Rotational Motion Speed at the top of the loop

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To find the speed of a motorcycle at the top of a vertical loop with a radius of 12 m, where the normal force is one-fourth of the driver's weight, the relevant equations include F=ma and a=v²/r. The calculation involves setting the net force equal to the difference between the centripetal force and the weight of the driver. The derived equation leads to a speed of 9.4 m/s, which matches the correct answer choice. This solution highlights the importance of understanding forces in rotational motion.
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Homework Statement



12. A motorcycle travels around a vertical 12 m radius loop. What is its speed at the top of the loop if the normal force exerted by the seat on the driver is equal to ¼ of his weight?

a. 7 m/s

b. 8.1 m/s

*c. 9.4 m/s

d. 15 m/s

e. 88 m/s

Homework Equations



F=ma
W=mg
T=F-W
a=v2/r

The Attempt at a Solution



I did (1/4)W=m(v2/r)-W and I got 12.1 m/s
 
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I get the same answer as you.
 

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