A 800·kg elevator is attached to a cable whose tension is 7800·N.
Which of the following statements could describe the motion of the elevator? Choose all that apply.
slowing down as it moves upward
moving upward at constant speed
speeding up as it moves downward
slowing down as it moves downward
speeding up as it moves upward
moving downward at constant speed
it is at rest
The weight of the elevator is M*g = 7840 N. The cable tension is slightly less than that. These conditions could apply:
slowing down as it moves upward
speeding up as it moves downward
To determine the motion of the elevator, we can analyze the forces acting on it.
First, let's consider the forces when the elevator is moving upward:
1. The force of gravity acts downwards on the elevator, given by the formula F_gravity = m * g, where m is the mass of the elevator and g is the acceleration due to gravity.
2. The tension in the cable also acts upwards on the elevator, given as 7800 N.
If the tension in the cable is greater than the force of gravity (tension > F_gravity), the elevator will accelerate upward. This means it is speeding up.
If the tension in the cable is equal to the force of gravity (tension = F_gravity), the elevator will move upward at a constant speed.
If the tension in the cable is less than the force of gravity (tension < F_gravity), the elevator will decelerate or slow down as it moves upward.
Now, let's consider the forces when the elevator is moving downward:
1. The force of gravity still acts downwards on the elevator, given by F_gravity = m * g.
2. The tension in the cable acts upwards on the elevator, given as 7800 N.
If the tension in the cable is greater than the force of gravity (tension > F_gravity), the elevator will decelerate or slow down as it moves downward.
If the tension in the cable is equal to the force of gravity (tension = F_gravity), the elevator will move downward at a constant speed.
If the tension in the cable is less than the force of gravity (tension < F_gravity), the elevator will accelerate downward. This means it is speeding up.
Based on this analysis:
- The elevator could be moving upward at a constant speed.
- The elevator could be moving downward at a constant speed.
The following statements do not apply:
- The elevator is not at rest, as tension is acting on it.
- The elevator is not speeding up as it moves upward, as the tension in the cable must be greater than the force of gravity for that to occur.
- The elevator is not slowing down as it moves downward, as the tension in the cable must be less than the force of gravity for that to occur.