How Acceleration and Forces Affect Crates in an Elevator
Acceleration of Crate A vs. Crate B
In this scenario, crate A has a greater mass than crate B. As the elevator slows down while moving downward, the acceleration of crate A will be less than that of crate B.
According to Newton's second law, the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. Since crate A has a greater mass than crate B, and the net force on both crates is the force of gravity acting downward, crate A will experience a smaller acceleration compared to crate B.
Free-Body Diagrams
The free-body diagram for each crate will show the force of gravity acting downward, which is the weight of the crate (mg), where m represents the mass of the crate and g is the acceleration due to gravity. Additionally, there will be a normal force exerted by the elevator floor, which counteracts the gravitational force and prevents the crates from sinking through the floor. The magnitude of the normal force will be equal to the weight of each crate.
Ranking Forces on the Crates
According to Newton's third law, for every action, there is an equal and opposite reaction. The normal force exerted by the floor on the crates is equal in magnitude but opposite in direction to the gravitational force exerted by the crates on the floor. Therefore, the normal forces experienced by both crates are equal.
Net Force on Each Crate
As the elevator slows down, the net force on each crate will be the difference between the force of gravity and the normal force. If the net force on either crate is zero, it should be explicitly stated. The net force on crate A will be greater in magnitude compared to crate B, as crate A has a greater mass.
Two crates, A and B, are in an elevator. The mass of crate A is greater than mass of B. As the elevator approaches its destination, its speed decreases. (It continues to move downward.)i. How does the acceleration of crate A compare to that of B? Explain.
ii. In the space provided below, draw and label separate free-body diagrams for the crates in this case.
iii. Rank the forces on the crates according to magnitude, from largest to smallest. Explain your reasoning, including how you used Newton's second and third laws.
iv. In the space provided, draw arrows to indicate the direction of the net force on each crate. If the net force on either crate is zero state so explicitly. Explain.
Is the magnitude of the net force acting on crate A greater than, less than, or equal to that on crate B? Explain.
Answers to the questions are provided in the content section above.