Simple little motion problem(at least for you guys)

[Melchoire]

The mass m3 is tied to m2 with an idealized string and m2 rests on m1. There is a rough
interface between m2 and m1 with a coefficient of friction μ. The mass m1 rests on a frictionless
surface. The pulley is “ideal,” that is, massless and frictionless. All three masses move together
as if m1 and m2 were solidly attached.
(a) Draw free body diagrams for the three masses showing all forces and directions of acceleration.
Find expressions for the following in terms of g, m1, m2 and m3:
(b) the acceleration of each mass.
(c) the tensions T2 and T3.
(d) the smallest value of the coefficient of friction μ to permit the above motion
http://img407.imageshack.us/img407/9299/m1m2m3.jpg

I drew the free body diagrams that wasn't really complicated. But I'm stuck on all the rest. For 'b' I wrote out Newtons second law for each mass where 'a' was equal in all but that didn't get me anywhere. When I think about it I know that the larger the masses of m1 and m2 the slower the acceleration of system. But I don't know how to get that in my equations.

Any help would be appreciated. =]

 

[rl.bhat]

Write down Newtons second law for m1, m2 and m3.
Let us see whether you done it properly.
Then we will provide further hint.

 

[Melchoire]

m3:
Fnet = T3-m3*g = m3*a
m2:
Fnet = Fn + Fg + Ff + T2= Ff = us*m2*g + T2 = m2*a
m1:
Fnet = Fn + Fg + T2 = T2 = m1*a

the magnitude of T2 and T3 are equal.

Do I have those right? Did I calculate the static friction force properly?

 

[rl.bhat]

m3:
If you take -g then acceleration must be -a.
m2.
frictional force acts in the opposite direction to T
So m2a = ...?
m1
On m1 only reaction to the frictional force act in the forward direction.
So m1a = ...?

 

[Melchoire]

m3:
If you take -g then acceleration must be -a.
m2.
frictional force acts in the opposite direction to T
So m2a = ...?
m1
On m1 only reaction to the frictional force act in the forward direction.
So m1a = ...?

You're kinda confusing me a little, you probably didn't mean to but 'a' can't be equal to 'g'...or is that not what you meant?

But from the rest I got this:
m2*a=T2+Ff

m1*a = T2

Am I right?

 

[rl.bhat]

What I meant is that T - m3g = - m3a
Second one
T -μm2g = m2a.

 

[Melchoire]

What I meant is that T - m3g = - m3a
Second one
T -μm2g = m2a.

Ok so my final f=ma equations are:

-m3*a = T - m3*g
m2*a = T - us*m2*g
m1*a = T? (am I right for this one?

But from the first one I know that T = -m3*a+m3*g = m3(g-a). So then I can just use an equivalency to solve 'a' in terms of m1,m2,m3 and g.

 

[rl.bhat]

Last one is wrong.
m1a = μs*m2*g

 

[Melchoire]

Why is that? I thought that since m1 and m2 are moving together then the force acting on m1 should be the tension force.

 

[rl.bhat]

In this problem a is same for all the masses. T is not connected to m1.
Force on m1 is reaction of the frictional force acting on m2.

 

[Melchoire]

In this problem a is same for all the masses. T is not connected to m1.
Force on m1 is reaction of the frictional force acting on m2.

Alright that makes sense. I hope I can remember this stuff for the mid term on friday. Anyways I'll try the other questions on my own and if I need help I'll come back.

 

[rl.bhat]

OK. All the best for mid term examination.

 

[Melchoire]

I'm still stuck on the first one after using equivelancy I got these equations:
a = us*m2*g/m1
a = T-us*m2*g/m2
a = m3*g-T/m3

But the question is asking to express a in terms off m1,m2, m3 and g. the closest thing I have is the first equation, but it's missing m3.

 

[rl.bhat]

First of find the tension T. Then find a.

 

[Melchoire]

T = m3*g right?

 

[rl.bhat]

No.
Equate eq. 2 and 3 from your post# 13 and solve for T.

 

[Melchoire]

Ok I get
T = m2*m3*g(1+us)/(m3+m2)

Which equation do I plug it into?

 

[rl.bhat]

In either eq. 2 or 3

 

[Melchoire]

K got it. How would I approach D?

 

[rl.bhat]

m1 and m2 will start moving when μm2g = (m1 + m2)a
Find μ.

 

[Melchoire]

so u >= (m1+m2)a/m2g?

 

[rl.bhat]

Yes.

 

[Melchoire]

Finally got something right :p Thanks for your help =]