Acceleration of two pulleys help

AI Thread Summary
The relationship between the accelerations of two masses, m1 and m2, is established as a1 = 2*a2. This conclusion is derived from a practical visualization involving a string wrapped around a coffee cup, illustrating how pulling one end of the string affects the movement of the cup. When one end of the string is pulled up a distance x, the cup moves only x/2, demonstrating the acceleration relationship. Understanding this concept helps clarify the mechanics of the pulley system. The discussion emphasizes the importance of visualization in grasping physics concepts.
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Homework Statement



If a1 and a2 are the accelerations of m1 and m2, respectively, what is the relation between these accelerations?

Homework Equations



Link to the diagram :
http://www.webassign.net/serpop/p4-38.gif

The Attempt at a Solution



The answer is a1 = 2*a2, but I'm having trouble visualizing/understanding how it was gotten. Is there a specific way to do this?
 
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Get a string or shoe lace and wrap it around a coffee cup. Hold one end of the string still and pull the other end of the string up some distance x, the coffee cup will move x/2.
 

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I get it now; thanks a lot! I can't believe I didn't even see that in the first place.
 
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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