🚀 Motion of a Body in a Lift (Elevator)

👉 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):

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