Physics Loop Question

[farnell]

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I'm having trouble understanding the concept of this practice problem.

A 1kg block slides down a ramp and then around a circular loop of radius 10m. If there is no friction, what is the minimum height of the ramp so that the block makes it all the way around the loop without falling?

While the answer is 25m in my book, what I don't understand is why the answer is not simply 20m. Assuming no friction, if the ramp is exactly 20m high, shouldn't all of the potential energy be converted into kinetic energy at the bottom, and then shouldn't this be enough to get the block back up to 20m (top of the loop) again?

Thanks in advance for the help

 

[milski]

Just getting to the top is not enough. You need the block to be moving fast enough at the top so that all the gravity force is needed to maintain the circular motion. That means that the magnitude of the acceleration is exactly mg at the top. But a=v^2/r=mg. Solve for v, from there you'll have how much kinetic energy you need at the top - that would be how much above the 20 m you want the object to start.