A woman stands on a scale in a moving elevator. Her mass is 68.0 kg, and the combined mass of the elevator and scale is an additional 713 kg. Starting from rest, the elevator accelerates upward. During the acceleration, the hoisting cable applies a force of 9000 N. What does the scale read (in N) during the acceleration?
To find out what the scale reads during the acceleration, we need to consider the forces acting on the woman.
First, let's calculate the total force acting on the woman in the elevator. We can start by finding the total mass of the woman, elevator, and scale combined.
The mass of the woman is given as 68.0 kg, and the combined mass of the elevator and scale is an additional 713 kg. So, the total mass is:
Total mass = mass of the woman + mass of the elevator and scale
= 68.0 kg + 713 kg
= 781 kg
Now, we know that force is equal to mass multiplied by acceleration (F = ma). In this case, the acceleration is provided indirectly through the force applied by the hoisting cable, which is 9000 N.
So, we have:
Force on the woman = Total mass × Acceleration
= 781 kg × 9000 N
= 703,500 N
Now, let's consider the forces acting on the woman. We have the force of gravity acting downward, which is equal to the weight of the woman. The scale exerts an equal and opposite force upwards to counterbalance the force of gravity.
During the acceleration, there will be an additional force acting on the woman, provided by the hoisting cable. However, note that this additional force does not affect the reading on the scale because it is not transmitted through the scale.
Therefore, the scale only measures the force due to gravity, which is the weight of the woman. So, the scale will read:
Scale reading = Force due to gravity
= Weight of the woman
= mass of the woman × acceleration due to gravity
= 68.0 kg × 9.8 m/s^2
= 666.4 N
Therefore, the scale will read 666.4 N during the acceleration.