2. (22 points) Assume the height of a roller coaster, shown in the figure below,

Question

2. (22 points) Assume the height of a roller coaster, shown in the figure below, is y 40 m at point A and y = 25m at point C (take the reference point y = 0 m, as the bottom of the roller coaster hill at point B) and there is no friction. The mass of the car is m 100 kg 40 m 25 m a) (5 points) What is the change in potential energy of the car as it goes from point A to B? b) (5 points) What is the change in potential energy of the car as it goes from point B to C? c) (5 points) If the car started from rest at point A, what is its speed at point B? d) (7points) If the car started from rest at point A, what is its speed at point C?

Explanation / Answer

2. (A) delta(PE) = m g delta(H)
= 100 x 9.81 x - 40

= - 39240 J

(B) delta(PE) = 100 x 9.81 x 25

= 24525 J

(C) Applying energy conservation,

0 = - 39240 + 100 v^2 / 2

v = 28 m/s

(D) 39240 =24525 + 100 v^2 / 2

v = 17.2 m/s

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