Question
A suitcase is pulled 20 feet along a flat sidewalk with a constant upward force of 80 lb at an angle of \( 23^{\circ} \) with the horizontal. Calculate the work done. The work done is \( \square \) foot-pounds. (Round to the nearest foot-pound as needed.)
Ask by Luna Coleman. in the United States
Feb 03,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The work done is approximately 1473 foot-pounds.
Solution
To calculate the work done when pulling the suitcase, we use the formula:
\[
\text{Work} = F \cdot d \cdot \cos(\theta)
\]
where:
- \( F = 80 \) lb (the force applied)
- \( d = 20 \) feet (the displacement)
- \( \theta = 23^\circ \) (the angle of the force above the horizontal)
First, calculate the horizontal component of the force:
\[
F_{\text{horizontal}} = F \cdot \cos(\theta) = 80 \cdot \cos(23^\circ)
\]
Using \(\cos(23^\circ) \approx 0.9205\):
\[
F_{\text{horizontal}} \approx 80 \cdot 0.9205 = 73.64 \text{ lb}
\]
Now, calculate the work done:
\[
\text{Work} = F_{\text{horizontal}} \cdot d = 73.64 \cdot 20 = 1472.8 \text{ foot-pounds}
\]
Rounded to the nearest foot-pound:
\[
\text{Work} \approx 1473 \text{ foot-pounds}
\]
**Answer:** 1473 foot-pounds
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Simplify this solution Mind Expander
To calculate the work done, we use the formula: \[ \text{Work} = \text{Force} \times \text{Distance} \times \cos(\theta) \] In this scenario, the force is 80 lb, the distance is 20 feet, and \(\theta\) (the angle with respect to the horizontal) is \(23^{\circ}\). First, we find the component of the force that acts in the direction of the distance: \[ \text{Work} = 80 \, \text{lb} \times 20 \, \text{ft} \times \cos(23^{\circ}) \] Calculating \(\cos(23^{\circ})\) approximately gives us 0.920. Now, substituting the values: \[ \text{Work} \approx 80 \times 20 \times 0.920 \approx 1472 \, \text{foot-pounds} \] Thus, the work done is approximately \( \text{1472} \) foot-pounds.
