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A person of mass 60 kg is inside a lift of mass 940 kg and presses the button on control panel. The lift starts moving upwards with an acceleration 1.0 m/$s^2$. If g = 10 m $s^{-2}$, the tension in the supporting cable is
A
1200 N
B
8600 N
C
9680 N
D
11000 N
Detailed Solution
Total mass supported by the cable = mass of lift + mass of person = 940 + 60 = 1000 kg.
Forces on the system: tension T upward and weight $(M + m)g$ downward.
The lift accelerates upward, so $T - (M + m)g = (M + m)a$
$T = (M + m)(g + a)$
$T = 1000\times(10 + 1) = 11000$ N
Forces on the system: tension T upward and weight $(M + m)g$ downward.
The lift accelerates upward, so $T - (M + m)g = (M + m)a$
$T = (M + m)(g + a)$
$T = 1000\times(10 + 1) = 11000$ N