A person with weight W stands on a bathroom scale in a motionless elevator. When the elevator begins to move, the scale briefly reads only 0.75 of the person's original weight. If up is considered to be the positive direction, what is the acceleration of the elevator when it begins to move?
To determine the acceleration of the elevator, we can use Newton's second law of motion, which states that the force acting on an object is equal to the mass of the object multiplied by its acceleration.
Let's start by analyzing the forces acting on the person in the elevator.
1. Gravity: The weight of the person (W) is the force exerted by gravity on the person, which is equal to their mass (m) multiplied by the acceleration due to gravity (g).
Force due to gravity = mg
2. Normal force: The normal force is the force exerted by the scale on the person. It acts in the opposite direction to gravity and can be calculated as the weight of the person multiplied by the scale reading (0.75).
Normal force = 0.75W
Now, when the elevator starts moving, we should consider the forces acting on the person. The normal force will be less than the force due to gravity because the scale only reads 0.75 of the person's original weight.
Since the normal force is equal to the mass of the person multiplied by the acceleration of the elevator, we have:
0.75W = m * a
Now, we can cancel out the mass (m) from both sides of the equation:
0.75W/m = a
The mass of an object cancels out when calculating acceleration, which means that the acceleration of the elevator does not depend on the mass of the person. Therefore, the acceleration of the elevator when it begins to move is 0.75 times the acceleration due to gravity (0.75g).