# A momentum problem

1. Mar 12, 2005

### Anzas

a mass of 4kg is tied to a spring, the spring's constant is K = 100n/m
a second mass of 6kg is moving towards the spring at a speed of 10m/sec

1.what is the spring's shrinking.
2.what is the final speed of both masses.

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2. Mar 12, 2005

### futb0l

1. Conservation of Energy

$$\frac{1}{2}m_1v_1^2 = \frac{1}{2}kx^2$$

The kinetic energy of the moving mass is converted into the strain energy of the spring. This energy is then converted into kinetic energy of the two masses.

2. Assign the right direction as positive. Now, you have two equations, conservation of momentum and conservation of energy, so assuming no external forces and energy loss, it's going to be just like an elastic collision.

I found that:

$$v_1' = 2 m/s$$
$$v_2' = 12 m/s$$

Check it for yourself, I might've got it completely wrong.