An elevator weighing 6000 kg is pulled upward by a cable with an acceleration of `5ms^(-2)` . Taking g to be `10 ms^(-2)` , then the tension in the cable is

Options

A. 6000 N
B. 9000 N
C. 60000 N
D. 90000 N

Answer

To find the tension in the cable pulling the elevator upward, we can use Newton's second law of motion. Here are the steps to solve the problem:

### Step 1: Identify the known values
- Mass of the elevator (m) = 6000 kg
- Acceleration due to gravity (g) = 10 m/s²
- Acceleration of the elevator (a) = 5 m/s²

### Step 2: Calculate the weight of the elevator
The weight (W) of the elevator can be calculated using the formula:
\[ W = m \cdot g \]
Substituting the known values:
\[ W = 6000 \, \text{kg} \cdot 10 \, \text{m/s}^2 = 60000 \, \text{N} \]

### Step 3: Apply Newton's second law
According to Newton's second law, the net force (F_net) acting on the elevator is given by:
\[ F_{\text{net}} = T - W \]
Where:
- T is the tension in the cable
- W is the weight of the elevator

Since the elevator is accelerating upward, we can express the net force as:
\[ F_{\text{net}} = m \cdot a \]

### Step 4: Set up the equation
Combining the equations, we have:
\[ T - W = m \cdot a \]
Substituting the values we have:
\[ T - 60000 \, \text{N} = 6000 \, \text{kg} \cdot 5 \, \text{m/s}^2 \]

### Step 5: Calculate the right side
Calculating the right side:
\[ 6000 \, \text{kg} \cdot 5 \, \text{m/s}^2 = 30000 \, \text{N} \]

### Step 6: Solve for Tension (T)
Now we can substitute this back into the equation:
\[ T - 60000 \, \text{N} = 30000 \, \text{N} \]
Adding 60000 N to both sides gives:
\[ T = 30000 \, \text{N} + 60000 \, \text{N} \]
\[ T = 90000 \, \text{N} \]

### Step 7: Convert to kilonewtons
To express the tension in kilonewtons:
\[ T = 90000 \, \text{N} = 90 \, \text{kN} \]

### Final Answer
The tension in the cable is **90 kN**.

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