What Are the Tensions in Two Blocks With Friction and Acceleration?

[Zywo]

Homework Statement

Two blocks of mass m1=80 kg and m2=100 kg and attached by a string, another sting comes off of mass m1 and is pulled horizontally (kinda looks like this) (T1 & T2 are tensions)
m2--T2--m1--T1--> there is a coefficient of friction u=.14 for both blocks, what is the tension in both strings while the system accelerates at 2 m/s^2?

Homework Equations

Fnet=ma
Ff=u(N)

The Attempt at a Solution

Ok so for m1 horizontal forces are T1 to the right, T2 to the left and friction.
T2=(100)(9.8)(.14)=137.2 N Friction for m1=(80)(9.8)(.14)=109.8
So T1-T2-Ff = m1*a therefore T1=(80)(2)+(109.8)+137.2= 407 N
Is this Correct??
Thanks!

 

[jegues]

First consider the 2 block system as a 1 block system (combine their masses) then you can solve T1. Once you have this you can distribute T2 appropriately.

 

[kerimek]

Your approach is correct, but there is a slight error in your calculation for T1. The correct value for T1 would be (80)(2) + 109.8 - 137.2 = 271.8 N. This is because the net force on m1 is equal to its mass times its acceleration, which is 80 kg * 2 m/s^2 = 160 N. Therefore, T1 must be equal to this net force minus the friction force and the force from m2 (which is T2). Keep up the good work!