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.
Well, well, well! Look at this balancing act we've got going on here! It's like a human-crate tower!
(a) Now, let's talk about the normal force that the floor exerts on the crate. We know that the crate is resting on the floor, which means there must be an equal and opposite force pushing up from the floor to keep it in place. So, the magnitude of the normal force that the floor exerts on the crate is equal to the weight of the crate. The weight is just the mass of the crate multiplied by the acceleration due to gravity (9.8 m/s²). So, the normal force would be (40.6 kg) × (9.8 m/s²).
(b) Phew, now let's move on to the crate exerting a force on the person standing on it. This is where things get a bit interesting. Since the person is standing on the crate, their weight (mass × acceleration due to gravity) is being supported by the crate. So, the magnitude of the force that the crate exerts on the person is equal to the person's weight. Therefore, it would be (69.1 kg) × (9.8 m/s²).
And there you have it! Physics meets balancing acts!
To solve this problem, we need to consider the forces acting on each object and apply Newton's third law.
(a) The magnitude of the normal force that the floor exerts on the crate:
The crate is in contact with the floor, so there are two forces acting on the crate - its weight (due to gravity) and the normal force. According to Newton's third law, these forces are equal in magnitude and opposite in direction.
The weight of the crate can be calculated using the formula:
Weight = mass * gravitational acceleration
The gravitational acceleration is approximately 9.8 m/s^2.
Weight of the crate = 40.6 kg * 9.8 m/s^2 = 398.68 N
Therefore, the magnitude of the normal force that the floor exerts on the crate is also 398.68 N.
(b) The magnitude of the normal force that the crate exerts on the person:
Again, we need to consider two forces acting on the person - their weight and the normal force. The normal force here will be equal in magnitude to the weight of both the person and the crate combined.
The weight of the person can be calculated using the same formula:
Weight of the person = mass * gravitational acceleration
Weight of the person = 69.1 kg * 9.8 m/s^2 = 677.38 N.
Now, the total weight on the person is the sum of the weights of the crate and the person:
Total weight on the person = Weight of the crate + Weight of the person
Total weight on the person = 398.68 N + 677.38 N = 1076.06 N
Therefore, the magnitude of the normal force that the crate exerts on the person is also 1076.06 N.
To determine the magnitude of the normal force, we need to understand that the normal force is the force exerted by a surface to support the weight of an object resting on it. In this case, we have a person standing on a crate, and the crate is resting on the floor.
(a) To find the magnitude of the normal force that the floor exerts on the crate, we need to consider the forces acting on the crate. There are two forces acting on the crate:
1. The force due to gravity acting downwards, which is given by the weight of the crate and the person on it. The weight can be calculated by multiplying the mass by the acceleration due to gravity (g = 9.8 m/s^2):
Weight = (crate mass + person mass) * g
Weight = (40.6 kg + 69.1 kg) * 9.8 m/s^2
2. The force exerted by the floor on the crate, which is the normal force we are trying to find. It acts in the upwards direction, perpendicular to the floor.
According to Newton's third law of motion, the normal force is equal in magnitude but opposite in direction to the force exerted by the crate on the floor. Therefore, the normal force must be equal to the weight of the crate and the person:
Normal force = (crate mass + person mass) * g
Substituting the values:
Normal force = (40.6 kg + 69.1 kg) * 9.8 m/s^2
Calculate the value to find the magnitude of the normal force.
(b) To determine the magnitude of the normal force that the crate exerts on the person, we need to realize that according to Newton's third law, the force exerted by the crate on the person (the normal force) is equal in magnitude but opposite in direction to the force exerted by the person on the crate (due to their weight).
Therefore, the magnitude of the normal force that the crate exerts on the person is the same as the magnitude of the weight of the person:
Weight = person mass * g
Weight = 69.1 kg * 9.8 m/s^2
Calculate the value to find the magnitude of the normal force.