Consider a circular roller coaster loop of radius 11.9 m. You already know that

Question

1. Consider a circular roller coaster loop of radius 11.9 m. You already know that if the car starts from a height of 2.5 r at rest, the normal force acting on the car at the top will vanish.
   
   
   Now assume the car starts from a level track, a height of 11.9 m above the ground. The track first guides the car to ground level and then into the loop. At which initial speed must the car move on the elevated track (height 11.9 m) such that it still has the required speed at the top of the loop for the normal force to vanish?
   

Consider a circular roller coaster loop of radius 11.9 m. You already know that if the car starts from a height of 2.5 r at rest, the normal force acting on the car at the top will vanish.


Now assume the car starts from a level track, a height of 11.9 m above the ground. The track first guides the car to ground level and then into the loop. At which initial speed must the car move on the elevated track (height 11.9 m) such that it still has the required speed at the top of the loop for the normal force to vanish?
Consider a circular roller coaster loop of radius 11.9 m. You already know that if the car starts from a height of 2.5 r at rest, the normal force acting on the car at the top will vanish.


Now assume the car starts from a level track, a height of 11.9 m above the ground. The track first guides the car to ground level and then into the loop. At which initial speed must the car move on the elevated track (height 11.9 m) such that it still has the required speed at the top of the loop for the normal force to vanish?

Explanation / Answer

At the top of the loop, we know that mv^2/r = mg

Thus v = sqrt(rg)

v = sqrt(11.9)(9.8) = 10.8 m/s

Now we are going to apply conservation of energy

At the top of the loop it will have PE and KE

At the initial start point it will also have PE and KE

mgh + .5mv^2 = mg2r + .5m(10.8)^2

(9.8)(11.9) + .5(v^2) = (9.8)(2)(11.9) + .5(10.8)^2

v = 18.7 m/s

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