A person pulls a sledge for a distance of 35.0 m along the snow with a rope directed `25.0^(@)` above the snow. The tension in the rope is 94.0 N. How much work is done on the sledge by the tension force ?

Options

A. 1390J
B. 2740J
C. 2980J
D. 3290J

Answer

To find the work done on the sledge by the tension force, we can use the formula for work done, which is given by:

\[ W = F \cdot d \cdot \cos(\theta) \]

Where:
- \( W \) is the work done,
- \( F \) is the force applied (in this case, the tension in the rope),
- \( d \) is the distance over which the force is applied,
- \( \theta \) is the angle between the force and the direction of motion.

### Step-by-step Solution:

1. **Identify the Given Values:**
- Tension in the rope, \( F = 94.0 \, \text{N} \)
- Distance pulled, \( d = 35.0 \, \text{m} \)
- Angle above the horizontal, \( \theta = 25.0^\circ \)

2. **Calculate the Work Done:**
- We need to find the horizontal component of the tension force, which is given by:
\[ F_{\text{horizontal}} = F \cdot \cos(\theta) = 94.0 \cdot \cos(25^\circ) \]
- Now, calculate \( \cos(25^\circ) \):
\[ \cos(25^\circ) \approx 0.9063 \]
- Therefore, the horizontal component of the force is:
\[ F_{\text{horizontal}} = 94.0 \cdot 0.9063 \approx 85.2 \, \text{N} \]

3. **Substitute into the Work Formula:**
- Now, substitute \( F_{\text{horizontal}} \) into the work formula:
\[ W = F_{\text{horizontal}} \cdot d = 85.2 \cdot 35.0 \]
- Calculate the work done:
\[ W \approx 2982 \, \text{J} \]

### Final Answer:
The work done on the sledge by the tension force is approximately **2982 Joules**.