Find Mass M1 Given Acceleration, Angle, and Friction

[thatguy101]

Homework Statement

M1 and M2 are two masses connected as shown (M2 hangs over the table). The pulley is light (massless) and frictionless. Find the mass M1, given that M2 (3.0 kg) accelerates downwards at 2.31 m/s^2, q is 20°, and μk is 0.41.

Homework Equations

F=ma
μn=friction

The Attempt at a Solution

Well I thought I could find tension using F=3*2.31 but that didn't get me anywhere. I drew a force diagram for m1, but it looks like there's too much missing to be able to continue. Is the tension part at least right?

 

[tiny-tim]

hi thatguy101! welcome to pf!

(we usually use "T" for tension )

Well I thought I could find tension using F=3*2.31

is that F_total = ma?

what about gravity? ​

 

[thatguy101]

so then would I subtract gravity?
Ft=3*2.31-3*9.81?

 

[grzz]

Why not give us the diagram so that we know what q = 20$^{o}$ refers to?

 

[thatguy101]

Sorry. It's suppose to say θ.
m1 is on an incline of 20°, and m2 is hanging off the incline.

 

[thatguy101]

Ok so my diagram looks like this.
For m1 I have forces in the y direction as y: Fg*cosθ-Fn=0
And the forces in the x direction as x:Ft-Fg*sinθ-Ff=a.
And then for m2 there are none in the x direction but for y I have y: Fg-Ft=ma.
Am I right so far?

 

[tiny-tim]

Ok so my diagram looks like this.
For m1 I have forces in the y direction as y: Fg*cosθ-Fn=0
And the forces in the x direction as x:Ft-Fg*sinθ-Ff=a.
And then for m2 there are none in the x direction but for y I have y: Fg-Ft=ma.
Am I right so far?

yes, except in your second equation, you need to check the signs (and you forgot to write the m before the a)

 

[thatguy101]

Thank you. I figured it out.
So I had Ft-mg*sinθ+μ*mg*cosθ=ma
so Ft=mg*sinθ+μ*mg*cosθ+ma
factor out the m, Ft=m(g*sinθ+μ*g*cosθ+a)
then solved for m. and since Ft= m2g-m2a, I just put in the numbers and came up with 22.47 N amd just plugged in everything else into the equation above and got 2.38 kg