A box is pushed through 4.0 m across floor offering 100 N resistance.How much work is done by the resisting force?

Explanation

To solve the problem of how much work is done by the resisting force when a box is pushed through a distance of 4.0 m against a resistance of 100 N, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Given Values**:
- Displacement (d) = 4.0 m
- Resistance Force (F) = 100 N

2. **Understand the Direction of Forces**:
- The box is pushed in one direction (let's say to the right), and the resisting force acts in the opposite direction (to the left).

3. **Determine the Angle Between the Force and Displacement**:
- Since the resisting force acts in the opposite direction to the displacement, the angle (θ) between the resisting force and the displacement is 180 degrees.

4. **Use the Work Done Formula**:
- The work done (W) by a force is given by the formula:
\[ W = F \cdot d \cdot \cos(\theta) \]
- Here, \(F\) is the magnitude of the resisting force, \(d\) is the displacement, and \(\theta\) is the angle between the force and the direction of displacement.

5. **Substitute the Values into the Formula**:
- Since \(\cos(180^\circ) = -1\), we can substitute the values:
\[ W = 100 \, \text{N} \cdot 4.0 \, \text{m} \cdot \cos(180^\circ) \]
\[ W = 100 \, \text{N} \cdot 4.0 \, \text{m} \cdot (-1) \]

6. **Calculate the Work Done**:
- Now, calculate the work done:
\[ W = 100 \cdot 4.0 \cdot (-1) = -400 \, \text{J} \]

7. **Conclusion**:
- The work done by the resisting force is \(-400 \, \text{J}\).

### Final Answer:
The work done by the resisting force is \(-400 \, \text{J}\).

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