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Amusement Park Ride, Find Velocity at Point C

  1. Oct 13, 2013 #1
    1. The problem statement, all variables and given/known data

    A car in an amusement park ride rolls without friction around the track shown in the figure (Figure 1) . It starts from rest at point A at a height h above the bottom of the loop. Treat the car as a particle.

    If the car starts at height h= 5.00 R and the radius is R = 16.0m , compute the speed of the passengers when the car is at point C, which is at the end of a horizontal diameter.


    2. Relevant equations

    Conservation of Energy


    3. The attempt at a solution

    Using conservation of Energy

    PE_i + KE_i = PE_f + KE_f

    mgh = mgh + 1/2mv^2

    mg(5R) = mg(R) + 1/2mv^2 (We are solving for V, so..)

    mg(5R) - mg(R) = 1/2mv^2

    (Cancel out mass)

    g(5R) - g(R) = 1/2v^2

    2(g(5R) - g(R)) = v^2

    sqrt(2(g(5R) - g(R))) = V

    (Plug in R)

    sqrt(2(g(80) - g(5))) = V

    If this is correct so far, is g just gravity or is it centripetal acceleration? I loose confidence at this step..Lead me in the right direction?

    Thanks!
     

    Attached Files:

  2. jcsd
  3. Oct 13, 2013 #2

    gneill

    User Avatar

    Staff: Mentor

    Looks like you're doing alright.

    Note that during your simplifications you could make mg(5R) - mg(R) into mg4R and save a lot of number pushing later on down the page.
     
  4. Oct 13, 2013 #3
    Ok great, submitted my answer and it was right. Thanks for the tip for subtracting the R's. I didn't know if I was doing the right process. Thanks again
     
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