A child rolls a marble of mass m and initial speed v down a loop of track. The t

Question

A child rolls a marble of mass m and initial speed v down a loop of track. The track includes many curves, dips, and hills. After the marble makes one complete loop around the track, its speed is 0.25v. What fraction of the marble's initial mechanical energy is lost to dissipative forces? A child rolls a marble of mass m and initial speed v down a loop of track. The track includes many curves, dips, and hills. After the marble makes one complete loop around the track, its speed is 0.25v. What fraction of the marble's initial mechanical energy is lost to dissipative forces?

Explanation / Answer

speed = 0.25v
angular velo = 0.25v/r
I = 2mr^2/5
Fraction lost to friuction = (Initial KE - final Ke)/initial KE = [1 -[ (0.25)^2 + (0.1)^2]]/ 1 = 0.9275

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