Solving Bowling Ball Slipping Problem with Conservation of Total Energy

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A bowling ball with an initial velocity of 5 m/s and a coefficient of friction of 0.08 is analyzed for the distance it travels before rolling begins. The discussion centers on using the conservation of total energy to account for energy lost due to friction. The calculated distance before rolling starts is 7.8 meters, although initial attempts yielded incorrect results. Participants express a need for clarity on applying conservation of energy principles effectively in this context. Understanding the forces involved is crucial for accurate calculations in similar problems.
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a bowling ball is slipping woth initial velocity of 5m/s with coeficient of friction being .08.
how far does it travel before it started to slip?

i used conservation of total energy and accounted for the energy lost in friction until it starts to roll.

both i and my teacher got double the actual answer of the problem.

i think i need to know the force that keeps the ball from rolling for the duration of x.
but I am not completely sure, does anyone know how to use conservatin of total energy?
 
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the answer is 7.8 meters if anyone was wondering
 
I did a quick calculation and got 7.8 m. Please post the steps of your calculation.
 
i used V=Rw to solve it correctly, you should get 7.8m

but i wnat to know how to use conservbation of total energy because it makes conceptual sense but it does not provide the correct answer.
 
(edit to the first post by me)

*a bowling ball is sliding without rolling with initial velocity of 5m/s and coeficient of friction being .08.
how far does it travel before it starts to roll?*

that should make more sense
 
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
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