A 33.6-kg crate rests on a horizontal floor, and a 64.7-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.
1. N1=(m(per) +m(cr))g
2. N2=m(per)g
To determine the magnitude of the normal force, we need to consider the forces acting on each object.
For (a) the normal force exerted by the floor on the crate:
The normal force is the force exerted by a surface to support the weight of an object resting on it. Since the crate is at rest on the floor, the normal force exerted by the floor on the crate balances the weight of the crate.
The weight of the crate can be calculated using the formula: weight = mass × acceleration due to gravity
where mass = 33.6 kg and acceleration due to gravity = 9.8 m/s^2.
Weight of the crate = 33.6 kg × 9.8 m/s^2 = 329.28 N
Since the crate is at rest, the normal force exerted by the floor on the crate is equal in magnitude but opposite in direction to the weight of the crate.
Therefore, the magnitude of the normal force exerted by the floor on the crate is 329.28 N.
For (b) the normal force exerted by the crate on the person:
Similarly, the normal force exerted by the crate on the person balances the weight of the person.
The weight of the person can be calculated using the same formula:
weight = mass × acceleration due to gravity
where mass = 64.7 kg and acceleration due to gravity = 9.8 m/s^2.
Weight of the person = 64.7 kg × 9.8 m/s^2 = 633.06 N
Since the person is at rest, the normal force exerted by the crate on the person is equal in magnitude but opposite in direction to the weight of the person.
Therefore, the magnitude of the normal force exerted by the crate on the person is 633.06 N.