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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).

Find the work done by a force F of 21 pounds acting in the direction <2,5> in-example-1
User Jammycakes
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2 Answers

4 votes

Answer:

Work done, W = 54.59 foot-pounds

Explanation:

It is given that,

Force, F = 21 pounds

From the figure it is clear that,


cos\theta =(2)/(√(29) )

Distance, d = 7 feet

Work done is given that,


W=Fdcos\theta


W=21* (2)/(√(29))* 7

W = 54.59 foot-pounds

So, the correct option is (A).

Hence, this is the required solution.

Find the work done by a force F of 21 pounds acting in the direction <2,5> in-example-1
User Prmottajr
by
8.2k points
1 vote

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((5)/(2))=68.2 degrees

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


F_(x)=54.593feet-pound

Thus, A is the correct option

Find the work done by a force F of 21 pounds acting in the direction <2,5> in-example-1
User Matkins
by
8.3k points

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