A person stands on a bathroom scale on a motionless elevator. When the elevator begins to move, the scale briefly reads 200 percent of the person's regular weight. Calculate the acceleration of the elevator, a_{elevator}.
Use SI units
To calculate the acceleration of the elevator, we can use the concept of apparent weight.
First, let's consider the forces acting on the person in the elevator. When the elevator is at rest, the two main forces acting on the person are their weight (mg) and the normal force exerted by the scale (N). According to Newton's second law, the net force acting on the person is equal to their mass (m) times the acceleration due to gravity (g), so we have:
Net Force = mg
When the elevator starts moving, there is an additional force acting on the person - the force due to the acceleration of the elevator (ma_elevator).
Now, let's consider the situation when the scale reads 200% of the person's regular weight. The normal force (N) exerted by the scale is equal to the apparent weight of the person. Since the scale reading is double the person's regular weight, we can write:
N = 2mg
Now, let's equate the forces:
Net Force = ma_elevator
mg = ma_elevator + N
Substituting the value of N from above, we get:
mg = ma_elevator + 2mg
Simplifying the equation, we find:
ma_elevator = mg
Dividing both sides by m, we have:
a_elevator = g
Therefore, the acceleration of the elevator, a_elevator, is equal to the acceleration due to gravity, g.
In SI units, the acceleration due to gravity is approximately 9.8 m/s^2. So, the acceleration of the elevator is 9.8 m/s^2.