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

Options

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

Answer

To solve the problem, we need to find the acceleration of the lift when the tension in the supporting cable is given. Here are the steps to arrive at the solution:

### Step 1: Identify the known values
- Mass of the lift (m) = 2000 kg
- Tension in the cable (T) = 28000 N
- Acceleration due to gravity (g) = 10 m/s² (standard value)

### Step 2: Calculate the weight of the lift
The weight (W) of the lift can be calculated using the formula:
\[ W = m \cdot g \]
Substituting the values:
\[ W = 2000 \, \text{kg} \cdot 10 \, \text{m/s}^2 = 20000 \, \text{N} \]

### Step 3: Apply Newton's Second Law of Motion
According to Newton's second law, the net force (F_net) acting on the lift is equal to the mass of the lift multiplied by its acceleration (a):
\[ F_{\text{net}} = m \cdot a \]

### Step 4: Determine the net force acting on the lift
The net force can be determined by subtracting the weight of the lift from the tension in the cable:
\[ F_{\text{net}} = T - W \]
Substituting the values:
\[ F_{\text{net}} = 28000 \, \text{N} - 20000 \, \text{N} = 8000 \, \text{N} \]

### Step 5: Calculate the acceleration of the lift
Now, we can use the net force to find the acceleration:
\[ F_{\text{net}} = m \cdot a \]
Rearranging the formula to solve for acceleration (a):
\[ a = \frac{F_{\text{net}}}{m} \]
Substituting the values:
\[ a = \frac{8000 \, \text{N}}{2000 \, \text{kg}} = 4 \, \text{m/s}^2 \]

### Conclusion
The acceleration of the lift is \( 4 \, \text{m/s}^2 \) in the upward direction.

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