Hollow sphere rolling up a ramp

AI Thread Summary
A hollow sphere rolling at 5 m/s encounters a 30-degree incline, prompting a discussion on how far it will roll up before reversing direction. The conservation of energy is identified as the appropriate approach, using the equation 1/2mv^2 + 1/2Iω^2 = mgh. Participants note that for rolling without slipping, the relationship v = rω applies, although the radius is not explicitly provided. It is suggested that the radius can be treated as a variable "r" to simplify calculations. The conversation emphasizes understanding rotational inertia and the conditions for rolling without slipping.
mjolnir80
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Homework Statement


a hollow sphere is rolling long a horizontal floor at 5 m/s when it comes to a 30 degree incline. how far up the incline does it roll before reversing direction?

Homework Equations


The Attempt at a Solution


it seems like conservation of energy would work best for this problem
1/2mv^2 + 1/2I\omega^2 = mgh
im just having some problems finding \omega
am i doing this right? and if so any clues on how to find \omega?
thanks in advance
 
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Assuming the sphere is rolling without slipping, ω and v are directly related. (What's the condition for rolling without slipping?) What's the rotational inertia of a hollow sphere?

Your method is fine.
 
v=\omegar right? but we don't have the radius of the sphere
or do we....?
 
mjolnir80 said:
v=\omegar right?
Right.
but we don't have the radius of the sphere
or do we....?
Maybe you don't need it. :wink: (Just call it "r" and see what happens.)
 
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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