Impulse - Initial velocity of bullet

[xicor]

1. Homework Statement [/b]

Bullet B weighs 0.5 oz and blocks A and C both weigh 3 lb. The coeffient of friction between the block and the plane is $$\mu$$_k = .25. Initially the bullet is moving at v₀ and blocks A and B are at rest. After the bullet passes through A it becomes embedded in block C and all three objects come to stop in the position shown. Determine the initial speed of the bullet v₀.

mv₁ + Imp(1 $$\rightarrow$$ 2) = mv₂

Imp(1 $$\rightarrow$$ 2) = int[F(t)dt]

U(1 --> 2) = T₂ - T₁ where T is kinetic energy and U is potential energy

U(1-->2) = int[F.dr]

The Attempt at a Solution

I'm not really sure where to actually start with the problem besides starting from the second block. I tried using the impulse priniciple but that gives me an unknown time, force, and velocity and I'm not sure if the force would just be the fictional force. I also tried appying the work energy theorem but I'm not confident of that being useful here and it ended up giving me a huge velocity.

Thanks to anybody that is willing to helps me.

 

[tiny-tim]

Hi xicor!

… I also tried appying the work energy theorem but I'm not confident of that being useful here and it ended up giving me a huge velocity.

That should do fine … the work done should give you the initial speed of each block.

What did you get?​

 

[xicor]

Alright I used the work energy theorem on the second block and got v₁^2 = $$\sqrt{(2/3 )(32.2)}$$ --> v_1/ =4.633 ft/s which I'm not sure is right but it seems to be. After that I than tried to find the speed of the bullet between the two blocks by conservation of momentum(m1v1 =m2v2) nd found the v = 449.4 ft/s. Once I found this value I used the W.E.T on the first block where T₁ is the kinetic energy of the block when hit by the bullet and T₂ is the kinetic energy of the bullet after going through the block. From W.E.T I get the initial velocity of the first block to be 45.5 ft/s which seems way to big and using linear momentum again I get the initial velocity of the bullet as 4413.6 ft/s which is way to big a velocity in the problem.

I don't know where I'm going wrong here.

 

[tiny-tim]

Hi xicor!

(just got up :zzz: …)

No, you haven't used µ = 0.25 in finding the work done on the block.

Try the problem in this order:

i] use the work-energy theorem (twice!) to find the initial speed of both blocks

ii] then write out the two separate conservation of momentum equations for the two separate collisions