Roller coaster problems (work energy) A 2,082-kilogram roller coaster car starts

Question

Roller coaster problems (work energy)

A 2,082-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 11 m. Find the height required at point A, such that the normal force acting on the car in point B is 69% of the weight. Make sure to practise how to explain your work and also how to evaluate your result. Draw proper diagrams to support your work. Below answer with the height.

Explanation / Answer

m =2.082 kg , R =11 m

TB = 0.69mg

From Newton seocnd law net force at point B is

TB - mg = -mvB^2/R

0.69 mg -mg =- mvB^2/R

0.31 mg = mvB^2/R

KB = (1/2)mvB^2 = (0.31/2)mgR = 0.155mgR

From Conservation of energy at point A and B

UA+KA =UB+KB

mgH +0 = mgR + 0.155mgR = 1.155mgR

H = 1.155*11

H =12.705 m

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