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 nature of the work done by the frictional force, we can analyze different scenarios. Here’s a step-by-step breakdown of the solution:

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

### Step 2: Analyzing Different Scenarios
We will consider three different scenarios to analyze the work done by the frictional force.

#### Scenario 1: Positive Work Done
- **Example**: A person walking on a road.
- **Analysis**: In this case, the frictional force acts in the same direction as the displacement (forward). Therefore, the work done by the frictional force is positive.
\[ W = F_{\text{friction}} \cdot d \cdot \cos(0^\circ) = F_{\text{friction}} \cdot d \]
- **Conclusion**: Work done is positive.

#### Scenario 2: Negative Work Done
- **Example**: A block being pulled across a table.
- **Analysis**: Here, the frictional force acts in the opposite direction to the displacement. Thus, the work done by the frictional force is negative.
\[ W = F_{\text{friction}} \cdot d \cdot \cos(180^\circ) = -F_{\text{friction}} \cdot d \]
- **Conclusion**: Work done is negative.

#### Scenario 3: Zero Work Done
- **Example**: A block on a surface where the applied force is exactly balancing the weight.
- **Analysis**: If the applied force at an angle results in no normal force (for instance, if the force is vertical and equal to the weight), the frictional force becomes zero. Therefore, the work done by the frictional force is zero.
\[ W = 0 \]
- **Conclusion**: Work done is zero.

### Step 3: Conclusion
From the analysis of these scenarios, we can conclude that the work done by the frictional force can be:
- Positive (when friction assists motion),
- Negative (when friction opposes motion),
- Zero (when there is no frictional force).

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

### Final Answer
**D: The work done by the frictional force may be positive, negative, or zero.**

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