1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Circular Motion in a Roller Coaster

  1. Apr 9, 2012 #1
    1. The problem statement, all variables and given/known data
    In a certain loop-the-loop roller coaster ride, the coaster is given an intial speed of v ms-1. The coaster then rolls freely under the influence of gravity. The coaster travels down a 10m high slope before arriving at the start of the loop. It then travels the loop which has a diameter of 20m. Calculate the minimum value of v required for the coaster to make the loop.

    2. Relevant equations
    mv^2/r = mg
    E(kinetic) = 0.5mv^2
    E(potential) = mgh

    3. The attempt at a solution
    I found the increase in speed due to gravity using motion formulae
    Assuming up is positive and down is negative,
    v^2 = u^2 + 2as
    v^2 = 0^2 + 2(-9.8)(10)
    v = 14 ms-1 down

    When the train reaches the loop it has completely horizontal velocity, therefore its velocity at the bottom of the loop is v+14 ms-1 horizontally

    To successfully travel the loop, F(centripetal) must equal F(gravity)
    Fc = Fg
    mv^2/r = mg
    v^2/r = g
    v^2 = 10 x 9.8
    v = 9.9 ms-1 at the top of the loop

    v+14 ms-1 must be able to travel the 20m and still achieve a speed of 9.9ms-1 at the top
    E(potential) = mgh
    E(potential) = m x 9.8 x 20
    E(potential) = 196m

    Since Ep at top equals Ek at bottom,
    Ep(top) = Ek(bottom)
    196m = 0.5mv^2
    196/0.5 = v^2
    v = 19.8 ms-1

    19.8ms-1 is the speed required to reach the top, 9.9ms-1 is the speed it must have at the top, therefore the total speed required is 19.8+9.9 =29.69ms-1

    Since 14ms-1 is provided by the travel down the slope,
    v = 29.69-14 = 15.7ms-1

    Can someone tell me if i am right, and correct me if im not? Your help is much appreciated =)
  2. jcsd
  3. Apr 9, 2012 #2

    What about Ek at the top?
  4. Apr 9, 2012 #3
    That was added on after that calculation, 9.9ms-1 is the Ek at the top
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook