Calculating Height After Bump: A Physics Problem

[physx_matter]

Hello fellow physicists, I am seeking help on the following problem:

A bicycle is moving over a speed bump at 6.9m/s. Calculate the height reached by the bicycle once it looses contact with the speed bump. Radius of the speed bump is 1.7m and mass of the bicycle is 83 kg. For this problem consider the bicycle as a point mass. Height of the speed bump is 10.2 cm.

You can consider that the bicycle is moving as a projectile once it has lost contact with the speed bump.


Any help much appreciated.

 

[physx_matter]

Just a note: I have not done physics for around two years now and saw this question and found it interesting. I have tried to use the v=u+at and other equations and simply cannot find how to go about this. I studied physics at A-level but did am doing Pharmacy at university. It's not for homework or anything just something I was curious about! Thanks.

 

[tiny-tim]

Welcome to PF!

Hello physx_matter! Welcome to PF!

The bicycle will lose contact when the normal force is zero.

So use F = ma in the normal direction, and the centripetal acceleration formula, a = v²/r, to find the angle at which is loses contact. After that, use conservation of energy.

 

[physx_matter]

Thanks for the welcome Tiny tim and also great advice! I need to brush up my physics as I enjoyed it quite alot. Might bring out my old A-level textbook once uni exams are done. I'm off to hit the notepad.

:) Thanks again.

 

[physx_matter]

Hello again Tiny Tim, I am still stuck on this question. If the normal forceis 0 the a=0 aso does it not? Also to find the angle it leaves the bump I would need a formula that has theta in it as far as I can remember. WIll I not need to use the angular velocity equation? This has me in loops now :(.

 

[tiny-tim]

No, a = v²/r, where r is the radius of curvature.

Yes, you need to find θ, but you don't need the angular velocity.