Understanding the Forces
* Weight (mg): This is the force of gravity acting on you, always directed downwards. It's calculated as (75 kg) * (9.8 m/s²) = 735 N.
* Normal Force (N): This is the force the scale exerts on you, acting upwards. It's what the scale actually measures.
* Apparent Weight: The reading on the scale, which is equal to the normal force (N).
Scenario Breakdown
1. At Rest: Before the elevator starts moving, the scale reads your actual weight: 735 N
* The normal force (N) is equal to your weight (mg).
2. Accelerating Downwards: When the elevator accelerates downwards, you experience a sensation of feeling lighter. This is because:
* The normal force (N) is less than your weight (mg).
* To calculate the normal force during acceleration, we need to consider the net force:
* Net Force (F_net) = ma = 75 kg * (-2.0 m/s²) = -150 N (negative because acceleration is downwards)
* N = mg + F_net = 735 N - 150 N = 585 N
* The scale will read 585 N.
3. Constant Speed: When the elevator moves at a constant speed, you feel normal.
* The net force is zero (F_net = 0).
* The normal force (N) equals your weight (mg) again: 735 N.
* The scale will read 735 N.
Summary
* At Rest: 735 N
* Accelerating Downwards: 585 N
* Constant Speed: 735 N
Key Point: The scale reading reflects the normal force, which changes depending on the net force acting on you. When the elevator accelerates downwards, the normal force is less than your weight. When it moves at a constant speed, the normal force is equal to your weight.
