Question

You are conducting an experiment inside an elevator that can move in a vertical shaft. A load is hung vertically from the ceiling on a string, and is stationary with respect to you. The tension in the string is measured to be 10% less than the weight of the load. No other forces are acting on the load. Which of the following statements about the elevator are correct?

The elevator is an inertial frame of reference.
The elevator is not an inertial frame of reference.
The elevator may be at rest for the duration of the entire experiment.
The elevator may be moving at a constant velocity upward.
The elevator may be moving at a constant velocity downward.
The elevator must be accelerating

Answer 1

The elevator must be accelerating downwards since the measured tension in the string is 10% less than the weight of the load. This means that it is not an inertial frame of reference and cannot be at rest or moving with constant velocity.

Step-by-step explanation:

If the tension in the string holding the load in the elevator is 10% less than the weight of the load, this indicates that the elevator must be accelerating. Since no other forces are acting on the load, the only way for the tension to be less than the weight is if the elevator is accelerating downwards. This is because the acceleration reduces the apparent weight of the load, which the tension in the string must balance. Here are the options contextualized:

• The elevator is not an inertial frame of reference, because it is accelerating.
• The elevator cannot be at rest, as the difference in tension indicates acceleration.
• The elevator cannot be moving at a constant velocity upward, as this would result in a tension equal to the weight of the load.
• The elevator cannot be moving at a constant velocity downward for the same reason as above.
• The elevator must be accelerating downward for the tension to be less than the weight.

The choice that the elevator must be accelerating is the correct statement about the elevator movement given the condition described.

Answer 2

The elevator must be accelerating

This is the case because the tension is not equivalent to the load's weight, which means there must another force acting on the system.