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 applied force,
- \( d \) is the distance moved in the direction of the force,
- \( \theta \) is the angle between the force and the direction of movement.
Given:
- \( F = 115 , N \)
- \( d = 1,600 , m \)
- \( \theta = 25^\circ \)
First, we need to calculate \( \cos(25^\circ) \):
\[ \cos(25^\circ) \approx 0.9063 \quad (\text{using a calculator}) \]
Now, plug in the values into the work formula:
\[ \text{Work} = 115 , N \times 1,600 , m \times \cos(25^\circ) \] \[ \text{Work} = 115 , N \times 1,600 , m \times 0.9063 \] \[ \text{Work} \approx 115 \times 1,600 \times 0.9063 \] \[ \text{Work} \approx 166,761.12 , J \]
Rounding it to the nearest whole number:
\[ \text{Work} \approx 166,761 , J \]
Thus, the work done is approximately 166,761 J.
The correct answer from the given choices is 166,761 J.
1 answer