Understanding Pendulum Work and Energy: A Scientist's Perspective

[coile3]

I am having dificulty with a problem involving a pendulum. Basically the pendulum is at rest at a specified height. The pendulum is then allowed to swing and it strikes a cart at the base of it's arc and then the cart rolls up a ramp while the pendulum swings back to a lesser height than originally. I need the initial mechanical energy for the system, which I think should be the potential energy of the pendulum (grav*mass*height). I also need the amount of energy converted from mechanical to non-mechanical during the motion, which I think I can find by finding the new potential energy (grav*mass*height2) and subtracting this from the initial potentioal energy. Lastly, I need to know how far the cart will travel if no energy is converted. I didn't post numerical values because I would like help in understanding what is happening and I would like to lknow if any of my thoughts are wrong.

Thanks

 

[dextercioby]

At the point of the contact,assuming you've chosen it to be the "0" of the gravit.pot.energy,the bob of the pendulum has only KE (and momentum,of course) which he transfers to the body (cart) it hits,making it go up the ramp (assuming no friction on the ramp).It's really nice to assume a perfect elastic collision.

I didn''t get the converting part.Basically,if yo make that assumption,total mechanical energy (KE + grav.potential) is conserved in every interaction.

Daniel.

 

[Davorak]

Yep just make sure to conserve energy and momentum at each step. Problems like this often show up on the physics GRE.

 

[coile3]

What would then happen to the cart. I know it get sent on it's way up the ramp but how does this motion change if there is no loss to the mechanical energy in the system.

dextercioby: The conversion is the amount of energy changed from mechanical to some other form (ie. heat).

 

[dextercioby]

Heat,means,in the case of the cart,friction on the ramp.Again,u must/are invited to use the theorem of variation of KE:

$$\Delta KE=\mbox{Total work}$$

,where "Total work" stands for the total work done by the forces acting on the cart:gravity & friction.

Daniel.

 

[coile3]

I am still having trouble with the last part of the problem. In the event that there is no mechanical energy lost (100% conserved) how high up the ramp will the cart rise? I can't seem to figure out how to go about this part of the problem. We are only looking at work/energy in the problem. Is it possible that the cart will rise forever because there is no mechanical energy being converted to slow it down (Newton's object in motion will stay in motion until acted upon.

Thanks for the quick responses earlier.

 

[dextercioby]

Nope,gravity (the tangential component) is pulling it down,making it eventually to stop and then fall down again.

Use the theorem.

Daniel.