Question

A 40kg girl is riding in an elevator going up , while standing on a scale it shows that she weighs 500 Newton’s. What is the upward acceleration of the elevator?

Answer 1

To find the elevator's upward acceleration, subtract the girl's weight from the scale reading of 500 N to get the net force. Divide this net force by her mass to obtain an acceleration of 2.69 m/s².

Step-by-step explanation:

To calculate the upward acceleration of the elevator, we must first understand that the scale measures the normal force exerted on the girl by the floor of the elevator, which, in a non-accelerating frame, would be equal to her weight due to gravity. However, since the scale shows 500 Newtons, which is more than her actual weight (40 kg × 9.81 m/s² = 392.4 N), the difference is due to the additional force applied by the elevator's acceleration.

Using Newton's second law, Fnet = ma, we can set up an equation with the net force being the reading on the scale minus her weight:

1. Fnet = Fscale - W
2. ma = 500 N - 392.4 N
3. ma = 107.6 N
4. a = Fnet / m
5. a = 107.6 N / 40 kg
6. a = 2.69 m/s² (upward)

Therefore, the elevator is accelerating upward with an acceleration of 2.69 m/s².