Question

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 $g = 10\, ms^{-2}$, the tension in the supporting cable is

• A. 8600 N
• B. 9680 N
• C. 11000 N
• D. 1200 N

Answer 1

The Correct Option is C

To solve this problem, we need to calculate the tension in the cable supporting the lift. The total mass involved is the sum of the mass of the person and the lift.

Given Data:

• Mass of the person, m_1 = 60\, \text{kg}
• Mass of the lift, m_2 = 940\, \text{kg}
• Acceleration of the lift, a = 1.0\, \text{m/s}^2
• Acceleration due to gravity, g = 10\, \text{m/s}^2

Steps to Calculate Tension:

1. Calculate the total mass of the system:
   M = m_1 + m_2 = 60 + 940 = 1000\, \text{kg}
2. Calculate the net force acting on the system using the equation for tension in the cable:
   T = M \cdot (g + a)
3. Substitute the values into the equation:
   T = 1000 \cdot (10 + 1) = 1000 \cdot 11 = 11000\, \text{N}

Therefore, the tension in the supporting cable is 11000 N.

Explanation:

The tension calculated accounts for both the gravitational force pulling the lift down and the additional force required to accelerate the lift upwards. The sum of these forces gives us the total force, which is the tension in the cable.

Conclusion:

The correct answer is 11000\, \text{N}, which corresponds to the correct choice from the provided options.