Problem Statement:

We are tasked with calculating the work done by a person who exerts 450 N of force while carrying goods at a 50° angle and traveling a distance of 110 feet. The person weighs 115 lbs. However, the person's weight is not needed to solve the problem, as the focus is on the force exerted and the distance traveled.

Formula for Work:

The work $W$ done by a force is calculated by the formula:

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

Where:

• $W$ is the work done (in joules),
• $F$ is the force applied (in newtons),
• $d$ is the distance traveled (in meters),
• $\theta$ is the angle between the force and the direction of motion (in degrees).

Given:

• Force applied $F = 450 \, \text{N}$,
• Distance traveled $d = 110 \, \text{feet}$,
• Angle $\theta = 50^\circ$.

Step 1: Conversion of distance to meters:

We need to convert the distance from feet to meters. The conversion factor is:

$1 \, \text{foot} = 0.3048 \, \text{meters}$

So,

$d = 110 \, \text{feet} \times 0.3048 \, \frac{\text{meters}}{\text{foot}} = 33.528 \, \text{meters}$

Step 2: Calculate the work done:

Now that we have the distance in meters, we can substitute the values into the work formula:

$W = 450 \, \text{N} \times 33.528 \, \text{m} \times \cos(50^\circ)$

We'll calculate the cosine of $50^\circ$ and then the work:

$\cos(50^\circ) \approx 0.6428$

Now,

$W = 450 \, \text{N} \times 33.528 \, \text{m} \times 0.6428$

$W \approx 450 \times 33.528 \times 0.6428$

$W \approx 9674.36 \, \text{Joules}$

Final Answer:

The work done by the person is approximately:

$\boxed{9674.36 \, \text{Joules} \, (\text{J})}$

This is the amount of work done in moving the goods under the specified conditions.

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Do you need further details or clarifications? Here are 5 follow-up questions:

1. How does the angle of force affect the work done?
2. How would the work change if the angle increased or decreased?
3. What is the importance of converting units to SI units in physics problems?
4. How does force differ from work in physical terms?
5. What would happen if the person applied the force vertically instead of at an angle?

Tip: Always ensure that all units are converted to the correct SI units before performing calculations in physics.