Calculating Acceleration in a Pulley System with Inclined Boxes

[zaga04]

Homework Statement

They're two boxes connected on a pulley, each weighing 2 kg. Box 1 is on a 30 degree incline and box 2 is on a 60 degree incline.
a. Find the acceleration ignoring friction
b. Find the acceleration if the coefficient of kinetic friction is 0.1.

Homework Equations

F=ma
F_fr=u_kF_N

The Attempt at a Solution

I drew the free-body diagram. We are missing the pulling of pushing force (F_p), the tension force and the acceleration (which we are trying to find).

So this what I did for part a (ignoring friction):
BOX 1-
- ∑F_x1=F_p+mgsinΘ-F_T=m₁a₁
- F_t=F_p + mgsinΘ - m₁a₁

I solved for tension force since we don't have that.

BOX 2-
- ∑F_x2=F_p-mgsinΘ+F_T=m₂a₂
I substituted the equation from Box 1 for F_t so I could eliminate it.
- F_p+F_p+mgsinΘ-mgsinΘ - m₁a₁=m₂a₂
- 2F_p/m₁m₂=a

So I am left with F_p still, which we don't know. I am confused.

For part b, with coefficient of kinetic friction of .1, I did the same thing but I added F_fr for box #2 because I made it so that the pulling force and the tension force were in the same direction while the frictional force would obviously be opposing that. For box #1 I thought that F_t would be like the frictional force since it's opposing force (I made the box going down in #1) so I didn't even add it for that part.

Can you tell me what I am doing wrong.

 

[cepheid]

There is no external applied force (Fp) unless it is explicitly stated that there is. You seem to be under the impression that somebody needs to "do something" to get this system moving. Gravity is perfectly capable of doing that just fine. The system is exactly as described, nothing more, nothing less.

 

[zaga04]

Alright, I'll go see if I can solve it without having an applied force.

 

[zaga04]

So ignoring Fp would it go something like this...

Box 1:
Ft-mgsin30=m1a1
Ft=m1a1 + mgsin30

Box 2:
Ft-mgsin60=m2a2
m1a1+mgsin30-mgsin60 = m2a2
mgsin30-mgsin60/m1+m2 = a
a= -1.8 m/s^2

-------------------------
b.
Box 1
Ft-mgsin30-ukFn=ma
Ft=ma + mgsin30+ukFn
*Fn=mgcos30=16.97*

Box 2
Ft-mgsin60-ukFn=ma
m1a1 + mgsin30 - uk1Fn1 - mgsin60 - uk2Fn2 = m2a2
mgsin30 - uk1Fn1 - mgsin60 - uk2Fn2/m1+m2 = a
9.8 - (.1)(16.97) - 16.97 - (9.8) (.1)/4 = a
a = -1.61 m/s^2

correct?