The problem provided involves calculating the work done when a suitcase is pulled along a flat sidewalk. Let's break down the given information:

• The suitcase is pulled 25 feet.
• The constant force applied is 10 pounds.
• The angle at which the force is applied with respect to the horizontal is 75°.

Formula for Work Done

The work done $W$ by a force is calculated using the formula: $W = F \times d \times \cos(\theta)$ where:

• $F$ is the magnitude of the force (10 pounds),
• $d$ is the distance over which the force is applied (25 feet),
• $\theta$ is the angle between the force and the direction of motion (75°),
• $\cos(\theta)$ is the cosine of the angle, which accounts for the direction of the force relative to the direction of motion.

Calculation

1. Calculate $\cos(75^\circ)$: $\cos(75^\circ) \approx 0.2588$

2. Compute the work done: $W = 10 \times 25 \times 0.2588$ $W \approx 64.7 \text{ foot-pounds}$

Rounding to the nearest foot-pound: $W \approx 65 \text{ foot-pounds}$

The work done is 65 foot-pounds.

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Do you want further details or have any other questions?

Here are some related questions:

1. What would the work done be if the angle was 0° instead of 75°?
2. How does the angle affect the amount of work done?
3. What happens to the work done if the force applied is doubled?
4. How would the work change if the distance was halved?
5. What if the surface wasn't flat, how would that affect the calculation?

Tip: When dealing with forces at an angle, always remember to use the cosine of the angle to find the component of the force that actually does work in the direction of motion.