 the coefficient of friction is 0.33.What is the final speed of the crate?

To determine the magnitude of the normal force exerted by the floor on the crate, we need to consider the forces acting on the crate.

(a) The forces acting on the crate are:
1. Weight of the crate downward (mg, where m is the mass of the crate and g is the acceleration due to gravity)
2. Normal force exerted by the floor upward

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

To calculate the weight of the crate, we can use the formula: weight = mass × acceleration due to gravity.

Given that the mass of the crate is 40.6 kg, and the acceleration due to gravity is approximately 9.8 m/s^2, we can calculate the weight of the crate using the formula:

weight = 40.6 kg × 9.8 m/s^2 = 398.68 N (approximately)

Hence, the magnitude of the normal force exerted by the floor on the crate is 398.68 N.

(b) To determine the magnitude of the normal force exerted by the crate on the person, we need to consider the forces acting on the person.

The forces acting on the person are:
1. The normal force exerted by the crate upward
2. The weight of the person downward (m × g, where m is the mass of the person and g is the acceleration due to gravity)

Since the person is standing on the crate, the magnitude of the normal force exerted by the crate on the person will be the same as the weight of the person. Again, we can calculate the weight of the person using the formula: weight = mass × acceleration due to gravity.

Given that the mass of the person is 69.1 kg, and the acceleration due to gravity is approximately 9.8 m/s^2, we can calculate the weight of the person using the formula:

weight = 69.1 kg × 9.8 m/s^2 = 677.38 N (approximately)

Therefore, the magnitude of the normal force exerted by the crate on the person is 677.38 N.