QuestionJune 9, 2025

An object is pulled along the ground by exerting a force of 25 pounds a rope that makes a 25^circ angle with the ground. How much work is done dragging the object 31 feet? foot-pounds

An object is pulled along the ground by exerting a force of 25 pounds a rope that makes a 25^circ angle with the ground. How much work is done dragging the object 31 feet? foot-pounds
An object is pulled along the ground by exerting a force
of 25 pounds a rope that makes a 25^circ  angle with the
ground. How much work is done dragging the object 31
feet?
foot-pounds

Solution
4.4(317 votes)

Answer

701.5 foot-pounds Explanation 1. Identify the force component parallel to the ground The work done is calculated using the force component parallel to the direction of movement. Use **F_{\text{parallel}} = F \cdot \cos(\theta)** where F = 25 pounds and \theta = 25^\circ. Thus, F_{\text{parallel}} = 25 \cdot \cos(25^\circ). 2. Calculate the work done Work is given by **W = F_{\text{parallel}} \cdot d**, where d = 31 feet. Substitute F_{\text{parallel}} from Step 1 to find W = 25 \cdot \cos(25^\circ) \cdot 31.

Explanation

1. Identify the force component parallel to the ground<br /> The work done is calculated using the force component parallel to the direction of movement. Use **$F_{\text{parallel}} = F \cdot \cos(\theta)$** where $F = 25$ pounds and $\theta = 25^\circ$. Thus, $F_{\text{parallel}} = 25 \cdot \cos(25^\circ)$.<br /><br />2. Calculate the work done<br /> Work is given by **$W = F_{\text{parallel}} \cdot d$**, where $d = 31$ feet. Substitute $F_{\text{parallel}}$ from Step 1 to find $W = 25 \cdot \cos(25^\circ) \cdot 31$.
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