If the tension in the cable of 1000 kg elevator is 1000 kg weight, the elevator

Options

A. Is accelerating upwards
B. Is accelerating downwards
C. May be at rest or accelerating
D. May be at rest or in uniform motion

Answer

To solve the problem, we need to analyze the forces acting on the elevator and determine its state of motion based on the given information.

### Step-by-Step Solution:

1. **Identify the Weight of the Elevator:**
The weight (W) of the elevator can be calculated using the formula:
\[ W = m \cdot g \]
where \( m = 1000 \, \text{kg} \) (mass of the elevator) and \( g = 10 \, \text{m/s}^2 \) (acceleration due to gravity).
\[ W = 1000 \, \text{kg} \cdot 10 \, \text{m/s}^2 = 10000 \, \text{N} \]

2. **Identify the Tension in the Cable:**
The tension (T) in the cable is given as:
\[ T = 1000 \, \text{kg} \cdot g = 1000 \, \text{N} \]

3. **Set Up the Equation of Motion:**
Since the elevator is subject to two forces: the weight (downward) and the tension (upward), we can write the equation of motion:
\[ T - W = m \cdot a \]
where \( a \) is the acceleration of the elevator.

4. **Substitute the Known Values:**
Substitute \( T \) and \( W \) into the equation:
\[ 1000 \, \text{N} - 10000 \, \text{N} = 1000 \, \text{kg} \cdot a \]
Simplifying this gives:
\[ -9000 \, \text{N} = 1000 \, \text{kg} \cdot a \]

5. **Solve for Acceleration (a):**
\[ a = \frac{-9000 \, \text{N}}{1000 \, \text{kg}} = -9 \, \text{m/s}^2 \]
The negative sign indicates that the acceleration is directed downward, meaning the elevator is accelerating downwards.

6. **Determine the State of the Elevator:**
Since the tension in the cable is less than the weight of the elevator, the elevator cannot be at rest or moving with uniform velocity. Instead, it is accelerating downwards.

### Conclusion:
The elevator is accelerating downwards.