(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

A rifle bullet with mass 8.00g strikes and embeds itself in a block with mass 0.992 kg that rests on a frictionless, horizontal surface and is attached to a coil spring. The impact compresses the spring 15.0 cm. Calibration of the spring shows that a force of 0.750 N is required to compress the spring 0.250 cm. (a) Find the velocity of the block right after impact (b) what was the initial speed of the bullet?

The book lists the answers to be (a) 2.60 m/s and (b) 325 m/s.

2. Relevant equations

Kenetic Energy = .5mv^2

Hooke's Law: F=kx

m1v1=m2v2

3. The attempt at a solution

Alright, I have tried it 2 different ways (and gotten 2 sets of completely different answers) but I think I'm missing something.

First train of thought:

1. Find the spring constant, k, using the calibration information, gives me a k=300

2. Find the impact of compression by solving F=kx with my compression distance (.15 meters) and 'k' value (F=45Newtons)

3. Find velocity for (a) using KE=(1/2)mv^2 which gives me the velocity=9.49 m/s.

4. Initial speed of bullet for (b) via m1v1=m2v2, Plug values in, giving me a v1=1186.25 m/s

Second train of thought:

1. Momentum of block with bullet=momentum of bullet

so .5V^2=.5(.008)v^2

2. Force constant of spring 'k' = (Force/Compression) = .75/.0025 = 300 Newton/meter (same as previous method)

3. Potential Energy in Spring: .5kx^2=3.375 Joules

4. Kinetic Energy of Block = Potential Energy of Spring, thus (from step 1), .004v^2=3.375 Joules ---> v=29.05 m/s (for part (b))

5. Velocity of Block w/ Bullet V=.008v = .8216 m/s (for part (a)).

Any suggestions would be most useful, thank you :)

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Inelastic Collision of a Bullet into a Block

**Physics Forums | Science Articles, Homework Help, Discussion**