Frictional forces between two blocks (one over the other)

[Hernaner28]

Homework Statement

A block of mass M_2 can move over another bigger block M_1=5.0M_2 . The coefficient of static friction between the small and big blocks is \mu _s=0.40 , the kinetic coefficient between them is \mu _{k,2}=0.30 , and the kinetic coefficient between the big block and the floor is \mu _{k,1}=0.50 . In a previous moment showed in the picture, a person had given the blocks a velocity v giving a boost.

Homework Equations

Does the small block slide? Calculate the aceleration of both blocks.

The Attempt at a Solution

I draw two diagrams, for each block. But I'm not sure if I'm missing something or if the friction forces are directionally correct. Besides I have no idea how to go on after that... these are my diagrams:

When it says "¿estatica o dinamica?" I am just wondering if that force is static or kinetic.Edit:

I think the diagram of block 2 is missing a friction force which is caused by m1 as a reaction.. Anyway I do know how to write up the friction force for the floor and big block:

f_{floor}=0.50\cdot N_2
N_2=m_1g+m_2g=6m_1g
f_{floor}=0.50\cdot 6m_1g

But then?

Thanks for your help!

 

[gulfcoastfella]

In your attempt at a solution, it looks like you may have swapped M1 and M2. M1 is the larger mass on the bottom and M2 is the smaller mass on top, based on the problem description you gave.

 

[Hernaner28]

Could you please me show me how it would be the correct way to represent the forces and how to proceed? Thanks

 

[Hernaner28]

Alright I made this diagram for M1. Please I want to know if it is OK. I see nobody is replying... is quite hard...

 

[Hernaner28]

I am told to do this exercise from an inercial reference... so... I can't represent the inercial force in the small block, right? I cannot figure it out... no ideas? I know it's hard, but maybe you have just an idea, is that so hard? Can't believe anybody has replied lol

 

[Hernaner28]

I progressed... attached a drawing which I scanned

 

[gulfcoastfella]

Everything looks correct, all the way up until the last equation on the whiteboard. I think there may be some algebraic mistakes there. Once you get the algebra sorted, though, you can equate the "f_{block}" terms and discover the acceleration, assuming as you did that the block is on the verge of slipping.

There's something strange going on with the problem statement, though. The problem statement says that the blocks are traveling at a velocity "v", but it says nothing about acceleration. Without knowing the acceleration, you can't know if the block will slip or not (obviously for zero acceleration there is zero slippage.) If you were asked to find the acceleration at which slippage begins, then you could equate the "f_{block}" terms in the last two equations to each other and solve for "a".

 

[gulfcoastfella]

Sorry, ignore the comment about the last equation being incorrect; I just had trouble following what you did. So the equations you arrived at will tell you the frictional force and the acceleration present when "Mass 2" is on the verge of slipping.

 

[Hernaner28]

The problem asks me to see if the smaller block (the one which is over the other) slips and we know that if it doesn't slip both acelerations (a1 and a2) are equal! That's what I wrote at the end of my notes - the equality is a1 = a2 but how could I know they're different or equal having that?

Thanks for your reply

 

[gulfcoastfella]

That's what I don't understand; you're asked to determine if the small block slides, but you're not given the acceleration which would or would not cause the slippage. Does the problem mention any forces at all?

 

[Hernaner28]

No. We are supposed to draw the diagrams and know which forces are on each mass. The problem only give us the information I posted in the first one, that's all. I think we have to use the max. friction force that the block could have to not slide or something like that. I am currently at Calculus but when I return to Physics I will take a deeper look and I'll try to finish this once and for all.

Thanks.

 

[Hernaner28]

Ideas? Nobody?