2. A roller coaster goes through a 360 degree vertical circular loop, just barely making through the top of the loop without falling off the tracks. Draw a sketch of the roller coaster at the top of the loop and show the forces acting on it at that point. The net force in the radial direction acting on the roller coaster at the top of the loop must be the centripetal force keeping it moving around in a circular path. If the loop has a radius of 50 meters, what is the minimum velocity of the roller coaster at the top of the loop to ensure it maintains circular motion keeping it on the tracks at that point? If the roller coaster began at the top of a hill, then rolled down and entered the 360 degree vertical loop starting at the bottom of the hill, what is the minimum height of the initial hill to ensure that it has enough velocity at the top of the loop to match what you calculated in the above question. [hint: the hill will need to be taller than twice the radius of the loop since it will need to reach that height within the loop and still have enough velocity remaining to keep it moving around the circle staying on the tracks]