A woman stands on a scale in a moving elevator. Her mass is 65.0 kg, and the combined mass of the elevator and scale is an additional 757 kg. Starting from rest, the elevator accelerates upward. During the acceleration, the hoisting cable applies a force of 9550 N. What does the scale read (in N) during the acceleration?
To determine what the scale reads during the acceleration, we need to calculate the net force acting on the woman.
To start, let's analyze the forces involved:
1. Force due to gravity (weight): This force is always acting downward and can be calculated using the woman's mass (m) and the acceleration due to gravity (g ≈ 9.8 m/s²). The formula for calculating weight is Fg = m × g.
2. Normal force (normal reaction): This force is exerted by a surface to support an object resting on it. In this case, the scale exerts a normal force on the woman, which balances the force due to gravity. The normal force is equal in magnitude and opposite in direction to the force due to gravity when the object is at rest or moving with constant velocity.
3. Force applied by the hoisting cable: This is the force exerted by the elevator's hoisting cable, which accelerates the woman and the elevator. This force is key to calculating the scale reading.
Now, let's calculate the net force on the woman during the upward acceleration:
Net force = Force applied by hoisting cable - Force due to gravity
The force due to gravity can be calculated as follows:
Fg = m × g
= 65.0 kg × 9.8 m/s²
≈ 637 N
Since the elevator is accelerating upward, the net force will be in the upward direction, opposite to the direction of gravity. So the net force on the woman is:
Net force = 9550 N - 637 N
= 8913 N
Now, the net force acting on the woman is the same as the normal force exerted by the scale. Therefore, the scale will read 8913 Newtons during the upward acceleration.