Exploring Energy Loss on a Ramp with Rolling/Sliding Ball

[daniel_i_l]

Lets say you have a ball on a ramp (hight h). It rolls down to the ground and then starts moving at aconstant speed - no friction (ok don't kill me, it's not really rolling either, just sliding). Now to the point of view of someone moving at the final speed of the ball and in the same direction, let's call it v, the ball starts with hoight h and with speed -v, and at the end it has hight 0 and speed 0. Were did all the energy go?
I think that since the ramp can't have infinate mass it must go a little backwards as the ball goes forwards (momentum conservation), in the first case the ramp starts with 0 speed and then gets a little from the ball, and in the second case the ramp starts with -v and then gets more from the ball so the difference is much bigger (for example,
11^2 - 10^2 > 2^2 - 1^2). This difference in energy is equal to the energy lost by the ball. (I calculated it and it worked)
Is this the right answer? What happens if the ramp has infinate mass(theoreticly)?
Thanks.

 

[denni89627]

Maybe a better question is what happens if you anchor the ramp. If the coefficient of friction between the ramp and the ground is 0 (which i think is what you're getting at), than the ramp would always move in a direction opposite the ball, less and less as the mass of the ramp increases compared to the ball. If the ramp was anchored (which I'm hoping you take as a substitute for infinite mass) the force that wants to push it backwards is still there, it just will be in the opposite direction -the ball- until that force is greater than the static coefficient of friction of the ramp (which we can consider way higher by anchoring it)

 

[sir-pinski]

Yes, your explanation is correct. The energy lost by the ball is equal to the energy gained by the ramp due to momentum conservation. This is known as the principle of conservation of energy. In the case of an infinitely massive ramp, the energy lost by the ball would still be equal to the energy gained by the ramp, but the difference in energy would be much smaller since the ramp's mass is infinitely large and therefore its speed would not change significantly. In this case, the energy would mostly be converted into heat due to friction between the ball and the ramp. This concept is known as the law of conservation of energy and it is a fundamental principle in physics.