The statement below arises from a marble and track lab, and I’m enthralled to figure out a generalized equation ( variables only ) for energy lost per meter of track. Track is 12 feet long, but can be curved for hills and loops.
Using a small section of track and marble, determine the average energy lost per meter of track.
The track has 2 loops and 2 hills, and starts at a certain height with potential energy only.
2. Relevant equations
PEi + KEi + WEi(friction) = KEf + PEf + WEf
3. The attempt at a solution
1. KE = PE – WE
2. KE = PE – μ*m*g*x(distance)
3. 1/2mv^2 = mgh – ( μ * m * g * x)
4. v^2 = 2(g * initial height) – (μ * g * x)
5. v = √(2*g*h – (μ * g * x))
6. The answer above is final velocity and you can plug that into 1/2mv^2 and compare the energy to the amount it would be without friction v = √(2gh) and find the difference between the two, which in my theory would give the average amount of energy lost per meter.
7. I’m just confused if this is the right solution or even the right direction to go with this problem.