Simple yet complex problem - 2 mass 1 spring system

[mokk01]

Hi could someone help me solve this problem?

there are 2 masses on a table connected by a spring with unknown stiffness. Mass of block I is m1 and mass of block II is m2. Also unknown friction coefficient u (same for both masses)

I need to find the minimum constant force applied to block II so that block I moves (at least a little bit)

thanks

btw I have no idea how to derive the final answer. I know that the force acting on block II needs to overcome static friction. And once block II moves it will do work on the spring and this work stored in the spring will move block I.

 

[Hootenanny]

Hi could someone help me solve this problem?

there are 2 masses on a table connected by a spring with unknown stiffness. Mass of block I is m1 and mass of block II is m2. Also unknown friction coefficient u (same for both masses)

I need to find the minimum constant force applied to block II so that block I moves (at least a little bit)

thanks

btw I have no idea how to derive the final answer. I know that the force acting on block II needs to overcome static friction. And once block II moves it will do work on the spring and this work stored in the spring will move block I.

Welcome to PF mokk01,

The trick here is to consider each block separately. Suppose that you apply a force F to block II, what is the condition on F for block II to move?

Now, once block II begins to move the spring will compress, as you say, and exert a force (say T) on block I. What is the condition on T for block I to move?

 

[mokk01]

Welcome to PF mokk01,

The trick here is to consider each block separately. Suppose that you apply a force F to block II, what is the condition on F for block II to move?

Now, once block II begins to move the spring will compress, as you say, and exert a force (say T) on block I. What is the condition on T for block I to move?

Thanks for the reply, but i have considered what you have said. Force on block II must overcome spring and static friction to move the block. After the spring compresses/stretches this will create a force on block I which if greater than block I's static friction will make it move. Using this I end up with an equation that is of the form : F = 3/2 u1m1g + u2m2g. i.e the force is independent of the spring. This doesn't seem to be correct. I have been told to use an 'energy balance' to solve this problem but all i know is that the work done on the spring is 1/2kX^2 and that work = force . displacement.

Any ideas??