Question

Find the work done by a force F of 21 pounds acting in the direction <2,5> in moving an object 7 feet from (0,0) to (7,0).

Answer 1

Answer:

Work done, W =  54.59 foot-pounds

Step-by-step explanation:

It is given that,

Force, F = 21 pounds

From the figure it is clear that,

$cos\theta =\dfrac{2}{\sqrt{29} }$

Distance, d = 7 feet

Work done is given that,

$W=Fdcos\theta$

$W=21\times \dfrac{2}{\sqrt{29}}\times 7$

W = 54.59 foot-pounds

So, the correct option is (A).

Hence, this is the required solution.

Answer 2

Please find the attachment for a better understanding of the solution provided here.

We have been asked to find the work done by a force F of 21 pounds acting in the direction <2,5> in moving an object 7 feet from (0,0) to (7,0).

As we can see clearly from the question above that the object moves exclusively in the direction of the x axis and thus, the component of the force acting is only the x component. So, our main aim will be to find the x component of the force. Once it is found we will simply multiply it with the distance travelled in the x axis to find the work done as asked in the question.

Let us call the x component of the force as $F_{x}$.

From the diagram in the attachment, we can see that the $\angle BAC=\arctan(\frac{5}{2})=68.2$ degrees

Thus, $F_{x}=21 cos(68.2)=7.799$feet

$F_{x}=54.593$feet-pound

Thus, A is the correct option