Master the Art of Free Body Diagrams: Understanding Vectors and Scalars

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Discussion Overview

The discussion revolves around the interpretation and representation of vectors and scalars in free body diagrams, particularly in the context of physics education. Participants explore the nuances of how forces are depicted and understood in these diagrams, addressing both theoretical and practical aspects.

Discussion Character

  • Debate/contested
  • Technical explanation
  • Conceptual clarification

Main Points Raised

  • Some participants assert that free body diagrams treat vectors as scalars, while others challenge this notion, emphasizing that forces are inherently vectors and should be represented as such.
  • One participant points out that forces are depicted as magnitudes multiplied by direction, suggesting that the direction is evident in the diagram.
  • Another participant clarifies that free body diagrams isolate objects and show all acting forces as vectors, questioning the initial claim about treating them as scalars.
  • A participant provides a mathematical example using Newton's second law, illustrating how to calculate acceleration from forces, while noting that the teacher's approach may lack clarity in presenting the steps involved.
  • There is a mention of the importance of writing Newton's laws in vector form, with a participant highlighting the implications of forces acting at angles.
  • Concerns are raised about the lack of information regarding motion in the y-direction, even when acceleration in the x-direction is determined to be zero.

Areas of Agreement / Disagreement

Participants express disagreement regarding the treatment of vectors and scalars in free body diagrams. While some argue that vectors are being treated as scalars, others maintain that forces must always be considered as vectors. The discussion remains unresolved with multiple competing views presented.

Contextual Notes

Some participants note that the lack of explicit steps in calculations may lead to confusion, and there are unresolved questions about the implications of forces acting at angles and the overall motion of the body in different directions.

primarygun
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When we do free body diagram, we usually consider the vector as scalar.
I think this is a very important point, but why my teacher didn't clarify a lot?
 
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primarygun said:
When we do free body diagram, we usually consider the vector as scalar.
I think this is a very important point, but why my teacher didn't clarify a lot?
No, we don't.
What you might be thinking of, is that we often write the vector as a MAGNITUDE (a non-negative scalar quantity) multiplied with a DIRECTION (a unit vector)
The direction is, of course, "readily" seen from the diagram.
 
primarygun said:
When we do free body diagram, we usually consider the vector as scalar.
When you do a free body diagram, you are isolating a particular object and showing all the forces acting on it. These forces are certainly vectors, usually depicted as arrows in the diagram. What makes you think you are treating them as scalars?
 
Note: Forces in x-axis are 5N and -5N. Find the acceleration.
My teacher would suggest us to
F=ma
5N-5N=ma
Hence, a=0.
The equation is the same,though, he never tells us 5N+(-5N)
 
Forces are vectors.Period.The laws of Newton must be written in vector form...ALWAYS.
In your example,what if one of the forces would act as to make an angle (different from 0 or pi) with the direction of the other force...?

Daniel.
 
primarygun said:
Note: Forces in x-axis are 5N and -5N. Find the acceleration.
My teacher would suggest us to
F=ma
5N-5N=ma
Hence, a=0.
The equation is the same,though, he never tells us 5N+(-5N)

It would make things more explicit to write out all the steps like this:

\bold F_{net} = m \bold a

{\bold F}_1 + {\bold F}_2 = m \bold a

F_{1x} + F_{2x} = m a_x

(+5N) + (-5N) = m a_x

5N - 5N = m a_x

0 = m a_x

0 = a_x

And of course if the y-components of the forces are zero, then a_y is zero also, so \bold a (the vector) equals zero.

But nobody ever actually writes out all those steps, in practice. I might do it that way once, when teaching it, just to clarify things.
 
The way the problem is actually posted,it says nothing about an accelereration (or simply a nonzero velocity) in the "y" direction,so even if you come up with the conclusion that a_{x}=0,you still wouldn't tell how that body's moving.

Daniel.
 

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