Help With Understanding Resultant Forces By Connecting Vectors

In summary, the resultant force is the vector that has the same magnitude and direction as the other two vectors that were connected head to tail. It is determined by the order in which the vectors are connected. If the object is initially at rest and the three given forces are the only forces acting on the object, then the object would begin moving in the direction of the resultant force. If the forces remain constant, then the object would continue to move in that direction with constant acceleration.
  • #1
tomtomtom1
160
8
Homework Statement
Using Resultant Forces By Connecting Vectors Head To Tail
Relevant Equations
NA
Hi all

I am trying to get my head around resultant forces.

I am happy that if I have a vector diagram with 2 forces I can work out graphically the resultant forces by connecting the head of one of the vectors to the tail of the second vector.

The confusion comes in when I have 3 or more vectors, for example the vector diagram has 3 forces and I am trying to figure our the resultant for graphically.

vectors.JPG


My resultant force changes depending on the order I connected the 3 vectors, the different shapes I get when I connect the vectors is as follows:-
vectorsssssss.JPG


Is there a set convention that is used when connecting vectors head to tail to determine the resultant?

Can you help?

Thank you.
 
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  • #2
Welcome to PF.

tomtomtom1 said:
Homework Statement: Using Resultant Forces By Connecting Vectors Head To Tail
Homework Equations: NA

Hi all

I am trying to get my head around resultant forces.

My resultant force changes depending on the order I connected the 3 vectors, the different shapes I get when I connect the vectors is as follows:-View attachment 251675

Is there a set convention that is used when connecting vectors head to tail to determine the resultant?

Can you help?

Thank you.
Actually, you get the same resultant vector no matter which order you add the vectors. Your resultant is the red vector. For the three cases in your figure, the red vectors are all equal to one another.

1571793021973.png
The red vectors have the same magnitude and the same direction.
 
  • #3
What matters is the length and direction of the resultant. Not where it starts and ends.

Always put the tail of the first vector at the origin if you want to avoid ambiguity and have the end point of the resultant give you the components. As you have not done this, this seems to be the source of your confusion.
 
  • #4
Hi all

Thank you for your help.All the vectors I drew were all the same I just did not realize it so thank you for clearing up the confusion.I was able to work out the magnatuide & direction of the resultant force but I wanted to ask a follow on question which is given that I started with the diagram:-

vectors.JPG


If we assume that these forces were acting on an object and the resultant force is:-

resultant.JPG


Then would I be correct in thinking that after the forces are applied the object would move along the red arrows (my resultant force)?

Is this correct?

Thanks
 
  • #5
tomtomtom1 said:
Then would I be correct in thinking that after the forces are applied the object would move along the red arrows (my resultant force)?

Is this correct?
If the object is initially at rest and the three given forces are the only forces acting on the object, then the object would begin moving in the direction of the resultant force. If the forces remain constant, then the object would continue to move in that direction with constant acceleration.

[To be picky, this assumes that you are working in an inertial reference frame. But, that would be the natural assumption.]
 
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  • #6
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FAQ: Help With Understanding Resultant Forces By Connecting Vectors

1. What is a resultant force?

A resultant force is the single force that represents the combined effect of multiple forces acting on an object. It is the vector sum of all the individual forces, taking into account their magnitude and direction.

2. How do I calculate the resultant force?

To calculate the resultant force, you must first identify all the forces acting on an object and their respective magnitudes and directions. Then, use vector addition to find the sum of all the forces, taking into account their direction. The resultant force will be the final vector that represents the combined effect of all the forces.

3. What is the difference between a scalar and a vector quantity?

A scalar quantity is a physical quantity that has only a magnitude, whereas a vector quantity has both magnitude and direction. In the context of resultant forces, the individual forces acting on an object are vectors, while the resultant force is a single vector quantity.

4. Can the resultant force be zero?

Yes, the resultant force can be zero if the individual forces acting on an object are balanced. This means that the forces are equal in magnitude and opposite in direction, resulting in a net force of zero.

5. How does understanding resultant forces help in real-world applications?

Understanding resultant forces is crucial in various scientific and engineering fields, such as mechanics, aerospace, and structural design. It allows us to analyze and predict the motion and stability of objects under the influence of multiple forces, leading to the development of efficient and safe designs and systems.

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