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 force due to gravity on the load. No other forces are acting on the load. Which of the following statements about the elevator are correct?
Which of the following statements are true

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

Answer: The elevator must be accelerating.

Explanation:

As the tension force is opposing to the the force of gravity on the load which is hung vertically, and the tension force can adopt any value in order to comply with Newton's 2nd law, if the tension force is less than the force due to gravity, this means that all system is not in equilibrium, so it must be accelerating.

If we assume that the downward is the positive direction, we can write:

mg - T = ma

If T = 0.9 mg, ⇒ mg (1-0.9) =0.1 mg = m a ⇒a = 0.1 g , in downward direction.