Consider a roller coaster that moves along the track shown in the figure below.

Question

Consider a roller coaster that moves along the track shown in the figure below. Assume all friction is negligible and ignore the kinetic energy of the roller coaster's wheels.

(a) Is the mechanical energy of the roller coaster conserved?

Yes or No    

(b) Add a coordinate system to the sketch in the figure.

(c) If the roller coaster starts from rest at location A, what is its total mechanical energy at point A? (Take y = 0 to be at the same height as point C. Use the following as necessary: m, g, and hA.)

EA =

(d) If vB is the speed at point B, what is the total mechanical energy at point B? (Take y = 0

EB =

(e) Find the speed of the roller coaster when it reaches locations B and C. (Assume hA = 25 m and hB = 13 m.)

Explanation / Answer

A) yes,since only gravityational force(Conservative force) is acting on the body

B) vertical direction is the Y-axis and horizontal direction is x-axis

C) total mechanical energy at A is EA= m*g*h = m*g*hA

D) total mechanical energy at every point is same

EB= m*g*hA

E) at B = vB = sqrt(2*g*(hA-hB) = sqrt(2*9.81*(25-13)) = 15.34 m/s

at c = vC = sqrt(2*g*hA) = sqrt(2*9.81*25) = 22.2 m/s

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