Question about the Two-Body systems

[Ronel]

Two blocks of identical material are connected by a light rope on a level surface. An applied force of 55N

causes the blocks to accelerate. While in motion, the magnitude of the force friction on the block is 44.1 N. Calculate the acceleration of the blocks.


20 kg|---------------------10kg | -----------------


(sorry about the diagram it looks ugly)

Fnet= Fapp - Ff
Fnet= 55 N - 44.1
Fnet= 10.9N

Fnet=ma
a=Fnet/mt

a=10.9 N/30 kg which is equal to .363

Here's another question: Refer to the information above. The force on friction on the 10-kg block has a magnitude of 14.7 N.

a) calculate the tension in the rope connecting the two blocks

My solution

Ff= μ Fn

μ= Ff/Fn
μ= 44.1/196.2
μ= .2247

I know how to get the Ff2 this is what I did -----> Total Friction(44.1) - 14.7(Ff1 =Friction of 10Kg) = Ff2= 29.2 (20Kg)
My question is can you still answer the a) question without knowing the Friction of 10kg ? (Ff1) I got question a right but just wondering if you can still answer it without know the Friction of 10kg (Ff1).​

 

[haruspex]

I don't see where you arrive at the tension.
The easiest way is to think about the following ratios:
- frictional force, blk1 v. blk2 v. combined
- accelerational force, blk1 v. blk2 v. combined
- tension in RH rope v. tension in LH rope