Solve Spring Gun Problem: Recoil Speed Calculation

[Raymond Huang]

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...

 

[Elvis 123456789]

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.