Static friction 2 boxes and force question

[weinbergshaun]

Question:
A large box of mass M is pulled across a horizontal, friction-less surface by a horizontal rope with tension T. A small box mass m sits on top of the box. The coefficients of static and kinetic frciton between the two boxes are Us and Uk. find an expreeion for the maximum tension Tmax for which the small box rides on top of the large box without slipping. Relevant equations
None given

The Attempt at a Solution

Know formulas:
FFriction (or FF) = m2 x a (the friction of the top on lower box)
FTension (or FT) - FFriction = m1 x a
the two forces must have the same acceleration in the second formula, will get both acc. alone on both formulasand equal them.

Top block acc. is:
FT = m2 x a (get a alone)
a = FF/m2

Bottom block acc. is:
FT - FF = = m1 x a
FT – (m2 x a) = m1 x a (substituting Ff for the m2 x a value in order to have one force value only)
FT = m1 x a + m2 x a
FT = a(m1 + m2)
a = FT/(m1 + m2)

a = a, getting Tension or FT alone:
FF/m2 = FT/(m1 + m2)
FT = FF(m1 + m2)/m2
FMax = m1 x g x Us (m1 + m2)/m2 (substituting FT with max as it will represent max).

Is this correct, thank

 

[BvU]

Relevant equations
None given

The idea is that here you list the equations you're using in the solution attempt. Like $F = ma$ and $F_{\rm fric, max} = \mu_s N$...
In particular the subscript max is important: that's the friction force that determines the maximum T. But you understand that already.

And don't change notation on the way: if your problem statement uses Tmax, stay with it and don't change to Fmax.

FT = m2 x a (get a alone)

You mean FF

Other than that, it looks flawless to me

 

[Mastermind01]

What's m1 and m2?

 

[weinbergshaun]

The idea is that here you list the equations you're using in the solution attempt. Like $F = ma$ and $F_{\rm fric, max} = \mu_s N$...
In particular the subscript max is important: that's the friction force that determines the maximum T. But you understand that already.

And don't change notation on the way: if your problem statement uses Tmax, stay with it and don't change to Fmax.

You mean FF

Other than that, it looks flawless to me

Thanks! Late nights for me, i sometimes makes mistakes lol!

 

[weinbergshaun]

What's m1 and m2?

M1 is top box M2 is bottom box

 

[BvU]

Go to bed !

 

[Mastermind01]

Your answers wrong. You isolated the acceleration incorrectly for the top block. This is what happens if you change notation.

 

[BvU]

I rest my case

And don't change notation on the way: if your problem statement uses

in this case M and m

How about m1 = bottom box and m2 = top box ?

 

[Mastermind01]

I rest my case
in this case M and m

How about m1 = bottom box and m2 = top box ?

I think it's still wrong, if I remember the general solution correctly.

 

[Mastermind01]

Yep, I worked it out, it's wrong. Though I can't find out where he went wrong through all the m1 and m2's.

EDIT: Found it, you messed up the last step.

 

[weinbergshaun]

I rest my case
in this case M and m

How about m1 = bottom box and m2 = top box ?

Sorry lol, m1 is bottom, m2 is top! Spot on

 

[weinbergshaun]

Yep, I worked it out, it's wrong. Though I can't find out where he went wrong through all the m1 and m2's.

EDIT: Found it, you messed up the last step.

sorry m2 is top box, m1 is bottom box.

 

[Mastermind01]

sorry m2 is top box, m1 is bottom box.

I get it, you still messed up the last step

 

[BvU]

You are absolutely correct, MM, through all the m1 and m2 he missed FF = m2 μ g and filled in m1 in the last step.

When wbh wakes up he'll see it more clearly. I should go too for overlooking that !

 

[weinbergshaun]

sorry m2 is top box, m1 is bottom box.

Where did i mess up last step, sorry been spending a week on this question lol

 

[Mastermind01]

Bvu is correct, that's where you messed up. Go to sleep now!

 

[weinbergshaun]

You are absolutely correct, MM, through all the m1 and m2 he missed FF = m2 μ g and filled in m1 in the last step.

When wbh wakes up he'll see it more clearly. I should go too for overlooking that !

Ah ok lol i see, thanks for your help!

 

[BvU]

been spending a week on this question

Then it's really time to go !

And: you're welcome. Well done, MM, wbh and me

 

[weinbergshaun]

Bvu is correct, that's where you messed up. Go to sleep now!

Thanks! Yes off to bed!

 

[weinbergshaun]

Then it's really time to go !