Work Energy Momentum Homework: Find Plank Velocity After Block Departs

[zorro]

Homework Statement

A plank of mass 5 kg is placed on a frictionless horizontal plane. Further a block of mass 1 kg is placed over the plank. A massless spring of natural length 2 m is fixed to the plank by its one end. The other end of the spring is compressed by the block by half of spring's natural length. The system is now released from rest. The spring constant is 100 N/m. What is the velocity of plank when the block leaves the plank?

Homework Equations

The Attempt at a Solution

Since the plank acquires some velocity, there must be some friction in between the two blocks.

Applying Energy conservation just after the block is released,
1/2 kx^2 = 1/2 mv^2
x=1 and m=1
v=10m/s

Applying momentum conservation to the block-plank system,
m x v= m x v1 + M x v2 where v1 is the velocity of the block just before leaving the plank

I can't find another equation after this.

 

[hikaru1221]

Since the plank acquires some velocity, there must be some friction in between the two blocks.

There is also the elastic force from the spring. The spring exerts forces on both the mass m and the plank M.
The question doesn't mention anything about friction between m and M. But we can think of a tricky way to refute the existence of friction: In 2 extreme cases, the behaviors of the system are different. When friction is too small, of course m and M will move. When friction is too large, m and M remain at rest. If we are to find the state of motion of the system, that means the system must obtain one and only one state of motion. Besides the question mentions that m leaves M. Therefore the most likely situation is that there is no friction. Anyway, I would say that this is a mistake of the question.

So with that assumption, we have 2 equations: energy conservation & momentum conservation. I guess it's now easy to you

 

[zorro]

There is also the elastic force from the spring. The spring exerts forces on both the mass m and the plank M.

How will the spring exert force on the plank M?. The spring is not attached to M. It only exerts a backward force on the wall (rigid support)

 

[physhelper301]

It's hard to tell what what this problem looks like from your description. Also, conservation of momentum does not apply if you have the energy being transferred from the spring to the block and plank. Anyway, there's some good Physics Solvers with Conversions at http://bluesolver.com, if that helps.

 

[hikaru1221]

How will the spring exert force on the plank M?. The spring is not attached to M. It only exerts a backward force on the wall (rigid support)

From the question statement: "A massless spring of natural length 2 m is fixed to the plank by its one end. The other end of the spring is compressed by the block". Is the wall mentioned in the question?

 

[zorro]

Thanks. I got the answer.