Ropes/Pulleys with moving weights

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AI Thread Summary
The discussion revolves around solving for the velocity of block B in a pulley system with blocks A and B having masses of 3kg and 5kg, respectively. The correct velocity for block B is stated as Vb = -35.8 m/s, but the initial attempts yielded incorrect results. Participants highlight the inconsistency in tension calculations, noting that tension should remain constant in an ideal rope, and emphasize that tension cannot equal the weights of the blocks due to acceleration. The conversation also points out errors in the equations used, particularly regarding the treatment of acceleration signs and factors. Overall, the focus is on correcting the approach to achieve a consistent solution.
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Homework Statement


Find the velocity of block B (the one to the right) A has a mass of 3kg and B a mass of 5kg. Pulleys and rope are ideal.

Homework Equations


F=ma

The Attempt at a Solution


I used two different methods, got the same WRONG answer. The correct answer is Vb= -35.8m/s
Let me know if you can't see what the pictures say

IMG_2768.jpg

IMG_2769.jpg
 
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How is it consistent for T=49.1 N but 2T=29.43 N if it's the same rope? Tension doesn't vary across an ideal rope, because the rope is massless.

You can't say the tensions are equal to the weights. The objects will accelerate; but if the tension equals the weight, how would the objects accelerate?
I would leave the tension unknown and eliminate it, no reason to solve for it.
 
I used this method:

 
Ah, I didn't see that you wrote "static analysis" above that part.

In either eq 2 or eq 3, you have an extra factor of -1 on the acceleration term.

Edit:
Actually, it could be fixed by slightly altering any of your 3 equations; they just need to be consistent.
You said, -ab = 2aa which implies that you're letting ab and aa represent the magnitudes and direction (one of them is negative) of acceleration; but then you have an extra factor of -1 on a3 in eq.3, which implies that you're taking aa and ab to be just the magnitude
 
Last edited:
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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