Question

The mass of a lift is $2000\, kg.$ When the tension in the supporting cable is $28000\, N,$ then its acceleration is

• A. $4\, ms^{-2} $ upwards
• B. $4\, ms^{-2}$ downwards
• C. $14\, ms^{-2}$ upwards
• D. $30\, ms^{-2}$ downwards

Answer 1

The Correct Option is A

 To find the acceleration of the lift, we need to use Newton's second law of motion, which states that the net force acting on an object is equal to the product of its mass and its acceleration. The formula can be expressed as:

\[ F_{\text{net}} = m \cdot a \]

Where:

• \(F_{\text{net}}\) is the net force acting on the lift.
• \(m\) is the mass of the lift.
• \(a\) is the acceleration of the lift.

 

Let's consider the forces acting on the lift:

• The lift has a weight force acting downwards, which can be calculated as \(W = m \cdot g = 2000\, \text{kg} \cdot 9.8\, \text{m/s}^2 = 19600\, \text{N}\).
• The tension in the cable, which is \(28000\, \text{N}\), acts upwards.

The net force acting on the lift is given by the difference between the upward tension and the downward gravitational force (weight):

\[ F_{\text{net}} = T - W = 28000\, \text{N} - 19600\, \text{N} = 8400\, \text{N} \]

Using the net force, we can find the acceleration of the lift using the formula:

\[ a = \frac{F_{\text{net}}}{m} = \frac{8400\, \text{N}}{2000\, \text{kg}} = 4\, \text{m/s}^2 \]

Therefore, the acceleration of the lift is \(4\, \text{m/s}^2\) upwards.

Thus, the correct answer is: \(4\, \text{ms}^{-2}\)upwards.