Two boxes of masses m and 3m are stacked. The surface between the more massive box and the horizontal surface is smooth and the surface between the boxes is rough. If the less massive box does not slide on the more massive box, what is the static friction force on the less massive box?

Question

anonymous · Answer

Here's the picture

ookawaiioo · Answer

static friction = does not move

So your only looking at  m and 3m. 

F=usN = us*mass*gravity

anonymous · Answer

what do i have to find first ?

anonymous · Answer

The weird part about this question is that they don't tell you if the larger box is experiencing any force or not; so it's sort of an incomplete question :P

anonymous · Answer

Hmmm thanks.. let me try again

anonymous · Answer

wait did you see the picture that came with the question tho ? i posted it :o
there's force moving right

anonymous · Answer

You're totally right! sorry :P

anonymous · Answer

ugh im so confused

anonymous · Answer

sorry, I meant that you're right that there is a force.  It made my solution wrong, so I'm trying to work it out.  Sorry for confusingness :P :/

anonymous · Answer

it's ok :D thanks for helping me

anonymous · Answer

So this is a weird one
For the big box, the singular force just equals ma.

$$\sum F_{big} = F = Ma$$
and so it's experiencing an acceleration of
$$ a = \frac{F}{M} = \frac{F}{3m}$$ 

For the little one, it's "feeling" the big box's acceleration; so even though the static friction is keeping it from falling off the block, it's technically the force of friction that's moving it forward in the frame of the little box; so

$$ \sum F_{tiny} = F_f = ma$$
and the acceleration is what we found up top!

$$ F_f = m\Big(\frac{F}{3m}\Big)$$
So the force if friction is
 
$$F_f = \frac{F}{3}$$

Does that make sense?

anonymous · Answer

Oh.... wait

anonymous · Answer

Is that not the right answer? :/

anonymous · Answer

oHH so you basically just substitute

anonymous · Answer

i get it...
thanks :D

anonymous · Answer

Yup yup ^_^  All you need to know is the acceleration of the "box system," and with that the frictional force is just what keeps the little box traveling at the same speed as the big box ^_^

anonymous · Answer

and welcome! ^^