A) A 1,258-kilogram roller coaster car is approaching a valley. At its bottom, t

Question

A) A 1,258-kilogram roller coaster car is approaching a valley. At its bottom, the valley can be described by a circle with radius 7 m. Find the speed required at point A, such that the normal force acting on the car in point B is 210% more than the weight. Below answer with the required speed at point A with units of m/s.

B) A 1,896-kilogram roller coaster car starts at point A almost at rest. It first runs downhill and then is approaching a hill. At its top, the hill can be described by a circle with radius 8 m. Find the height required at point A, such that the normal force acting on the car in point B is 51% of the weight.

C) A 2,456-kilogram roller coaster car starts at point A almost at rest. It runs downhill into a valley. At its bottom, the valey can be described by a circle with radius 10 m.

Find the height required at point A, such that the normal force acting on the car in point B is 290% of the weight.

Explanation / Answer

A) N = mg + 2.10mg = 3.10mg

at bottom:

N - mg = mv^2 / r

3.10mg - mg = mv^2 /r

2.10 mg = m v^2 / 7

v = 12 m/s

b)at top point,

mg - N = mv^2 / r

mg - 0.51mg = m v^2 / r

v = sqrt(0.49 x 8 x 9.8 ) = 6.20 m/s at top

heigt differene from top and point A

mgh = mv^2 / 2

h = 6.20^2 / (2 x 9.8) = 1.96 m/s height above from the top of hill.

c) N - mg = mv^2 / r

2.90mg - mg = m v^2 / 10

v = sqrt(1.90 x 9.8 x 10) =13.65 m/s

and from energy conservation,

mgh = m v^2 /2

h = 13.65^2 / (2 x 9.8) = 9.5 m

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