Question

A 72 kg crate is on a freight elevator. It accelerates upwards at a rate of 0.2 m/s² while moving down. Determine the force of the cable on the elevator.

Answer 1

The force of the cable on the elevator is 720 N.

Step-by-step explanation:

To determine the force of the cable on the elevator, we need to consider the net force acting on the crate. The net force is equal to the product of the crate's mass and its acceleration.

First, let's determine the force when the elevator is accelerating upwards. The net force is given by the equation: net force = mass * acceleration. Plugging in the values: net force = 72 kg * 0.2 m/s² = 14.4 N.

Now, let's consider the case when the elevator is moving downwards with the same acceleration. In this case, the net force is equal to the force of gravity acting on the crate, which is given by: force of gravity = mass * acceleration due to gravity. Plugging in the values: force of gravity = 72 kg * 9.8 m/s² = 705.6 N.

Therefore, the force of the cable on the elevator is equal to the net force, which is the sum of the forces in both cases:

Force of the cable = net force (upward) + net force (downward) = 14.4 N + 705.6 N = 720 N.