- #1

Covenant32

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## Homework Statement

Two particles of mass m1= 2.2 kg and mass m2 = 4.5 kg that are free to move on a horizontal track are initially held at rest so that they compress a spring as shown in the figure below. The spring has a spring constant k = 395 N/m and is compressed 0.15 m. Find the final velocities of the two particles.

## Homework Equations

M1V1=M2V2

1/2M1V1^2 + 1/2M2V2^2 = 1/2 kx^2

## The Attempt at a Solution

I am copy/paste a solution for the problem that is exactly what I did but with different numbers.

Conservation of momentum:

m1 v1 + m2 v2 = 0 ...(1)

Conservation of energy:

m1 v1^2 / 2 + m2 v2^2 / 2 = kx^2 / 2

m1 v1^2 + m2 v2^2 = kx^2 ...(2)

From (1):

v2 = - m1 v1 / m2

Substituting for v2 in (2):

m1 v1^2 + m1^2 v1^2 / m2 = kx^2

m1 m2 v1^2 + m1^2 v1^2 = k m2 x^2

m1(m1 + m2)v1^2 = k m2 x^2

v1^2 = k m2 x^2 / [ m1(m1 + m2) ]

v1 = sqrt{ 395 * 4.4 * 0.11^2 / [ 2.3(2.3 + 4.4) ] }

v1 = 1.17 m/s to 3 sig. fig.

Similarly:

v2^2 = k m1 x^2 / [ m2(m1 + m2) ]

v2 = sqrt{ 395 * 2.3 * 0.11^2 / [ 4.4(2.3 + 4.4) ] }

v2 = 0.611 m/s to 3 sig. fig.

I did this and my answer is incorrect.

I ALSO tried:

0.5*k*x^2 = 0.5*m1*v1^2

0.5*k*x^2 = 0.5*m2*v2^2

and THAT was incorrect. I'm in the dark here.

By the way, this is my first post, though I've been browsing PF all semester! Thanks for all the previous help =)