A 2050 kg roller coaster is approaching a hill. At its top, the hill can be decr

Question

A 2050 kg roller coaster is approaching a hill. At its top, the hill can be decribed by a circle with a radius of 13 m.

a) Employ Newton's Law to find the speed that the car must have at point B such that the normal force acting on the car is half the height.
b) Employ conservation of energy to find the required heigh of the track at point A, such that starting almost at rest the car passes point B at the required speed.

Answers:
a) 7.99 m/s
b) 16.3 m

Please explain as unconvuluted as you can (as I was given a rather complicated solution) to arrive at the answers? Thank you.

A 2050 kg roller coaster is approaching a hill. At its top, the hill can be decribed by a circle with a radius of 13 m. a) Employ Newton's Law to find the speed that the car must have at point B such that the normal force acting on the car is half the height. b) Employ conservation of energy to find the required heigh of the track at point A, such that starting almost at rest the car passes point B at the required speed. Answers: a) 7.99 m/s b) 16.3 m Please explain as unconvuluted as you can (as I was given a rather complicated solution) to arrive at the answers? Thank you.

Explanation / Answer

apply . a = g = V^2/R

here R = half of 13 = 6.5 m

so V^2 = 9.8*6.5

V = 7.98 m/s

-------------------------------

Hmax = 7.98 *7.98/(2*9.8)

Hma x= 3.25

Hmax = 13+3.25 = 16.3 m

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