Verify (or Disprove) the Solution to a Physics Problem

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The discussion revolves around verifying the solution to a physics problem involving conservation of linear momentum and energy. The provided solution indicates a result of 25 cm, while the user calculates approximately 13.4 cm. A participant suggests that the user's result is incorrect and requests detailed work to understand the discrepancy. The conversation emphasizes the importance of showing calculations for accurate verification. The thread highlights the need for clarity in problem-solving to resolve differences in results.
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Homework Statement



See the attached photo for the problem statement.

Homework Equations


The Attempt at a Solution



The provided solution is 25 cm. I obtain about 13.4 cm, however. I am using the conservation of linear momentum and the conservation of energy (between the initial kinetic energy of the blocks and the final kinetic energy of the combined block system, along with the potential energy stored within the spring) simultaneously. Can someone verify (or disprove) my result?
 

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Syrus said:

Homework Statement



See the attached photo for the problem statement.


Homework Equations





The Attempt at a Solution



The provided solution is 25 cm. I obtain about 13.4 cm, however. I am using the conservation of linear momentum and the conservation of energy (between the initial kinetic energy of the blocks and the final kinetic energy of the combined block system, along with the potential energy stored within the spring) simultaneously. Can someone verify (or disprove) my result?

Holliday and Resnick are right and your result is wrong. Show your work in detail.


ehild
 
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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