Question

If F = 20 N, m1 = m2 = 3 kg and the acceleration is 0.5 m/s². What will be the tension in the connecting cord if the friction forces on the two blocks are equal. How large is the frictional force on either block?

Answer 1

First consider the 2 masses as a single object. Total mass = 3+3=6 kg 

Resultant force, F= ma = 6 x 0.5 = 3N 

Since an external force of 20N is being applied, the frictional force must be 20-3=17N 

(8.5N on each mass). 

Now consider m1 by itself. The resultant force on it = ma = 3 x 0.5=1.5N 
Let T = tension in rope joining m1 and m2 

The only 2 horizontal forces on m1 are T (to right) and 8.5N (friction to the left) 

Resultant horizontal force on m1 = T1 - 8.5 

T-8.5 = 1.5 

T = 10N

Answer 2

Let    f = friction ,     T = tension
Equations of motion for both masses:
           F - f - T = m a
           T - f = m a
Subtract (2) from (1) :    F = 2T     so  T = F/2 = 10 N
Friction = T - m a = 10 - 3 * 0.5 = 8.5 N