What causes a bathroom scale to display a different mass than the actual mass of a person standing on it inside an elevator?
The discrepancy in the reading of the bathroom scale inside an elevator is due to the additional force exerted by the acceleration of the elevator. When a person stands on a scale in an elevator, the scale not only measures the normal force exerted by the person's weight but also an additional force caused by the elevator's acceleration.
Understanding the Scenario
When a person stands on a bathroom scale, the scale measures the normal force exerted by the person's weight, which is equal to the force of gravity acting on the person. In a stationary elevator, the scale accurately reflects the person's mass based on this normal force.
However, when the elevator is in motion and accelerating either upwards or downwards, an additional force is exerted on the person by the acceleration of the elevator. This additional force affects the reading on the scale and leads to a different mass value being displayed.
Calculating the Acceleration
To determine the acceleration of the elevator when the scale misreads the person's mass, we can set up an equation based on Newton's second law of motion. The equation relates the force (weight) measured on the scale to the mass of the person and the acceleration of the elevator.
By substituting the given values and solving the equation, we find that the acceleration of the elevator can be approximated as approximately 3.19 m/s² in this scenario.
This calculation highlights the impact of acceleration on the reading of a scale in an elevator and demonstrates how the perceived mass can differ from the actual mass due to additional forces at play.