When Friction the block m2 start to move?

[navneet9431]

Homework Statement

A block m2 is placed on a surface where the coefficient of friction is μ2 and another block m1 placed over the block m2 where the coefficient of frictio is μ1.
A force F=k*t(Force as a function of time),is acting on the block m2.

Now my question is that when would the block m2 start moving?

Homework Equations

F=ma

Static Friction=Coefficient Of Friction*Normal Force

The Attempt at a Solution

I tried solving this by drawing the FBD of the objects.

See two forces fr1 and fr2 will be acting on the block m2.
So m2 would start to move when F>fr1+fr2.
Or simply we can say k*t=fr1+ft2.
So the block m2 would start to move just after time "t".
Is my result correct?

 

[Delta2]

Yes it is, just be careful on how you going to equate forces fr1 and fr2 with relation to the weights $m_1g$ and $m_2g$ and the static friction coefficients $\mu_1$ and $\mu_2$.

 

[navneet9431]

Yes it is, just be careful on how you going to equate forces fr1 and fr2 with relation to the weights $m_1g$ and $m_2g$ and the static friction coefficients $\mu_1$ and $\mu_2$.

Thanks for the reply!
So my result was correct.
See the pic I have uploaded.
Have I proceeded correctly?

 

[Delta2]

Yes your result seems correct to me. Actually a minor correction, it should be $t_0\geq…$ not just >.

 

[haruspex]

Static Friction=Coefficient Of Friction*Normal Force

There is a common blunder in that equation, and it is causing you to get the wrong answer.
For kinetic friction it works: $F_k=\mu_kF_N$, but for static friction there is a key difference.

 

[navneet9431]

There is a common blunder in that equation, and it is causing you to get the wrong answer.
For kinetic friction it works: $F_k=\mu_kF_N$, but for static friction there is a key difference.

You mean to say that my result is wrong?

 

[haruspex]

You mean to say that my result is wrong?

Yes.

 

[navneet9431]

Yes.

How?Please explain.
And,also mention the correct result!

 

[haruspex]

How?Please explain.
And,also mention the correct result!

Consider the situation when the applied force is zero. What are the frictional forces?

 

[navneet9431]

Zero

Consider the situation when the applied force is zero. What are the frictional forces?

 

[haruspex]

Zero

Right, so what is wrong with $F_s=\mu_sF_N$?

 

[Delta2]

Ah, I think @haruspex is right, it is the maximum static friction that is equal to $\mu_sF_N$. Static friction can take any value between zero and this maximum value.

When the box $m_2$ is about to move then the static friction between $m_2$ and the surface is indeed as you calculate $fr_2=\mu_2(m_1+m_2)g$ but box $m_1$ doesn't move with respect to box $m_2$ so the kinetic friction between m1 and m2 is just zero and also the static friction $fr_1$ is zero at the start of movement, later it gets bigger as the external force gets bigger.