Question 1034274
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When an object moves in a circular path, the centripetal force F varies directly as the square of the velocity v and 
inversely as the radius r of the circle. 
If F=200 when v=6 and r=5, find F when v=4 and r=8.
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First statement is translated as 

F = {{{k*(v^2/r^2)}}}         (1)

with the constant k.


Next statement ". . . F=200 when v=6 and r=5" is translated as 

200 = {{{k*(6^2/5^2)}}}.      (2)  

(simply plug in your  data into the formula (1)). Simplify (2) to get

200 = {{{k*(36/25)}}}  and then obtain  k = {{{(200*25)/36}}} = {{{5000/36}}}.

Now "find F when v=4 and r=8."
Use the formula (1) and the value k = {{{5000/36}}}:

F = {{{(5000/36)*(4^2/8^2)}}} = {{{5000/(36*4)}}} = 34.72.
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