A 39.7-kg crate rests on a horizontal floor, and a 65.3-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.
Floor pushes up total weight
= (39.7 + 65.3)(9.81)
crate pushes up on person
= (65.3)(9.81)
(a) The magnitude of the normal force that the floor exerts on the crate can be found by considering the forces acting on the crate. Since the crate is at rest on the horizontal floor, the net force on it must be zero.
The only vertical forces acting on the crate are its weight and the normal force. The weight of the crate can be calculated using the formula:
Weight = mass × gravity
Weight of the crate = (39.7 kg) × 9.8 m/s² = 388.86 N
Since the net force on the crate is zero, the magnitude of the normal force must be equal and opposite to the weight of the crate. Therefore, the magnitude of the normal force that the floor exerts on the crate is also 388.86 N.
(b) Now, let's consider the forces acting on the person standing on the crate. The person's weight acts downward, and the person is also exerting a force on the crate.
The weight of the person can be calculated using the same formula as before:
Weight of the person = (65.3 kg) × 9.8 m/s² = 639.94 N
The person is standing on the crate, so the force exerted by the crate on the person must be equal and opposite to the person's weight. Therefore, the magnitude of the force that the crate exerts on the person is also 639.94 N.
In summary, the magnitude of the normal force that the floor exerts on the crate is 388.86 N, and the magnitude of the force that the crate exerts on the person is 639.94 N.
To solve this problem, we need to consider the forces acting on both the crate and the person standing on it.
Let's start with part (a) - the magnitude of the normal force that the floor exerts on the crate.
The normal force is the force exerted by a surface to support the weight of an object resting on it. It acts perpendicular to the surface.
In this case, the crate is at rest on the horizontal floor, so there is no vertical acceleration.
We can use Newton's second law to analyze the forces in the vertical direction:
ΣF_y = ma_y
The only force acting in the vertical direction is the gravitational force (weight). The weight of an object can be calculated using the formula:
weight = mass * acceleration due to gravity
where the acceleration due to gravity is approximately 9.8 m/s^2.
For the crate, the weight is:
Weight_crate = mass_crate * acceleration due to gravity
Weight_crate = (39.7 kg) * (9.8 m/s^2) = 389.06 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.
So, the magnitude of the normal force exerted by the floor on the crate is:
(a) Normal force (floor on crate) = Weight_crate = 389.06 N
Moving on to part (b), let's determine the magnitude of the normal force that the crate exerts on the person.
For a person standing on an object, the normal force acts upward to support their weight. The normal force from the crate on the person is equal in magnitude and opposite in direction to the person's weight.
The weight of the person is:
Weight_person = mass_person * acceleration due to gravity
Weight_person = (65.3 kg) * (9.8 m/s^2) = 639.94 N
Therefore, the magnitude of the normal force that the crate exerts on the person is:
(b) Normal force (crate on person) = Weight_person = 639.94 N
To summarize:
(a) The magnitude of the normal force that the floor exerts on the crate is 389.06 N.
(b) The magnitude of the normal force that the crate exerts on the person is 639.94 N.
To determine the magnitude of the normal force that the floor exerts on the crate, we need to consider the force equilibrium in the vertical direction. The normal force is the force exerted by a surface to support the weight of an object resting on it. In this case, the weight of the crate and the person standing on it will be balanced by the normal force.
(a) The normal force on the crate:
The weight of the crate is given by the formula:
Weight = mass × gravity
Given that the mass of the crate is 39.7 kg, and the acceleration due to gravity is approximately 9.8 m/s², we can calculate the weight of the crate as:
Weight = 39.7 kg × 9.8 m/s² = 389.66 N.
Since the crate is at rest on the horizontal floor, the normal force provided by the floor must be equal to the weight of the crate:
Normal force = Weight of the crate = 389.66 N.
Therefore, the magnitude of the normal force that the floor exerts on the crate is 389.66 N.
(b) The normal force on the person:
To find the normal force exerted by the crate on the person, we consider the force equilibrium of the person. The person's weight is balanced by the normal force exerted by the crate:
Weight of the person = mass of the person × gravity
Weight of the person = 65.3 kg × 9.8 m/s² = 639.94 N.
To maintain equilibrium, the normal force exerted by the crate on the person must be equal to the person's weight:
Normal force = Weight of the person = 639.94 N.
Therefore, the magnitude of the normal force that the crate exerts on the person is 639.94 N.