Acceleration, friction, pulleys

AI Thread Summary
The discussion revolves around calculating the acceleration of a system involving a 27.5kg box and a 13.75kg box connected by a frictionless pulley. The initial question seeks clarification on whether the acceleration calculation includes both horizontal and vertical components, and how to isolate the downward acceleration. There is confusion about the setup, specifically whether both boxes are suspended or if one is on a surface. Ultimately, the original poster resolves their query independently. The conversation highlights the importance of clearly defining physical setups in physics problems.
jshaner858
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a 27.5kg box is connected to a 13.75kg box on a frictionless pulley. my question is if you calculate the acceleration does that include horizontal and vertical acceleration, and if so, how do you just find the downward acceleration?
 
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This is too vague, please explain the setup better. Are they both in the air, one on a table the other in the air?
 
nevermind, i figured it out myself...thanks
 
my work here is done! :-P
 
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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