Help With Understanding Resultant Forces By Connecting Vectors

[tomtomtom1]

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.

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:-

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

Can you help?

Thank you.

 

[TSny]

Welcome to PF.

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.

The red vectors have the same magnitude and the same direction.

 

[Orodruin]

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.

 

[tomtomtom1]

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:-

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

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

 

[TSny]

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.]

 

[tomtomtom1]

thanks