How Does Newton's 2nd Law Apply in Different Force Scenarios?

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SUMMARY

The discussion focuses on applying Newton's 2nd Law to two scenarios involving blocks A and B under different force applications. In Figure 5-51a, a constant horizontal force results in block A exerting a 20.0 N force on block B, leading to an acceleration calculation of 30 = 14a, which simplifies to an acceleration of approximately 2.14 m/s². In Figure 5-51b, block A exerts a 10.0 N force on block B, requiring a separate calculation for the force Fa. The combined mass of the blocks is 14.0 kg, which is crucial for determining the forces and accelerations involved.

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In Figure 5-51a, a constant horizontal force a is applied to block A, which pushes against block B with a 20.0 N force directed horizontally to the right. In Figure 5-51b, the same force is applied to block B; now block A pushes on block B with a 10.0 N force directed horizontally to the left. The blocks have a combined mass of 14.0 kg. What are the magnitudes of (a) their acceleration in Figure 5-51a and (b) force Fa?

Figure is attached

I drew a free body diagrams and came up with:
a) Fa +Fab = 14a
Fa + 20 = 14a

b) Fa -Fab = 14a
Fa - 10 = 14a

I don't know what to do from here. Any guidance is appreciated!
 

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30=14a for the first one
 

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