# Coplanar Forces help!

## Homework Statement

I Have to work out the following using mathematical and graphical methods

i have to work out the resultant force of

Vertical = 8kN

Horizontal = 6kN

we were given an example which i understood but with that we were given an extra component of 3kN at 45 degrees, so really not sure how to work this one out!

where would i draw my lines etc

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CAF123
Gold Member

## Homework Statement

I Have to work out the following using mathematical and graphical methods

i have to work out the resultant force of

Vertical = 8kN

Horizontal = 6kN

we were given an example which i understood but with that we were given an extra component of 3kN at 45 degrees, so really not sure how to work this one out!

where would i draw my lines etc
Set up a coordinate system and draw a vertical and horizontal vector (force is a vector) coinciding with the y and x axis respectively. Would you know how to compute the resultant of these two vectors?

Thats what i have done mate, horizontal is 6kN and vertical is 8kN , but this is where i am stuck as this is my first time doing it

the example i did was with 3 vectors and i joined the end of the 3'rd to the beginning and measured and got my answer if that makes sense

i have 6 of these but if i can understand this first one the others will be fine!

cheers dude

CAF123
Gold Member
Thats what i have done mate, horizontal is 6kN and vertical is 8kN , but this is where i am stuck as this is my first time doing it
Do you mean you are stuck after this or are you stuck in finding the resultant of these two vectors?
the example i did was with 3 vectors and i joined the end of the 3'rd to the beginning and measured and got my answer if that makes sense
Joined the end of the third vector to the beginning of what?

Do you mean you are stuck after this or are you stuck in finding the resultant of these two vectors?

Joined the end of the third vector to the beginning of what?
the resultant mate.. to do it graphically you have to draw another line and measure it dont you?

the start point mate (4kN vertical, 4kN horizontal then 3kN at 45 degrees from that, then joined the end of that to the very start of the vertical)

CAF123
Gold Member
the resultant mate.. to do it graphically you have to draw another line and measure it dont you?

the start point mate (4kN vertical, 4kN horizontal then 3kN at 45 degrees from that, then joined the end of that to the very start of the vertical)
Yes, find the resultant of the vertical and horizontal vectors and (vectorially) add this to the 3kN force at 45 degrees. In this case, it is probably easier to do a proper scale drawing and simply measure the magnitude of the resultant and it's angle from +ve x. You could also use various trig techniques (such as sine/cosine rules).
EDIT: did you notice your vectors have changed from having magnitudes 8 and 6 to 4 and 4?

Yes, find the resultant of the vertical and horizontal vectors and (vectorially) add this to the 3kN force at 45 degrees. In this case, it is probably easier to do a proper scale drawing and simply measure the magnitude of the resultant and it's angle from +ve x. You could also use various trig techniques (such as sine/cosine rules).
EDIT: did you notice your vectors have changed from having magnitudes 8 and 6 to 4 and 4?
thats what i have to do mate, i have to work out using a scaled drawing and using trig, and the vectors 4,4,3 was the one i did at college.. the one im struggling with at the moment is the 8 and 6 :/

i have drawn the lines on graph paper but have no idea how to get the resultant from it..

CAF123
Gold Member
thats what i have to do mate, i have to work out using a scaled drawing and using trig, and the vectors 4,4,3 was the one i did at college.. the one im struggling with at the moment is the 8 and 6 :/

i have drawn the lines on graph paper but have no idea how to get the resultant from it..
Have you done vector addition at all?
See for example
http://www.physicsclassroom.com/class/vectors/u3l1b.cfm

my scenario look like this picture

but with one vector 6kN and one 8kN , would my resultant be the red line?

CAF123
Gold Member
my scenario look like this picture

but with one vector 6kN and one 8kN , would my resultant be the red line?
Yes.

Yes.
thanks mate :) thats what i thought but didn't seem right..

what do i do after 6(2)+8(2) = 100?

do i square root it?

CAF123
Gold Member
thanks mate :) thats what i thought but didn't seem right..

what do i do after 6(2)+8(2) = 100?

do i square root it?
Yes, but do you know why?

Yes, but do you know why?
i dont mate.. care to enlighten me?

CAF123
Gold Member
i dont mate.. care to enlighten me?
You have two vectors that are perpendicular and when you add them together you get a vector going from tail of one to the head of another. You can now think of this as a vector triangle. If the resultant you think of as the hypotenuse of a right angled triangle, you would use Pythagoras to find the length.
Remember your intial problem is a special case (the vectors being orthogonal). You can't always use Pythagoras to find the length.

You have two vectors that are perpendicular and when you add them together you get a vector going from tail of one to the head of another. You can now think of this as a vector triangle. If the resultant you think of as the hypotenuse of a right angled triangle, you would use Pythagoras to find the length.
Remember your intial problem is a special case (the vectors being orthogonal). You can't always use Pythagoras to find the length.
cheers mate :)

how would i work out this one

its a horizontal line with a 45 degree vector going left and a 45 degree vector going right?

CAF123
Gold Member
I can't make much sense of that. Can you post a picture?

I can't make much sense of that. Can you post a picture?
number 4 mate

CAF123
Gold Member
At this point you have to provide an attempt (forum rules) before I can help. What have you learnt in the previous problem that can be applied here?

Well i would draw the first 12kN 45 degree vector, then on top of that i will do the other one, and draw a line from the start to the tip of the 2nd vector - then i would measure that line..

to do it mathematically im not sure.. as i cant use trig? 12(2)+12(2) and square it?

Last edited:
CAF123
Gold Member
Well i would draw the first 12kN 45 degree vector, then on top of that i will do the other one, and draw a line from the start to the tip of the 2nd vector - then i would measure that line..
What does that line look like? (i.e is it vertical, horizontal or inclined at some angle)
to do it mathematically im not sure.. as i cant use trig?
Are the vectors perpendicular in this example?

What does that line look like? (i.e is it vertical, horizontal or inclined at some angle)

Are the vectors perpendicular in this example?
inclined at an angle, so looks like half a kite like

\
/

and no as there's 45 degree angles and not a 90

CAF123
Gold Member
Also, in your last example, since force is a vector you necessarily have to specify a direction associated with it. Did you get this? You can do this most easily with a protractor.

yeah so both lines need to be at a 45degree angle?

CAF123
Gold Member
inclined at an angle, so looks like half a kite like
That is the addition of the two vectors. Now what is the resultant?

and no as there's 45 degree angles and not a 90
Are you sure they are not 90 degrees with respect to each other? How could you check?

P.s I need to go in a minute or two.

That is the addition of the two vectors. Now what is the resultant?

Are you sure they are not 90 degrees with respect to each other? How could you check?

P.s I need to go in a minute or two.
would the resultant not be from the top of the vector to the start ppoint? so like a straight line down?

well 45 and 45 is 90.. so does that make them perpendicular?

and dont worry mate, you have been a great help :)