Isn't the answer of this 32.9? How come it's not right?

Question

A 11.0 g bullet is fired horizontally into a 103 g wooden block that is initially at rest on a frictionless horizontal surface and connected to a spring having spring constant 147 N/m. The bullet becomes embedded in the block. If the bullet-block system compresses the spring by a maximum of 84.0 cm, what was the speed of the bullet at impact with the block?
m/s

Answer 1

0.84*147 J energy in bullet = 0.011*v^2/2 so
1.68*147/.011 = v^2

just under 150 m/s


Cannot tell why 32.9 (m/s) is not right unless you tell how you got there.

Added later : frothuk asks some good questions - here are some more : do you care what the maximum velocity of the bullet+block is? : what is the velocity of bullet+block when maximum spring extension is reached?

Answer 2

I didn't get 32.9 m/sec for the bullet velocity.

I didn't get 150 m/sec for the bullet either.

I do get 30.16m/sec for the maximum velocity of the combined bullet-block system.

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You don't show your working so its not possible to say where you are going wrong.

What is the maximum energy stored in the spring?
Where does this energy come from?
What is the maximum velocity of the combined spring + block + bullet system?
What type of collision is taking place between the bullet and the block?
When does conservation of energy apply?
When does conservation of momentum apply?

Answer 3

Let
Ek = Kinetic energy
Ep = Elastic Potential Energy of the spring
vf = final speed
vi = initial speed
xi = initial displacement
xf = final displacement
m = mass of the bullet in kg
M = mass of the block in kg

Ek (bullet and the block) = - Ep (spring)

[½ m (vf² - vi²) ] +[½ M (vf² - vi²) ] = - [½ k (xf² -xi²) ]
[½ 0.011 (0² - vi²) ] +[½ 0.103 (0² - vi²) ] = - [½ 147 (0.84² - 0²) ]
½ 0.114 (0² - vi²) = - ½ 147 (0.84² - 0²)
0.114 (0² - vi²) = - 147 (0.84² - 0²)
0.114 (- vi²) = - 147 (0.84²)
0.114 (vi²) = 147 (0.84²)

(vi²) = 147 (0.84²) / (0.114)

vi = √ [147 (0.84²) / (0.114) ]

vi = 30.16 m/s

vi = 30.2 m/s

Note: The additional work to embed the bullet needs the length of the bullet to be solve...