👉 Basic Concept:
When a body of mass m is placed on a weighing machine kept inside a lift, its actual weight is:
Actual weight = m × g
This force (m × g) acts on the weighing machine, which gives a reaction R. The reading of the machine is this reaction R.
📌 Important:
This reaction R is called the apparent weight of the body.
1️⃣ When the Lift is Moving Upward
🔼 Net upward force on the body:
F = R − m×g
Using Newton’s 2nd law:
m×a = R − m×g
Solving for R (apparent weight):
R = m(g + a)
📌 Result:
Apparent weight > Actual weight
✅ You feel heavier when lift moves up.
2️⃣ When the Lift is Moving Downward
🔽 Net downward force on the body:
F = m×g − R
Using Newton’s 2nd law:
m×a = m×g − R
Solving for R (apparent weight):
R = m(g − a)
📌 Result:
Apparent weight < Actual weight
✅ You feel lighter when the lift moves down.
ℹ️ Notes:
(i) If Lift is at rest or moving at constant speed (upward or downward):
Here, a = 0, so
R = m×g
📌 Apparent weight = Actual weight
(ii) If Lift is accelerating downward with a = g:
Then,
R = 0
📌 Apparent weight = 0 (Weightlessness)
✅ You feel weightless just like in space!
(iii) If Lift is accelerating downward with a > g:
Then,
R = −ve (negative)
📌 Apparent weight is negative! This means the person will lift off the floor and hit the ceiling.
✅ It feels like a jump or free-fall. 😲
📌 Extra Note (In Hinglish):
अगर लिफ्ट पर रिटार्डेशन (retardation) काम कर रहा है, तो एक्सेलेरेशन ‘a’ की direction हमेशा लिफ्ट की velocity के opposite होती है।
🎯 Summary Chart (Lift Motion vs Weight Feelings):
| Lift Condition | Acceleration | Apparent Weight |
|---|---|---|
| Lift at rest / constant speed | a = 0 | Normal (R = mg) |
| Moving upward with acceleration | a ↑ | More than normal |
| Moving downward with acceleration | a ↓ | Less than normal |
| Free fall (a = g) | a = g | Zero (weightlessness) |
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