Elevator Weight Physics Explained
A person's weight is determined by the normal force ($N$) exerted by the supporting surface (the elevator floor). This apparent weight equals the true weight (gravitational force, $mg$) only when the net force is zero.
Analyzing Forces in Moving Elevator
We apply Newton's Second Law ($\Sigma F = ma$) to the person inside the elevator. The forces involved are:
- The downward gravitational force ($mg$).
- The upward normal force from the floor ($N$).
The net force equation is: $N - mg = ma$ where '$a$' is the acceleration of the elevator.
Scenario: Constant Velocity Motion
The question implies a scenario where the weight does not change. This occurs when the elevator moves at a constant velocity (or is at rest). In this specific case, the acceleration ($a$) is zero.
Substituting $a = 0$ into the equation:
$N - mg = m(0)$ $N - mg = 0$ $N = mg$When $N = mg$, the apparent weight is equal to the true gravitational force. Thus, the person's weight does not change.
Conclusion: In a moving elevator at constant velocity, the apparent weight remains the same.
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