Question

A person is standing on a scale placed on the floor of an elevator. At time t1, the elevator is at rest and the reading on the scale is 500N. At a later time t2, the person is still standing on the scale and the reading on the scale is 400N . Based on the scale readings, which of the following statements about the motion of the elevator could be true at time t2?

a. The elevator is moving upward at constant speed.
b. The elevator is moving upward and slowing down.
c. The elevator is moving downward at constant speed.
d. The elevator is moving downward and slowing down.
e. The elevator is at rest.

Answer 1

The scale reading of 400N, which is less than the person's weight when the elevator is at rest, implies that the elevator is accelerating downward. The correct answer is option (d), the elevator moving downward and slowing down.

Step-by-step explanation:

The reading on the scale corresponds to the normal force exerted by the scale on the person. When an elevator is accelerating upward or downward, this force is different from the person's weight due to the additional acceleration. At time t1, the scale reads 500N, which we can assume to be the person's actual weight when the elevator is at rest. At time t2, the scale reads 400N, which is less than the person's weight. This implies that the elevator must be accelerating downward, as this would reduce the normal force.

Considering the options given, the correct one would be the elevator moving downward and slowing down. This scenario would result in a scale reading that is less than the person's weight as the acceleration is in the opposite direction, reducing the normal force, but not in free fall (where the reading would be zero). In an accelerating downward movement, not reaching free fall, the scale shows a reading between the weight of the person and zero. Hence, option (d), the elevator moving downward and slowing down, could be true at time t2.

Answer 2

the following statements about the motion of the elevator could be true at time t2 is

c. The elevator is moving downward at constant speed.

Step-by-step explanation:

• Under given situation, the elevator is at rest and the reading on the scale is 500N.
• After some time t2, the person is still standing on the scale and the reading on the scale is 400N .
• It is because if you stand on a scale in an elevator which is accelerating upward, your body will feel heavier because the elevator's floor pressure which presses harder on your feet, and this is why the scale will show a higher reading than the time when the elevator is at rest.
• Similarly on the other hand, when the elevator accelerates downward, your body will feel lighter. The force which is exerted by the scale is called as the apparent weight; which means it does not change with constant speed.
• Applying Newton's second law, which concludes about this particular statement about force exerted on a body when at rest and when in motion.