Solve the problem
-A force of 5 pounds acts in the direction of $9 ^ { \circ }$ to the horizontal. The force moves an object along a straight line from the point $( 9,3 )$ to the point $( 18,13 )$, with distance measured in feet. Find the work done by the force. Round the answer to one decimal place, if necessary.
A) $66.4 \mathrm { ft } - \mathrm { lb }$
B) $67.3 \mathrm { ft } - \mathrm { lb }$
C) $13.3 \mathrm { ft } - \mathrm { lb }$
D) $93.8 \mathrm { ft } - \mathrm { lb }$

Question

Quizplus · Accepted Answer

The work done by a force is given by the formula $W = Fd\cos(\theta)$, where $W$ is the work done, $F$ is the magnitude of the force, $d$ is the distance moved by the object, and $\theta$ is the angle between the force direction and the direction of motion. First, calculate the distance between the two points using the distance formula: $d = \sqrt{(18-9)^2 + (13-3)^2} = \sqrt{9^2 + 10^2} = \sqrt{181} \approx 13.5 \, \text{ft}$. Then, calculate the work done: $W = 5 \times 13.5 \times \cos(9^\circ) \approx 66.4 \, \text{ft-lb}$, rounding to one decimal place.

Solve the Problem -A Force of 5 Pounds Acts in the Direction

Solve the Problem
-A Force of 5 Pounds Acts in the Direction