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**1. Homework Statement**

A small toy car slides down an elaborate track. At one point during this trip, the car will go around a vertical loop with radius 15cm as shown. What is the minimum speed the car must have at the bottom of the loop in order to make it all the way around the loop without falling off?

**2. Homework Equations**

K

_{i}+ U

_{i}+ W

_{NC}= K

_{f}+ U

_{f}

K = (1/2)mv

^{2}

U

_{i}= mgh

W = Fdcosx

F = ma

a

_{c}= v

^{2}/r

**3. The Attempt at a Solution**

I tried using the work-energy theorem, using (1/2)mv

^{2}= mgh to find the velocity needed for the car to have zero potential energy at the top of the loop, but I know this problem also involves centripetal acceleration and that the car would also need to have some velocity at the top of the loop to finish going around it (zero velocity would cause it to fall downward), but I have no clue how to use this to solve the problem

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