To calculate the work done when a force is applied at an angle, we can use the formula:
\[ \text{Work} = F \cdot d \cdot \cos(\theta) \]
where:
- \( F \) is the force applied (in newtons),
- \( d \) is the distance moved (in meters),
- \( \theta \) is the angle between the force and the direction of motion.
Given:
- \( F = 115 , \text{N} \)
- \( d = 1600 , \text{m} \)
- \( \theta = 25^\circ \)
Now, we plug the values into the equation. First, calculate \( \cos(25^\circ) \).
Using a calculator:
\[ \cos(25^\circ) \approx 0.9063 \]
Now, substituting the values into the work formula:
\[ \text{Work} = 115 , \text{N} \cdot 1600 , \text{m} \cdot \cos(25^\circ) \] \[ \text{Work} = 115 , \text{N} \cdot 1600 , \text{m} \cdot 0.9063 \] \[ \text{Work} \approx 115 \cdot 1600 \cdot 0.9063 \] \[ \text{Work} \approx 115 \cdot 1450.08 \] \[ \text{Work} \approx 166.056 , \text{J} \]
Now we complete the calculation:
\[ \text{Work} \approx 166,056 , \text{J} \approx 167,000 \]
Therefore, the work done is approximately:
\[ \text{Work} \approx 166,056 , \text{J} \]
Thus, the final answer is:
\[ \text{Work} \approx 166,000 , \text{J} \text{ (or 166 kJ)} \]
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