An elevator is run by the cables at constant speed . The total work done by the elevator is :

Options

A. negative
B. positive
C. zero
D. positive or negative depending on the direction of motion .

Explanation

To solve the problem of the total work done by the elevator running at constant speed, we can follow these steps:

### Step 1: Understand the scenario
The elevator is moving at a constant speed, which means that the velocity of the elevator does not change. This implies that there is no net acceleration acting on the elevator.

**Hint:** Remember that constant speed means no change in kinetic energy.

### Step 2: Apply the Work-Energy Theorem
According to the work-energy theorem, the total work done on an object is equal to the change in its kinetic energy. Since the elevator is moving at a constant speed, the change in kinetic energy (ΔK) is zero.

**Hint:** Work-Energy Theorem states that \( W_{total} = \Delta K \).

### Step 3: Calculate the total work done
Since the change in kinetic energy is zero, we can conclude that the total work done on the elevator is also zero:
\[ W_{total} = 0 \]

**Hint:** If there is no change in kinetic energy, the total work done must be zero.

### Step 4: Consider the forces acting on the elevator
The forces acting on the elevator include the tension in the cables (upward force) and the weight of the elevator (downward force). The work done by these forces must balance out since the elevator is moving at constant speed.

**Hint:** Think about how the forces interact when there is no acceleration.

### Step 5: Analyze the work done by each force
- If the elevator is moving upward, the work done by the tension in the cables is positive, while the work done by the weight (mg) is negative.
- If the elevator is moving downward, the work done by the weight is positive, while the work done by the tension is negative.

**Hint:** Work done is calculated as \( W = F \cdot d \cdot \cos(\theta) \), where \( \theta \) is the angle between the force and the direction of displacement.

### Conclusion
The total work done by the elevator is zero, but the work done by the tension and the work done by the weight will be equal in magnitude and opposite in direction, depending on the direction of motion.

**Final Answer:** The total work done by the elevator is **zero**.

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