QuestionAugust 4, 2025

8. (7 points)A tree stump is dragged 30 m by a truck with a chain at 31^circ above horizontal and tension of 17 ,000 N. Find the work done. Round to the nearest N m.

8. (7 points)A tree stump is dragged 30 m by a truck with a chain at 31^circ above horizontal and tension of 17 ,000 N. Find the work done. Round to the nearest N m.
8. (7 points)A tree stump is dragged 30 m by a truck with a chain at 31^circ above horizontal and tension of 17 ,000 N. Find the work done. Round to the nearest N m.

Solution
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Answer

437,244 N m Explanation 1. Identify the formula for work Work is calculated using W = F \cdot d \cdot \cos(\theta), where F is force, d is distance, and \theta is the angle. 2. Substitute values into the formula Given F = 17,000 \, \text{N}, d = 30 \, \text{m}, and \theta = 31^{\circ}, substitute these into the formula: W = 17,000 \cdot 30 \cdot \cos(31^{\circ}). 3. Calculate cosine of the angle \cos(31^{\circ}) \approx 0.8572. 4. Compute the work done W = 17,000 \cdot 30 \cdot 0.8572 = 437,244 \, \text{N m}.

Explanation

1. Identify the formula for work<br /> Work is calculated using $W = F \cdot d \cdot \cos(\theta)$, where $F$ is force, $d$ is distance, and $\theta$ is the angle.<br />2. Substitute values into the formula<br /> Given $F = 17,000 \, \text{N}$, $d = 30 \, \text{m}$, and $\theta = 31^{\circ}$, substitute these into the formula: $W = 17,000 \cdot 30 \cdot \cos(31^{\circ})$.<br />3. Calculate cosine of the angle<br /> $\cos(31^{\circ}) \approx 0.8572$.<br />4. Compute the work done<br /> $W = 17,000 \cdot 30 \cdot 0.8572 = 437,244 \, \text{N m}$.
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