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

Options

A. `30ms^(-2)` downwards
B. `4ms^(-2)` upwards
C. `4ms^(-2)` downwards
D. `14ms^(-2)` upwards

Explanation

To solve the problem of finding the acceleration of the lift, we can follow these steps:

### Step 1: Identify the forces acting on the lift
The two main forces acting on the lift are:
1. The tension (T) in the supporting cable, which acts upwards.
2. The weight (W) of the lift, which acts downwards.

The weight of the lift can be calculated using the formula:
\[ W = mg \]
where:
- \( m = 2000 \, \text{kg} \) (mass of the lift)
- \( g = 10 \, \text{m/s}^2 \) (acceleration due to gravity)

### Step 2: Calculate the weight of the lift
Using the values provided:
\[ W = 2000 \, \text{kg} \times 10 \, \text{m/s}^2 = 20000 \, \text{N} \]

### Step 3: Apply Newton's second law of motion
According to Newton's second law, the net force acting on the lift is equal to the mass of the lift multiplied by its acceleration (A):
\[ F_{\text{net}} = mA \]

The net force can also be expressed as the difference between the tension and the weight:
\[ F_{\text{net}} = T - W \]

### Step 4: Set up the equation
Substituting the expressions for net force, we have:
\[ T - W = mA \]

### Step 5: Substitute the known values
We know:
- \( T = 28000 \, \text{N} \)
- \( W = 20000 \, \text{N} \)
- \( m = 2000 \, \text{kg} \)

Substituting these values into the equation gives:
\[ 28000 \, \text{N} - 20000 \, \text{N} = 2000 \, \text{kg} \cdot A \]

### Step 6: Simplify the equation
This simplifies to:
\[ 8000 \, \text{N} = 2000 \, \text{kg} \cdot A \]

### Step 7: Solve for acceleration (A)
Now, divide both sides by 2000 kg:
\[ A = \frac{8000 \, \text{N}}{2000 \, \text{kg}} = 4 \, \text{m/s}^2 \]

### Step 8: Determine the direction of acceleration
Since the tension is greater than the weight, the acceleration is directed upwards.

### Final Answer:
The acceleration of the lift is \( 4 \, \text{m/s}^2 \) upwards.

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