Potential Mistake in Free-Body Diagram

[TRB8985]

Homework Statement

No homework statement; conceptual question only.

Relevant Equations

W = mg

I had a question on the way I've set up my free-body diagrams in the past and was wondering if I've been making mistakes in the setup (despite arriving at the correct answer).

Imagine a very simple situation of stacked blocks, like the the following:

When drawing the free-body diagram of such a situation, previously I was combining the forces of the weights and the normal force acting on B, like this:

Here's my question: Is this equivalent to the "standard" way of drawing an FBD for this scenario as seen below?

My concern is that, while I was achieving the correct answer, I was being lazy in the setup/notation. Would appreciate any feedback, thanks!

 

[erobz]

Homework Statement: No homework statement; conceptual question only.
Relevant Equations: W = mg

I had a question on the way I've set up my free-body diagrams in the past and was wondering if I've been making mistakes in the setup (despite arriving at the correct answer).

Imagine a very simple situation of stacked blocks, like the the following:

View attachment 338891

When drawing the free-body diagram of such a situation, previously I was combining the forces of the weights and the normal force acting on B, like this:

View attachment 338892

Here's my question: Is this equivalent to the "standard" way of drawing an FBD for this scenario as seen below?

View attachment 338893

My concern is that, while I was achieving the correct answer, I was being lazy in the setup/notation. Would appreciate any feedback, thanks!

If you take $N_{A+B}$, and $W_{A+B}$ the you haven’t actually “freed” block B from block A. They are a taken together as a single system. The diagram does not accurately represent the isolated system(s) you actually chose.

 

[TRB8985]

Makes total sense and verifies my suspicion of being incorrect, thank you! Will avoid doing it that way in the future.

 

[erobz]

You might get away with it while problems are less demanding, but the inconsistency will likely cause you grief down the road if you didn’t address it. Good job for doing so.

 

[Steve4Physics]

Hi @TRB8985. I'd like to add this.

Assuming equilibrium (no acceleration, e.g. B resting on the ground)) then perhaps it’s worth noting the following:

For a FBD of A&B considered as a single object, we ignore internal forces. So there would be just two FBD forces: the total weight and the normal force from the ground.

For A considered alone, there are two FBD forces: its weight and the normal force of B on A.

For B considered alone, there are three FBD forces: its weight, the normal force of A on B and the normal force from the ground.

My personal preferences are to draw:
- each weight-arrow starting from the centre of gravity (approx);
- each contact force-arrow starting or ending on on the appropriate surface;
- each arrow’s length corresponding to the magnitude of the force (approx., if known);
- non-overlapping arrows.

For example my FBD for block B would be:

Edit. My diagram is not the best. The arrow for $F_{ground~on~B}$ is too short; its length should be the sum of the lengths of the 2 other arrows. And the weight arrow should start nearer B's centre (assuming B is uniform).

 

[TRB8985]

No worries, I understand exactly what you're trying to convey there. I had difficulty drawing them in the post LaTeX too - thankfully Powerpoint and screenshots worked nicely!

Thank you for the insight on that, appreciated.