Two crates are dropped from the same height in a vacuum. The mass and force of the crates are shown in the diagram. Which of the following statements is supported by the data?
a
Both of the crates are accelerating at the same rate.
b
Both of the crates are falling at a constant speed.
c
The momentum of both crates will be the same right before they hit the ground.
d
The normal force will be the same on both crates when they hit the ground.
a) Both of the crates are accelerating at the same rate.
In a vacuum, where there is no air resistance, all objects, regardless of mass, fall at the same rate of acceleration due to gravity. Therefore, the mass and force of the crates are not relevant to their acceleration, and both crates will accelerate at the same rate. Therefore, option a is supported by the data.
To determine the correct statement, let's analyze the provided data and apply some basic physics principles.
First, the statement (c) "The momentum of both crates will be the same right before they hit the ground" is incorrect for two reasons. Momentum is given by the formula: momentum = mass × velocity. While the mass of the crates is the same, the diagram does not provide any information about their velocities. Additionally, as the crates are falling, their velocities are not necessarily the same. Therefore, we cannot conclude that the momentum of both crates will be the same right before they hit the ground.
Now, let's consider the statement (d) "The normal force will be the same on both crates when they hit the ground." The normal force is the force exerted by a surface perpendicular to the contact point. In this case, the crates are falling in a vacuum, so there is no surface or any contact force acting on them. Therefore, the normal force is not applicable in this scenario, and we cannot conclude that the normal force will be the same on both crates when they hit the ground.
Next, let's analyze statement (b) "Both of the crates are falling at a constant speed." If the crates were falling at a constant speed, it would mean that the net force acting on each crate is zero. However, the force of gravity is acting on the crates, causing them to accelerate downwards. Therefore, the statement (b) is incorrect.
Finally, let's examine statement (a) "Both of the crates are accelerating at the same rate." According to Newton's second law of motion, the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. In this case, both crates experience the same force of gravity since they have the same mass. As a result, they will have the same magnitude of acceleration. Therefore, statement (a) is supported by the data and is the correct answer.
In summary, based on the provided data, we can conclude that statement (a) "Both of the crates are accelerating at the same rate" is supported, while the other statements are incorrect or not applicable to this scenario.
The correct answer is a) Both of the crates are accelerating at the same rate.
In a vacuum, there is no air resistance, so the only force acting on the crates is the force of gravity. According to Newton's second law of motion, the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. Since both crates have the same mass, they will experience the same force of gravity and therefore will accelerate at the same rate.