Question

The total mass of an elevator, with a 80 kg man in it, is 1000 kg. This elevator moving upward with a speed of 8 m/s is brought to rest over a distance 16 m. Then tension T in the cable supporting elevator is

• A. 3200N
• B. 5400N
• C. 6500 N
• D. 7800N

Answer 1

The correct option is D 7800N

Let us consider $a$ to be the acceleration of the elevator and given the mass of elevator and speed. Thus, let us apply the equation of motion to derive acceleration a of the elevator, $v^2-u^2=2as$

$0-8^2=2\times a\times 16$

$a=-2m{\sec }^2$

But, we are also given that the elevator is moving up. Hence, the force $ma$ balances the resultant force due to the cable and we have $T-Mg=-Ma$ (M be the total mass of the elevator)

$T=M(g-a)$

$=1000(9.8-2)$

$=7800N$.

Then tension T in the cable supporting elevator is $T=7800N$.