Work done by a frictional force is

Options

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

Answer

To determine the work done by a frictional force, we need to analyze the scenarios in which friction acts on an object. Here’s a step-by-step solution:

### Step 1: Understanding Work Done
Work done (W) is defined as the product of the force (F) applied on an object and the displacement (d) of that object in the direction of the force. Mathematically, it is given by:
\[ W = F \cdot d \cdot \cos(\theta) \]
where \(\theta\) is the angle between the force and the direction of displacement.

### Step 2: Analyzing the Case of Static Friction
When an object is at rest and a force is applied but does not overcome static friction, the object does not move. In this case:
- Displacement (d) = 0
- Therefore, work done by friction (W_friction) = 0.

### Step 3: Analyzing the Case of Kinetic Friction
When the applied force exceeds the static friction, the object starts to move. The frictional force now acts in the opposite direction to the displacement. In this case:
- Displacement (d) > 0
- The angle \(\theta\) between the frictional force and displacement is 180 degrees (since they are in opposite directions).
- Therefore, work done by friction (W_friction) = F_friction * d * cos(180°) = -F_friction * d, which is negative.

### Step 4: Considering Different Scenarios
1. **Static Case**: Work done by friction = 0 (object not moving).
2. **Kinetic Case**: Work done by friction = negative (object moving against friction).
3. **Friction on an Upper Block**: If friction acts on an upper block in the same direction as its displacement, then:
- Work done by friction = positive.

### Conclusion
From the analysis, we can conclude that the work done by a frictional force can be:
- Zero (when the object is at rest),
- Negative (when the object is moving against the friction),
- Positive (when friction acts in the direction of displacement).

Thus, the correct answer is that the work done by a frictional force may be positive, negative, or zero.

### Final Answer
The work done by a frictional force is: **Maybe positive, negative, or zero.**

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