# The Forces present on a system drawn with FBD's

• Mr LoganC
In summary, a first year physics student was struggling to draw a free body diagram of a system consisting of boxes 2 and 3 together, with specific forces listed. After several attempts, it was determined that the wording of the problem was incorrect and the correct solution was to only consider the forces acting on box 2, resulting in the answer of N,N,N,A,N.
Mr LoganC
Well, to start, I am actually in my second year of doing my Honors in Physics but am helping a first year student in understanding some of the concepts in her physics class. This question came up, and I myself cannot seem to find a solution to it. I'm quite puzzled about it...

## Homework Statement

There are 3 boxes, each with separate masses, all touch in a line.
A force of magnitude F pushes horizontally to the right against box 1 and pushes the boxes.
See diagram below:

We need to draw a free body diagram, as worded directly from the question, of all of the individual forces acting on the system consisting of boxes 2 and 3 together. Indicate the five forces listed below by choosing from the vectors in the diagram below. If none are present, then "N" is an option.

i) box 2 pushing on ground
ii)the applied force pushing on block 1
iii)the applied force pushing on block 2
iv)floor pushing on box 2
v)floor pushing on box 1

## Homework Equations

Well, we know from Newton's 3rd law that all forces have an action/reaction pair that are equal and opposite in direction. Well also know that not only is the applied horizontal force present, but also the gravitational force.

## The Attempt at a Solution

At first glance it seemed quite simple and straight forward!
i) Box 2 on ground = C from gravitational force
ii) F on block 1 = B
iii) F on block 2 = N because that is not the applied force. That would be F1 on 2
iv)Floor on box 2 = A which is the normal force that the floor pushes back with. (The action/reaction pair of gravity)
v)Floor on box 1 = A. Same logic as previous one.

Needless to say, this did not seem to work. So I tried multiple other combinations taking into account that the directions say that the system consists of boxes 2 and 3 together. I thought that perhaps box 1 was not part of the FBD. I also thought that there may be some confusing bits in the fact that it states some as "boxes" and some as "blocks"

Either way, I can't seem to get it to work. What's worse is that what I thought was fairly simple Newtonian physics, is stopping me in my tracks!

Any insight or perhaps something really simple and back to basics that I am forgetting?

Last edited:
Yes, according to wording of the problem, I would say that block 1 is not part of the system you are looking at.
What do you get for answers when you consider the system of blocks 2 and 3 together only?

When I considered that, I tried: C,N,N,A,N which didn't work.
I also tried C,N,B,A,N. I choose B thinking that perhaps since block 1 was not in the equation, that F1 on 2 would be the new applied force. But unfortunately, that didn't work either.

I get your first answer. Note, however, that for (i), C is correct, but it is from the Normal force of B on the ground, not the gravitational force of B on the ground.

Right, right, okay.
So would you think that there is the possibility of the questions answers being incorrect? Because I can't think of any other way that it'd work.

Yes, they talk about system 2 and 3, but ask questions about system 1 and 2. Looks like someone made an error. What answers do you get if you look at system 1 and 2? Maybe that works. Maybe not.

I got C,B,N,A,A if I take into account both systems.
Which again, does not seem to work...and I'm out of ideas! Maybe I'll give the professor an email and just ask what he thinks about.
Thanks for the help!

Mr LoganC said:
I got C,B,N,A,A if I take into account both systems.
Which again, does not seem to work...and I'm out of ideas! Maybe I'll give the professor an email and just ask what he thinks about.
Thanks for the help!
Oh i get it now, sorry. The problem asks for the free body diagram of the system 2 and 3. For (i) , although the block pushes down on the ground, that's a free body of the ground. They want the free body of the blocks.

In that case, I would get N,B,N,A,A which also was not correct.
And in the case that neither of the last two (floor pushing on them) are part of the FBD, because the floor itself is not in the diagram, I also tried N,B,N,N,N which didn't work.

Is that what you would have gotten also?

Perhaps N,B,B,A,A? Even though the applied force is not on block 2, in the FBD of 2, there is still a force on it pushing in the B direction.

Mr LoganC said:
In that case, I would get N,B,N,A,A which also was not correct.
And in the case that neither of the last two (floor pushing on them) are part of the FBD, because the floor itself is not in the diagram, I also tried N,B,N,N,N which didn't work.
I'm getting lost in these letters. The floor pushing on 2 is part of the FBD of 2/3, but the floor push on 1 is not part of the FBD of 2/3. Although the floor is not part of the FBD of 2/3, its contact force IS part of it.
Is that what you would have gotten also?
No.
Perhaps N,B,B,A,A? Even though the applied force is not on block 2, in the FBD of 2, there is still a force on it pushing in the B direction.
There is a force pushing on 2 in the B direction, but that force, as you noted earlier, F_12, the normal force of 1 on 2, is not the 'applied' force.

Oh right! I forgot about the whole "Only boxes 2 & 3 together" thing!

So in that case I tried N, N, N, A, N. Meaning the only force present on the diagram was the force of the floor pushing on box 2 in the vertical (A) direction.
And it worked! That was the solution!

So thank you very much for your help! I never would have thought of the whole forces on the ground not in the FBD detail!

Thanks again,
-LoganC

Yeah, I first missed it too...good thing you got it, there are 3125 ways of combining the letters...you did it in only after a half dozen tries...which shows that you cannot get this problem correct by guessing, unless you're real real lucky

## 1. What is a free body diagram (FBD)?

A free body diagram is a visual representation used to analyze the forces acting on a system. It is a simplified drawing of the system that includes all external forces acting on it, represented by arrows pointing in the direction of the force.

## 2. Why are FBDs important in scientific research?

FBDs are important in scientific research because they help to accurately analyze and understand the forces acting on a system. By breaking down a complex system into its individual forces, FBDs allow for more accurate calculations and predictions.

## 3. How do you draw a proper FBD?

To draw a proper FBD, you should start by identifying the object or system you want to analyze. Then, draw a simple outline of the object and label all external forces acting on it. Next, draw arrows to represent the direction and magnitude of each force.

## 4. What types of forces can be represented on a FBD?

Any type of force acting on a system can be represented on a FBD. This includes gravitational forces, normal forces, frictional forces, tension forces, and applied forces. It is important to include all forces acting on the system, even if they cancel out.

## 5. Can FBDs be used to analyze motion?

Yes, FBDs can be used to analyze motion by showing the net force acting on a system and using Newton's laws of motion to determine acceleration and velocity. FBDs are a useful tool in understanding the forces involved in motion and predicting the resulting motion of a system.

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