Homework Help: [Force] Two Prisms

1. The problem statement, all variables and given/known data
A prism has the mass m with the angle x = 45°(look at the picture) placed on the ground without friction. The other prism, which has the same mass m, is placed above the first prism(the first prism is bigger). A horizontal force F is given to the second prism so the displacement with respect to the first prism is zero( or not moving). What is the friction between the two prism ( in F, m, and g). g = earth gravitational acceleration

The picture -> http://i28.tinypic.com/nycih4.jpg

2. Relevant equations
[tex]F = m.a[/tex]

3. The attempt at a solution
[tex]F.cosx - f - m.g.sinx = m.a[/tex]

Since the prism is not moving, so a = 0

[tex]F.cosx - \mu.m.g.cosx - m.g.sinx = 0[/tex]
[tex]F.cosx = \mu.m.g.cosx - m.g.sinx[/tex]
[tex]\mu = \fric{F}{m.g} + tanx[/tex]


Then i have no idea what to do next. I haven't even used the mass of the first prism. I also don't quite understand how the forces work so can somebody help me please?

 

Thanks Tim,

I corrected the plus-minus mistake. It should be
[tex]F = mg(\mu + tanx)[/tex]

Then the acceleration of the prisms is

[tex]F = (m + m)a[/tex]
[tex]F = 2ma[/tex]
[tex]2ma = mg(\mu + tanx)[/tex]
[tex]a = \frac{g} {2}(\mu + tanx)[/tex]

Finally, i don't know how to relate the acceleration to the friction. Can you explain it to me?

 

Do you mean, i should throw in F.Sinx to my friction equation? Which i forgot to do.

 

Just for quick clarification, you mean like this?

Horizontal Components
[tex]\SigmaFx = 0[/tex]
[tex]F - f.cosx - mg.sinx.cosx = 0[/tex]

Sorry, i'm not used to talk physics in english.