A woman stands on a scale in a moving elevator. Her mass is 63.0 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?
To find what the scale reads during the acceleration, we need to determine the net force acting on the woman.
First, let's find the force due to gravity acting on the woman. The force due to gravity can be calculated using the formula:
F_gravity = mass x gravitational acceleration
where the mass of the woman is given as 63.0 kg and the gravitational acceleration is approximately 9.8 m/s².
F_gravity = 63.0 kg x 9.8 m/s² = 617.4 N
Since the elevator is accelerating upward, the net force on the woman will be the difference between the force due to gravity and the force of the hoisting cable:
Net force = F_cable - F_gravity
Given that the force of the hoisting cable is 9470 N:
Net force = 9470 N - 617.4 N = 8852.6 N
Now, since the woman and the scale are in contact with each other, the scale will read the net force acting on the woman. Therefore, the scale will read 8852.6 N during the upward acceleration of the elevator.