# Completely Inelastic Collisions

## Homework Statement

A block of mass m1=1.88 kg slides along a frictionless table with a speed of 10.3 m/s. Directly in front of it, and moving in the same direction, is a block m2=4.92 kg moving at 3.27 m/s. A massless spring with a force constant k=1120N/m is attached to the backside of m2. When the blocks collide, what is the maximum compression of the spring? (Hint: at the moment of maximum compression of the spring, the two blocks move as one, find the velocity by noting that the collision is compltely inelastic to this point).

## Homework Equations

m1v1+m2v2=(m1+m2)vf
1/2(m1+m2)Vf^2=1/2Kx^2

## The Attempt at a Solution

I solved for vf in the inelastic equation:

vf = (m1v1 + m2v2) / (m1 + m2)

and plugged it into the energy equation and solved for x:

[(m1v1 + m2v2)^2 / K(m1 + m2)]^1/2 = x

Plugged in numbers:

{[1.88(10.3) + 4.92(3.27)]^2 / 1120(1.88 + 4.92)}^1/2 = x

(1257/7620)^1/2 = x

x = .407 m = 40.7 cm

The book got 35.9 cm. Can anyone find my mistake, or if I did it completely wrong, can anyone tell me how to do it? Thanks in advance!

I did a problem similar to this one from a different text book with the values (everything is worded the same, except these values are in place):

m1: 2.00 kg
m2: 5.00 kg
v1: 10.0 m/s
v2: 3.00 m/s
K=1120 N/m

I approached this problem differenty when I drew the before and after reference frames of what it should look like. And I got:

m1v1+m2v2=(m1+m2)vf
2(10)+3(5)=7vf
vf=5 m/s

I went on to the energy conservation thing, but tweaked it according to my reference frame:

m1v1^2 + m2v2^2 + kx0^2 = (m1+m2)vf^2 + kx^2

Initially, the spring was compressed none, so:

2(10^2) + 5(3^2) = (7)(5^2) + 1120x^2

245 = 75 + 1120x^2

70 = 1120x^2

x= .25 m = 25 cm. I checked the answer for this problem from the different text book and I got it right. The problem in my original post have values similiar to this problem, but the answer is 35.9 cm. Any chance that they might've messed up? I proceeded to use these very steps on the problem above and wound up with an answer around 24.9 cm, or is it a HUGE coincidence that the way I did it for this problem is wrong, but wound up with the right answer anyways?