Friction Problem: Calculating Acceleration and Tension in a Pulley System

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To solve for the acceleration of the two blocks in the pulley system, the net force acting on the system must be calculated, considering the weight of both blocks. The acceleration can be determined using Newton's second law, where the difference in weights divided by the total mass yields the acceleration in m/s². Tension in the cord can be found by analyzing the forces acting on the hanging block, leading to a formula that incorporates both the weight of the hanging block and the calculated acceleration. Clear communication of the problem setup is crucial for accurate calculations, as assumptions about friction and mass impact the results. The final answers for acceleration and tension should be presented with detailed calculations for clarity.
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The weight of the block on a table is 494 N and that of the hanging block is 175 N. Ignore all frictional effects, and assuming the pulley to be massless.

(a) Find the acceleration of the two blocks.
m/s2 =?

(b) Find the tension in the cord.
N =?
 
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Please show your work.

Also, rereading your post, you talk about masses and then say that a pulley is frictionless. Please state the exact question, including how the situation is set up-- we're not mind-readers!
 
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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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