What is the minimum height of the "hill" in order to ensure that this happens?
You are building a display for a children's science museum in which a uniform, solid sphere of radius 0.199 m starts at rest at the top of a "hill" and rolls, without slipping, down a track and around a loop-the-loop of radius R = 1.66 m. You have already determined that the ball has to be moving at a speed no less than 3.79 m/s at the top of the loop in order to make it around the loop without falling.
Note: You should consider whether the ball will be above or below the track at the top of the loop.
What is the minimum height of the "hill" in order to ensure that this happens?
The loop on the bottom part of the track has a radius of 1.66m, so that means that the top of loop is 3.32m above the ground, so the value for h has to be more than 3.32m since it is above the top of the loop. The calculation needs to be done for the center of mass of the ball which will be below the track at the top of the loop.
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