Work done by frictional force

Options

A. Is always negative
B. Is always positive
C. Is zero
D. May be positive, negative or zero

Answer

To determine the work done by the frictional force, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Work Done**:
Work done (W) is defined as the dot product of force (F) and displacement (d). Mathematically, it can be expressed as:
\[ W = F \cdot d = F \times d \times \cos(\theta) \]
where \(\theta\) is the angle between the force and the direction of displacement.

2. **Identifying the Forces**:
In this scenario, we have a body on a rough surface. When a force is applied to move the body, it experiences a frictional force acting in the opposite direction of the applied force.

3. **Direction of Forces and Displacement**:
Let’s assume the applied force \(F\) is in the positive x-direction and the displacement \(d\) is also in the positive x-direction. The frictional force \(f\) acts in the negative x-direction.

4. **Determining the Angle \(\theta\)**:
Since the frictional force acts in the opposite direction to the displacement, the angle \(\theta\) between the frictional force and the displacement is:
\[ \theta = 180^\circ \]

5. **Calculating Work Done by Friction**:
Substituting the values into the work done formula:
\[ W = f \times d \times \cos(180^\circ) \]
We know that \(\cos(180^\circ) = -1\), so:
\[ W = f \times d \times (-1) = -f \times d \]
This indicates that the work done by the frictional force is negative.

6. **Conclusion**:
The negative sign indicates that the work done by the frictional force is always negative, as it opposes the motion of the body. Therefore, the work done by the frictional force is:
\[ W = -f \times d \]

### Final Answer:
The work done by the frictional force is negative.

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