A person of mass $60 ext{ kg}$ is inside a lift of mass $940 ext{ kg}$ and presses the button on control p

Question

A person of mass $60 	ext{ kg}$ is inside a lift of mass $940 	ext{ kg}$ and presses the button on control panel. The lift starts moving upwards with an acceleration $1.0 	ext{ m/s}^2$. If $g=10 	ext{ m/s}^2$, the tension in the supporting cable is:

Accepted Answer

1. **System Definition:** The tension in the supporting cable pulls the entire system upwards. Therefore, we must consider the total mass of the system.
   - Mass of person, $m = 60 	ext{ kg}$.
   - Mass of lift, $M = 940 	ext{ kg}$.
   - Total Mass, $M_{total} = M + m = 940 + 60 = 1000 	ext{ kg}$.
2. **Forces Analysis:**
   - Upward force: Tension ($T$).
   - Downward force: Total Weight ($W = M_{total}g$).
   - Net Acceleration: $a = 1.0 	ext{ m/s}^2$ (upwards).
3. **Equation of Motion:** Applying Newton's Second Law ($F_{net} = ma$) in the upward direction:
   $$ T - M_{total}g = M_{total}a $$
   $$ T = M_{total}(g + a) $$
   (Reference: NCERT Class 11, Physics Part I, Chapter 5, Laws of Motion, Section 5.9 Common Forces in Mechanics - similar logic applied to elevator problems).
4. **Calculation:**
   Substitute the values ($g = 10 	ext{ m/s}^2, a = 1.0 	ext{ m/s}^2$):
   $$ T = 1000 	ext{ kg} 	imes (10 + 1) 	ext{ m/s}^2 $$
   $$ T = 1000 	imes 11 $$
   $$ T = 11000 	ext{ N} $$

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