Question

A person of mass $40\text{kg}$ is inside a lift of mass $960\text{kg}$ and presses the button on the control panel. The lift starts moving upwards with an acceleration $2{\text{m/s}}^2$. If $g=10{\text{m/s}}^2$, the tension in the supporting cable is

• A. $8600\text{N}$
• B. $12000\text{N}$
• C. $11000\text{N}$
• D. $2000\text{N}$

Answer 1

The correct option is B $12000\text{N}$

Let mass of lift be $M=960\text{kg}$
mass of man is $m=40\text{kg}$
acceleration of lift is $a=2{\text{m/s}}^2$ vertically upwards.
From the frame of reference of lift $a_{\text{system}}=0$ for system of (man+lift)

$\Rightarrow$In the FBD of (man+lift) system from lift frame, a pseudo force will be applied in vertically downward direction i.e opposite to acceleration of lift.
$F_{\text{pseudo}}=(M+m)a$


From FBD for equilibrium of system i.e $a_{\text{system}}=0$ :
$\Rightarrow T=(M+m)a+(M+m)g$
$T=(M+m)(a+g)$
$\therefore T=(960+40)\times (2+10)=12000\text{N}$