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Old May 12th 2016, 12:45 AM   #1
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A ball rolling up a parabolic ramp

Hi guys! I'm Alan and I'm new here. I hope that we will discuss physics problem solving and concepts freely.

Today I need some help with this problem:
Assume there is gravity and no external force acting on the system. A ball has an initial velocity of 5 m/s and climbs up a parabolic ramp, which is defined by y=(x^2)/3. If the ball rolls exactly along the path of ramp and energy of the ball is conserved, starting from (0,0), calculate the time taken for the ball to climb to a height of y=1.

I solved it using differential equations but the differential I got is only numerical integratable (results given by wolfram alpha). I'm looking for an easier way to solve this problem. (Actually I'm a highschool student but I think this question should be posted here as it is not a question from my highschool material - I made it up.) So, guys, please help! Thanks!

Last edited by errwrsysalan; May 12th 2016 at 03:16 AM.
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Old May 12th 2016, 02:24 AM   #2
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If there is no friction the ball will not roll.
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Old May 12th 2016, 03:17 AM   #3
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Originally Posted by studiot View Post
If there is no friction the ball will not roll.
Thanks! Found my mistake. Changed it.
How about the solution?
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Old May 12th 2016, 11:13 AM   #4
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I don't think you can solve this problem with a closed-form solution, so numerical methods must be employed. The problem is that acceleration is not constant. I would also note that if the ball is rolling then you need to specify either the ball's moment of inertia or its radius (if we can assume the ball is solid).
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