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coldgirl [10]
4 years ago
13

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).

Mathematics
2 answers:
Rus_ich [418]4 years ago
8 0

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.

sertanlavr [38]4 years ago
4 0

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)=7.799feet

F_{x}=54.593feet-pound

Thus, A is the correct option

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