How Do You Calculate the Total Acceleration and Force on Two Touching Blocks?

[Heather_]

Homework Statement

For two touching blocks, a constant horizontal force Fa is applied to block A to the right, which pushes against block B with a 26.0 N force directed horizontally to the right. In figure (b), the same force Fa is applied to block B to the right (the blocks switched places); now block A pushes on block B with a 13.0 N force directed horizontally to the left. The blocks have a combined mass of 6.00 kg (A is smaller than B).

I need to know the system's total acceleration and the force being applied.

Homework Equations

Newton's laws; friction is being ignored

The Attempt at a Solution

is it safe to assume that the mass of A is half the mass of B? (a pushes on b with half the force that b forces on a). That would make the acceleration 52, which isn't correct. Have i missed something?

 

[PhanthomJay]

Hi Heather, welcome to Physics Forums!

is it safe to assume that the mass of A is half the mass of B? (a pushes on b with half the force that b forces on a).

Yes, this is a very good observation. Now since A is half of B, and together their mass is 6 kg, then A = ? kg and B = ? kg.

That would make the acceleration 52, which isn't correct. Have i missed something?

Please show how you arrived at this number. Draw free body diagrams of each block for each case, and a free body diagram of the system of 2 blocks.

 

[Heather_]

Well obviously that would make the mass of A 2 kg and the mass of B 4. My thinking was that the block that was being pushed by the other one would need to exert an opposite force, so if A is pushing on B with a 26 N force and weighs 2 kg, the acceleration would be 13, which doesn't work (if A pushes on B with 26N force, though, why isn't that the force being applied to the system). As for the 52...I understand now why that was wrong.

 

[PhanthomJay]

Well obviously that would make the mass of A 2 kg and the mass of B 4. My thinking was that the block that was being pushed by the other one would need to exert an opposite force, so if A is pushing on B with a 26 N force and weighs 2 kg, the acceleration would be 13, which doesn't work[

If , drawing a free body diagram of B, A pushes on B with 26 N, and B has a mass of 4 kg, then per Newton 2, a = ?

(if A pushes on B with 26N force, though, why isn't that the force being applied to the system).

The force applied to the system is not the same as the force between blocks. The force applied to the system (the applied force acting on A in your first case) must move BOTH blocks.