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

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.

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((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