- #1
MuIotaTau
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Homework Statement
A bowling ball is thrown down the alley with speed ##v_0##. Initially it slides without rolling, but due to friction it begins to roll. Show that its speed when it rolls without sliding is ##\frac{5}{7} v_0##.
Homework Equations
##K= \frac{1}{2}mv^2 + \frac{1}{2} I \omega^2##
The Attempt at a Solution
Because friction does no work in this case, energy is conserved. Equating the energy before and after rolling begins, I get $$\frac{1}{2}Mv_0^2 = \frac{1}{2}Mv^2 + (\frac{1}{2})(\frac{2}{5})MR^2\omega^2$$
Using the fact that ##v = R\omega##, I get $$Mv_0^2 = Mv^2 + \frac{2}{5}Mv^2$$
Solving for ##v##, I get $$v = \sqrt{\frac{5}{7}}v_0$$ What did I do wrong to make me off by a factor of ##\sqrt{\frac{5}{7}}##?