Complicated question about an inclined plane, a marble and friction. See Details.?

Question

Suppose you let a marble roll down an inclined plane. Initial velocity equals zero (crucial!).

Now, to find friction:

ΔE=[Ekin(initial)+Epot(initial)] - [Ekin(final)+Epot(final)]

Since initial velocity is zero the formula reads:

⇔ ΔE=[m*g*H]initial-[0.7*m*v^2+m*g*h]final

The tricky part: IF the final height is set to zero, the result is totally different than when the final height is some other number.

Should the final height be zero or some other number?

The first one who knows the answer and can explain it, gets the best answer! Good luck ;-)

Answer 1

If there is still height that the ball can go, then it must be taken in to account when the total energy is being calculated.

The second thing that must be taken in to account the friction. Energy is lost through heat given off from friction.

It is a common engineering trick to make calculations easier by moving the frame of reference so the bottom is where the rolling marble ends in this question. Then make the calculations and add any potential energy by the standard equation PE=mgh.

Answer 2

How do you measure the initial height "H"? I assume that this "H" is measured from the horizontal axis from the bottom of the inclined plane.

If this is so, the "h" (the final height in the above equation) should be zero.  

Answer 3

Look at your formula

ΔE=[Ekin(initial)+Epot(initial)] - [Ekin(final)+Epot(final)]

rearrange the terms

ΔE=[Ekin(initial) - Ekin(final)] + [Epot(initial)  - Epot(final)]

now put in the formulas for potential energy

ΔE=[Ekin(initial) - Ekin(final)] + [m*g*H(initial)  - m*g*H(final)]

now factor out the m*g term

ΔE=[Ekin(initial) - Ekin(final)] + m*g*[H(initial)  - H(final)]

the result only depends on the DIFFERENCE between the heights ∆H,  If you move both H's the same amount,  there is no change.   Absolute H is not by itself meaningful.   You can set the final height to zero by subtracting some amount, but you have to subtract the same amount from the initial height.  If you only change H(final) without changing H(initial), then you have made a modified the value of ∆H, and therefore the change in potential energy