Momentum & Kinetic Energy Conservation: 1kg Block & 2kg Block Collision

[xshezsciencex]

A 1kg block is at rest on a horizontal frictionless surface touching the end of an unstretched spring of spring constant 200N/m. Tjhe other end of the spring is fixed to a wall. A 2kg block traveling at a speed v(initial)=4m/s collides with the 1kg block, and the two blocks stick together.

I am not sure if momentum or kinetic energy is conserved in this collision, if it is please explain.
When the blocks momentarily stop, by what amount is the spring compressed?
I understand that when the spring expands it will accelerate the coupled blocks from rest so what is the speed of the blocks when they are 0.20m to the left of the spring's end?

 

[tiny-tim]

I am not sure if momentum or kinetic energy is conserved in this collision, if it is please explain.

Hi xshezsciencex!

Momentum is always conserved in collisions.

Energy is never conserved unless the question says so!

In this case, the question says that the collision is perfectly inelastic (whcih is just about the opposite of conservation of energy), in that the two final velocities are the same.

So use conservation of momentum, plus v_f1 = v_f2.

(After the collision, when the spring is being compressed, energy is conserved, and of course momentum isn't)

 

[Borek]

Energy is never conserved unless the question says so!

Perhaps putting "kinetic" at the beginning will make this phrase easier to swallow

 

[tiny-tim]

Hi Borek!

"mechanical" energy, actually!

 

[Borek]

Good point. At least we agree that the statement was a little bit bold