How Does Squaring Final Velocity Impact Spring Problem Solutions?

[pureouchies4717]

solved thanks to dicerandom... i forgot that vf is squared in the second formula. thanks so much

 

[dicerandom]

Your approach sounds good, I think you probably just made an algebraic mistake somewhere along the way. Use conservation of momentum to find the velocity of the bullet+block system in terms of the bullet's initial velocity, then use conservation of energy to relate the velocity of the bullet+block to the displacement of the spring.

Edit: Just for reference...

Conservation of momentum: $$m_i v_i = m_f v_f$$
Kinetic energy: $$\frac{1}{2} m v^2$$
Spring potential energy: $$\frac{1}{2} k x^2$$

 

[dicerandom]

Looks like you forgot to square the velocity in you kinetic energy term.

 

[pureouchies4717]

thanks a lot :!)

 

[dicerandom]

My pleasure