How Does a Cylinder Roll Down an Inclined Plane?

AI Thread Summary
The discussion centers on solving physics problems related to a cylinder rolling down an inclined plane. Participants are asked to create problems based on a provided image, focusing on variables like radius and initial velocity. One specific problem involves calculating the speed of a cylinder with a radius of 12 cm, released from rest on a smooth incline at a 30-degree angle, over a distance of 8 meters. The conversation emphasizes understanding the dynamics of rolling motion and energy conservation principles. Engaging with these problems will aid in preparation for final exams in physics.
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http://aixagent.com/physics/q1316.jpg

Can you guys give me some problems to solve, based on the picture provided?

You can choose which variables you want to be "given" -- I would just like some problems about rolling on an inclined plane to do to prepare for my final.
 
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bad question
this instead--sorry
if it has a radius R and an initial velocity V, determine the height.
 
Conversly, and with some numbers;

Find the speed of a cylinder of radius R = 12cm, when released from rest at the top of a smooth inclined plane at an angle \phi = \frac{pi}{6} from the horizontal and a slope length of d = 8m.
 
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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