To calculate the work done, we use the formula:

$W = F \cdot d \cdot \cos(\theta)$

where:

• $W$ is the work done,
• $F$ is the applied force (500 N),
• $d$ is the displacement (4.00 m),
• $\theta$ is the angle between the force and the direction of motion (45.0°),
• $\cos(\theta)$ accounts for the fact that the force is applied at an angle.

Let's calculate it:

$W = 500 \, \text{N} \times 4.00 \, \text{m} \times \cos(45.0^\circ)$

Since $\cos(45^\circ) = \frac{1}{\sqrt{2}} \approx 0.707$, we can plug in the values:

$W = 500 \times 4 \times 0.707$

Let me compute that.The work done is approximately $1414.2 \, \text{J}$ (Joules).

Would you like more details or have any questions? Here are some related questions:

1. How is the formula for work derived from basic physics principles?
2. What is the difference between work done at an angle and along a straight path?
3. How would the work change if the angle was 90°?
4. What are some real-world examples where work is done at an angle?
5. Can work be negative, and in what cases would that happen?

Tip: When calculating work, always ensure the force is in the direction of motion, or use the cosine of the angle between the force and the displacement to adjust.