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 find the work done by the resisting force when a box is pushed across a floor, we can follow these steps:

### Step-by-Step Solution:

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

2. **Understand the Concept of Work Done**:
- Work done (W) by a force is given by the formula:
\[ W = F \cdot d \cdot \cos(\theta) \]
- Where:
- \(W\) is the work done,
- \(F\) is the force applied,
- \(d\) is the displacement,
- \(\theta\) is the angle between the force and the direction of displacement.

3. **Determine the Angle**:
- In this case, the resisting force acts in the opposite direction to the displacement of the box. Therefore, the angle \(\theta\) is 180 degrees.

4. **Calculate the Cosine of the Angle**:
- The cosine of 180 degrees is:
\[ \cos(180^\circ) = -1 \]

5. **Substitute the Values into the Work Done Formula**:
- Now, we can substitute the values into the work done formula:
\[ W = F \cdot d \cdot \cos(\theta) = 100 \, \text{N} \cdot 4.0 \, \text{m} \cdot (-1) \]

6. **Perform the Calculation**:
- 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 \(-400 \, \text{J}\).