Speed of a Roller Coaster, Conservation of Energy

  • Thread starter LiquidPi
  • Start date
  • #1
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Homework Statement



A roller coaster travels on a frictionless track as shown in the figure.
(a) If the speed of the roller coaster at Point A is 5.0 m/s, what is its speed at Point B?
(b) Will it reach Point C?
(c) What speed at Point A is required for the roller coaster to reach Point C?

Please view the attached figure. In case the image is too blury, the height of Point A = 5.0 meters, and the height of Point C = 8.0 meters.

Homework Equations



KE = 0.5*m*v^2
PE = m*g*y, where y = vertical position

The Attempt at a Solution



KE = PE
0.5*m*v^2 = m*g*y
mass cancels
0.5*v^2 = g*y
v = √(2*g*y)

What confuses me is what to do with the starting speed at Point A, 5.0 m/s. If the velocity at the top was zero, then the problem would be relatively straightforward. Where do I go from here? Thanks in advance!
 

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Answers and Replies

  • #2
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A) PE at point a and KE = KE at point b
So m*g*h + 0.5*m*u^2 = 0.5*m*v^2
I think you can do the rest
B) Nope
C) KE lost = PE gained
I cant see the numbers on the image attached!
 
  • #3
2
0
A) PE at point a and KE = KE at point b
So m*g*h + 0.5*m*u^2 = 0.5*m*v^2
I think you can do the rest
B) Nope
C) KE lost = PE gained
I cant see the numbers on the image attached!
Excellent, thank you!
 

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