Solve Spring Gun Problem: Recoil Speed Calculation

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The discussion focuses on calculating the recoil speed of a mechanical gun after firing a bullet, using principles of conservation of momentum and energy. The initial attempt involved isolating the recoil speed of the gun (vgf) but did not fully utilize the conservation of energy equation. Participants emphasize the need to apply both conservation laws to solve for the recoil speed effectively. The conversation highlights the importance of integrating energy considerations alongside momentum to arrive at the correct solution. Ultimately, a complete understanding of both concepts is necessary for accurate calculations in this scenario.
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Homework Statement


A mechanical gun of mass M(g) uses a spring to shoot a bullet of mass M(b). The energy of the compressed spring before firing is E. Assuming the gun is at rest before firing, what is the recoil speed of the gun immediately after it shoots the bullet?

Homework Equations



Conservation of momentum (M(g)+M(b)vi= M(g)vbf+M(g)vgf
Conservation of Energy

The Attempt at a Solution


I first tried to isolate vgf(speed of gun after the bullet is fired), which gave me

-Vgf= M(b)vbf/M(g), I don't what to do after this...
 
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Raymond Huang said:

Homework Statement


A mechanical gun of mass M(g) uses a spring to shoot a bullet of mass M(b). The energy of the compressed spring before firing is E. Assuming the gun is at rest before firing, what is the recoil speed of the gun immediately after it shoots the bullet?

Homework Equations



Conservation of momentum (M(g)+M(b)vi= M(g)vbf+M(g)vgf
Conservation of Energy

The Attempt at a Solution


I first tried to isolate vgf(speed of gun after the bullet is fired), which gave me

-Vgf= M(b)vbf/M(g), I don't what to do after this...
On the relevant equations section, you wrote conservation of energy, yet you did not use it.
 
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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