- #1

jisbon

- 476

- 30

- Homework Statement
- Three objects lie on frictionless surface with the last one connected to a spring with constant k. Object on left travels at velocity to right v to the right and the other 2 remain stationery at first. Show that maximum change in length of spring is ##\sqrt\frac{4mv^2}{9k}## assuming collsion between the first 2 objects is elastic

- Relevant Equations
- COM: ##mv= mv_{a} + mv_{b} ##

COE: ##\frac{1}{2}mv^2 =\frac{1}{2}mv_{a}^2 + \frac{1}{2}mv_{b}^2##

Hola!

So my first approach to this is use both the conservation of energy and momentum equations since collision between the first two objects are elastic.

Let the 3 blocks be a,b and c (from left to right)

Does this means the following:

whereby

##v_{a} ##= speed of block a after collision

##v_{b}##= speed of block b after collision

COE:

##\frac{1}{2}mv^2 =\frac{1}{2}mv_{a}^2 + \frac{1}{2}2mv_{b}^2##

COM:

##mv= mv_{a} + 2mv_{b} ##

I'm not supposed to relate any of this equation to block C since it isn't directly involved in the collision with block a, is this correct?

Thanks