Question

The apparent weight of a passenger in an elevator is greater than his true weight. Which one of the following is TRUE?a)The elevator is moving at a constant speed downward.b)The elevator is speeding as it moves upward.c)The elevator is moving at a constant speed upward.d)The elevator is slowing down as it moves upward.

Answer 1

The apparent weight of a passenger is greater than his true weight when the elevator is speeding up as it moves upward, indicating upward acceleration.

Step-by-step explanation:

When the apparent weight of a passenger in an elevator is greater than his true weight, it indicates that there is an upward acceleration happening in the elevator, as the scale must exert a greater force upwards to accelerate the passenger. Therefore, option (b) "The elevator is speeding up as it moves upward." is the correct answer. As the elevator accelerates upward, the scale reading will increase due to the additional force required to not only counteract gravity but also to accelerate the passenger upwards. This is why passengers feel heavier than normal in an accelerating elevator.

In contrast, when the elevator is moving at a constant velocity, either upward or downward, the scale reading would equal the person's true weight because there is no acceleration involved; hence, option (c) and option (a) are incorrect in the context of increased apparent weight. Similarly, option (d) is incorrect because if the elevator were slowing down while moving upward, the apparent weight would decrease rather than increase.

Answer 2

Given that the apparent weight of a passenger in an elevator is greater than his true weight, let's select the correct statement.

We have:

• Net force on the passenger when the elevator moves upward with an increasing speed:

ma = N - mg

Where mg is the weight of the passenger which acts downwards

N is the normal force which acts upwards.

• Apparent weight of the passenger:

N = mg + ma

Hence, we can see the apparent weight is greater than true weight.

• Also, when the elevator moves downward with a decreasing speed, the Net force is:

N = mg + ma

The elevator is speeding as it moves upward while it is slowing down when it is moving downward.

Therefre, the correct statement is that the elevator is speeding as it moves upward.

ANSWER:

b)The elevator is speeding as it moves upward.