A woman stands on a scale in a moving elevator.

Her mass is 54.0 kg, and the combined mass of the elevator and scale is an additional 815 kg. Starting from rest, the elevator accelerates upward. During the acceleration, the hoisting cable applies a force of 9470 N. What does the scale read during the acceleration?

I've managed to get 48 kg as my answer. Am I correct in this case?

No, if it is accelerating UPWARD her mass should read more than 54kg.

To determine what the scale reads during the acceleration, we need to consider the forces acting on the woman.

1. Weight force: This is the force exerted by the gravity on the woman's mass. It can be calculated by multiplying her mass by the acceleration due to gravity (9.8 m/s^2):
Weight force = mass * acceleration due to gravity = 54.0 kg * 9.8 m/s^2

2. Normal force: This is the force exerted by the scale on the woman. It is equal in magnitude and opposite in direction to the weight force under normal circumstances (when there is no acceleration). In this case, since the elevator is accelerating upward, the normal force will be greater than the weight force.

3. Force due to acceleration: The hoisting cable applies a force of 9470 N to accelerate the elevator upward. This force is also transmitted to the woman and the scale.

To find the normal force, we need to consider the net force acting on the woman:

Net force = Force due to acceleration - Weight force

Since the normal force is equal in magnitude to the net force, we can calculate it:

Normal force = Force due to acceleration - Weight force

Plugging in the values:

Normal force = 9470 N - (54.0 kg * 9.8 m/s^2)

Calculating:

Normal force = 9470 N - 529.2 N

Normal force = 8940.8 N

Therefore, the scale would read a value of 8940.8 N during the acceleration.

Based on your response of 48 kg, it appears that there may have been an error in your calculations. Please double-check your work to ensure accuracy.