Why can't I show Newton's Third Law by different means?

[UseAsDirected]

Homework Statement

A small mass (1 kg) sits next to a larger mass (3 kg) on a table. A force of 5 Newtons pushes from left to right on the system while a force of 3 Newtons pushes from right to left on the system. Am I justified to conclude that the net force on the larger block has magnitude 2 Newtons?

Homework Equations

Why can't I get the same answer when I solve separately the force of block two onto block one (the larger onto the smaller)? I get the answer when I solve for F_12 and then state that F_21 is - F_12 by Newton's Third Law. But, why can't I do the reverse, F_21 solved first? Why do I get two separate answers?

The Attempt at a Solution

I correctly answer that the answer is no. In fact, the force on block two (the larger block) is actually 1.5 Newtons. First, I treat the whole as a single system to get the acceleration, which is

a = (F_right - F_left) / (m1 + m2) = 0.5 m/s^2

I then solve for the force of block one onto block two to get

F_12 = m2*a = [ m2 / (m1 + m2) ] * (F_right - F_left) = 1.5 Newtons (this is the answer)

To get the force of block 2 onto block one, I simply chant that because they are an interaction pair,

F_12 = - F_21.

[Onion]. BUT, if I start the problem solving for the force of block two onto block one, F21, I cannot get the answer. Actually, I get that the F_21 = 0.5 Newtons. This does not make any sense.

F_21 = m1*a = [ m1 / (m1 + m2) ] * (F_right - F_left) = 0.5 Newtons ? (why isn't it 1.5 N?)

My point is that I only get the right answer when I do it one way. When I try different ways to reinforce that I understand, being mathematically poetic, I quickly hit the skids.

Thank you and looking forward to see where I went wrong.Sidenote

Is it correct for me to write that the force on block one is

F_1 = F_right - F_21 = m1*a ?

and that that force on block two is

F_2 = F_12 - F_left = m2*a ?

 

[mfb]

Which mass is left, which one is right?

F_12 = m2*a

This is not correct, as F_12 is not the only force acting on mass 2. There is another one.
The other derivation has the same issue, so you get two wrong answers.

Is it correct for me to write that the force on block one is

F_1 = F_right - F_21 = m1*a ?

and that that force on block two is

F_2 = F_12 - F_left = m2*a ?

That is a better approach and it should lead to a correct answer.

 

[UseAsDirected]

Hello,

Block one is the left block and block two sits to its right. Do you mean that this is wrong, too? 'F_12 = m2*a = [ m2 / (m1 + m2) ] * (F_right - F_left) = 1.5 Newtons. ' 1.5 Newtons is the solution at the back of the book.

Thanks.

 

[mfb]

1.5 N is certainly not the force between the blocks.
An easy cross-check: the right, heavy block has a force of 3 N towards the left side and the force |F_12| in the opposite direction. It is accelerating to the right. Clearly |F_12| has to be larger than 3 N.

 

[UseAsDirected]

Yes, but there is also a force of 5 Newtons pushing to the right (on block one side). The 3 Newton force is pushing leftward on block two.

 

[mfb]

Sure, the 5 N force makes sure that the block accelerates to the right. Details are not relevant for the argument that the mutual force between the blocks has to exceed 3 N.