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

Question

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

Accepted Answer

1. **System Analysis:** Consider the lift and the person together as a single system. The total mass $M$ is the sum of the mass of the lift and the mass of the person.
   $$ M = 940 	ext{ kg} + 60 	ext{ kg} = 1000 	ext{ kg} $$
2. **Forces Involved:** 
   - The tension $T$ in the supporting cable acts vertically upwards.
   - The total weight of the system ($Mg$) acts vertically downwards.
3. **Equation of Motion:** Since the lift is accelerating upwards with acceleration $a = 1.0 	ext{ m/s}^2$, we apply Newton's Second Law ($F_{net} = Ma$) [NCERT Class 11, Physics Part I, Laws of Motion, Section 5.5]:
   $$ T - Mg = Ma $$
   $$ T = M(g + a) $$
4. **Calculation:** Substitute the values ($M=1000$, $g=10$, $a=1$):
   $$ T = 1000 	imes (10 + 1.0) $$
   $$ T = 1000 	imes 11 = 11000 	ext{ N} $$

Step-by-Step Solution

Practice All PHYSICS Questions