Speed of a bullet in ballistic spring system

[brunettegurl]

Homework Statement

You have been asked to design a "ballistic spring system" to measure the speed of bullets. A bullet of mass 6.20 g is fired into a block of mass 2.10 kg. The block, with the embedded bullet, then slides across a frictionless table and collides with a horizontal spring whose spring constant is k=63.0 N/m. The opposite end of the spring is anchored to a wall. What was the speed of the bullet if the spring's maximum compression is 12.1 cm?

Homework Equations

p_initial=p_final
E=0.5*k*x²
E= 0.5*m*v²

The Attempt at a Solution

m1= bullet and m2= block; v1= vbullet

i first solved m₁v₁+m₂v₂= m_total*v_final for Vfinal..so that looked like v_final= m1*v1/m_total

then i used the energy equations to get 0.5*k*x²= 0.5*m*v²
in v2 i substituted m1*v1/m_total
and then tried to solve for v1 which is the speed of the bullet we are looking for ...and my hwk app. is telling me my answer is wrong...so i was wondering if i made a mistake in the workings somewhere..

 

[Doc Al]

Your method looks fine. Provide your final equation for v in terms of m₁ and m₂.

Also: Check that you haven't made an arithmetic error.

 

[brunettegurl]

this is how my equation looks like
(k*x²)/m_bullet= (m₁*v₁/m_total)²

$$\sqrt{}(k*x^2)/mbullet$$ *M_total/m_bullet = vbullet²

the square root only applies to the k*x²/m_bullet

does that look right ??

 

[Doc Al]

this is how my equation looks like
(k*x²)/m_bullet= (m₁*v₁/m_total)²

That should be:
(k*x²)/m_total= (m₁*v₁/m_total)²

 

[brunettegurl]

i got the right answer but was wondering why it wouldn't be mass of bullet that would be divided by the energy of spring>>??

 

[Doc Al]

i got the right answer but was wondering why it wouldn't be mass of bullet that would be divided by the energy of spring>>??

Because after the collision, the KE of the system is ½m_totalv². The bullet and block are treated as one unit.