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Fabio
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what are the sources of energy loss for a ball rolling down slope?

I am experimenting in lab with an iron sphere rolling down a smooth aluminum ramp.

The final velocity is smaller than the one predicted assuming energy conservation, which implies some energy is lost.

At the top of the ramp (height $H$) the sphere is at rest and energy $E_{tot}=E_{pot}=mgH$. At the end of the ramp the sphere has height 0 and so all potential energy, in absence of lossed, should be converted in kinetic energy, which has two components (rotation and translation). Hence I get $mgH=\frac{7}{10}Mv^2\implies v=\sqrt{\frac{10}{7}gH}$. Using Euler-Lagrange equations I obtain that the balls should have constant acceleration: $$a=\frac{5}{7} g\sin{\alpha}$$ and the time it should take to get to the bottom og the ramp is: $$t = \sqrt{\frac{10}{7} l g\sin{\alpha}}$$

What are the mechanical causes of the energy loss in this experiment? I am interested in a qualitative conceptual answer, not in formulas.

A part from attrition with air (not so important here, as velocity is not that high and iron has a large density), I am not sure what are other contributing factors. The ball is rolling, not sliding, so there is no attrition. My wild guesses are:

  • perhaps the surfaces are not perfect so it makes micro bounces, instead of a perfect rolling?
  • perhaps the ball sticks to the surface at microscopic level?
Fabio
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