What Causes the Acceleration of the Smaller Mass in a Two-Mass Pulley System?

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The discussion focuses on calculating the acceleration of a smaller mass in a two-mass pulley system. The total mass of the system is determined to be 4.66 kilograms, leading to a net force of 45.668 N when considering gravitational acceleration. The acceleration of the smaller mass is calculated to be 23.1 m/s². Participants are asked to confirm the correctness of this calculation and seek assistance if needed. The inquiry emphasizes the importance of understanding the unbalanced forces acting on the system.
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Homework Statement



Two masses, 1.98 kilograms and 2.68 kilograms, are attached to a lightweight cord that passes over a pulley as shown below.

What is the acceleration of the smaller mass? Hint: For a system of connected objects, the unbalanced external force acts on the mass of the entire system.

Homework Equations



w=gm

Fnet=ma

The Attempt at a Solution



1.98+2.68=4.66kg

4.66kg(9.8)=45.668 N

45.668N/1.98kg = 23.1 m/s/s

Is this correct?
 
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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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