Introduction to Apparent Weight
Have you ever felt 'lighter' or 'heavier' when an elevator starts moving? This phenomenon is due to the Normal Force ($N$) exerted by the floor on you. When you stand on a scale, it measures this Normal Force, which we call your apparent weight.
The Physics Concept
According to Newton's Second Law, the net force on an object is equal to its mass times acceleration ($F_{net} = ma$). In an elevator, the two primary vertical forces acting on the student are:
- Gravity ($W$): Acts downwards, $W = mg$.
- Normal Force ($N$): Acts upwards, registered by the scale.
The net force is given by $N - W = ma$. If the acceleration $a$ is negative, it means the elevator is accelerating downwards.
Step-by-Step Solution
Given:
- True weight ($W$) = $550\,N$
- Apparent weight ($N$) = $450\,N$
- Acceleration due to gravity ($g$) $\approx 9.8\,m/s^2$
1. Find the mass ($m$)
Since $W = mg$, then $m = W/g = 550 / 9.8 \approx 56.12\,kg$.
2. Set up the equation of motion
$N - W = ma$ $450 - 550 = 56.12 \times a$ $-100 = 56.12 \times a$
3. Calculate acceleration
$a = -100 / 56.12 \approx -1.78\,m/s^2$
Conclusion: The magnitude of acceleration is $1.78\,m/s^2$ and the direction is downwards.