Josh Builds a \"loop of death\" in his backyard for his skateboard. The radius o

Question

Josh Builds a "loop of death" in his backyard for his skateboard. The radius of loop is 2.35m and it is sitting on the ground. Josh build a ramp that is connected to the roof of his house. To test the ramp out, Josh convinces Shayan to ride the loop. Shayan hops on the skateboard and leaves the top of the roof with almost no initial velocity. While visiting Shayan in the hospital, Josh decides to recheck his calculations. What is the minimum height that his ramp should have so that someone could make it all the way around the loop? Assume his skateboard loses no energy when it is rolling.

Explanation / Answer

First we use centripetal motion. At the top of the loop, the centripetal force would be force of gravity and normal force, but the normal force is about 0, assuming the speed to be just enough to get around. so mg=mv^2/r v^2 = gr v= 4.79 m/s Now we will use work/energy. At the top, it is all potential energy. Now at the top of the loop, we will make that all kinetic energy, but only for this equation. PE = mgh where h is the distance from top of the loop to the roof KE=.5mv^2 at top of loop mgh=.5mv^2 h=(.5)(4.79^2)/9.8 h= 1.17 meters from top of loop to roof The diameter is 2 x radius, or 4.7 m so 4.7 + 1.17 = 5.87 m is height of ramp

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