How Does Squaring Final Velocity Impact Spring Problem Solutions?

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Squaring the final velocity is crucial in solving spring problems, as it directly affects kinetic energy calculations. The discussion emphasizes using conservation of momentum to determine the velocity of the bullet-block system based on the bullet's initial velocity. It also highlights the importance of relating this velocity to the spring's displacement through conservation of energy principles. A common mistake noted is neglecting to square the velocity in the kinetic energy formula. Understanding these concepts is essential for accurate problem-solving in physics.
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solved thanks to dicerandom... i forgot that vf is squared in the second formula. thanks so much
 
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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
 
Looks like you forgot to square the velocity in you kinetic energy term.
 
thanks a lot :!)
 
My pleasure :smile:
 

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