Finding the Magnitude and Direction of Force one with the Resultant Given

Nacha

1. The problem statement, all variables and given/known data

Determine the magnitude and direction theata of F1 so that the resultant force is directed vertically upward and has a magnitude of 800N.

2. Relevant equations



3. The attempt at a solution

I have difficulty of where to start the problem? do i sum up the forces of the x axis with unknowns in it and forces of the y axis with the unknown forces...where should i start....and how do i start solving the problem????

Please someone help me with this....

Thanks,

Nacha

tiny-tim

Hi Nacha ! Welcome to PF!

Yes … split the force F₁ into F_x and F_y …

then do x and y separately …

finally combine F_x and F_y to give you F₁ and theta.

Nacha

Hi,

Thanks for helping me, but one more question, my Fx and Fy for F1 is unkown as shown in the diagram that i have posted earlier, so how do i go about solving for the magnitude of F1 and the direction of F1. Sorry for the trouble....

thanks
Nacha

tiny-tim

Hi,

Have you got Fx and Fy yet?

You can get them from the diagram.

Then use Pythagoras, and tangents.

sandra_abe

can anyone explain how to solve this problem in complete details? i don't understand the explanations. i have the same problem too.

tiny-tim

hi sandra! welcome to pf!

you need to get all the y-components adding to 800, and all the x-components adding to zero

that will give you two equations involving two unknowns (F₁ and θ), which should enable you to find the unknowns

what do you get?

sandra_abe

owhh.. how about to solve this question:

determine the magnitude and direction of P so that the resultant of P and the 900N force is a vertical force of 2700N directed downward.

is it using the same method also? it's almost the same right?

tiny-tim

right!

sandra_abe

thanks so much tiny-tim! i'm doing my engineering mechanics tutorial problems right now.. if i have any problem again, i'll ask your help later.. ;)

sandra_abe

err... do you online often? then, i'll know when can i ask for your help..

tiny-tim

sandra, just post a new thread any time …

somewhere in the world, there'll be someone awake and logged in ready to help, whatever time it is

sandra_abe

okie! will do..

Zlash

i got a similar problem but i dont have a resultant force :\ not sure on how to solve ive found theata using a parallelogram
theata is the one between the X axis and F1

Attached Images

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tiny-tim

Hi Zlash! Welcome to PF!

(have a theta: θ )

Sorry, I dont understand the question …

you have three forces (100N 350N and R), and also a line called X at 30º …

if X is equivalent to F₁ in Nacha's question, then changing the magnitude of X will give different directions for the resultant R (but a unique magnitude for each direction) …

if neither the magnitude nor the direction of R is given, I don't see how you can answer the question

Zlash

nah X' is a vector that cuts through.
in the quiz im doing it doesnt say anything about a resultant but im assuming we have to use the one given in the text book. so the resultant measured from the positive X' -the line- is 600N
i found θ as 60. θ being between F1 and the X axis( not x' )
im not sure how i can work through forces based on different axis kinda messes me up =/
im trying it now

haaaaa87

hi all
∑F x= 400cos30 – 600 cos36.87 + F1 sinØ =0
∑F y= 400sin30 – 600sin36.87 + F1 cosØ =0
R=√(〖fx〗^2+〖fy〗^2 )
800=√((〖298.35+f1sinØ)〗^2+〖(560+f1 cosØ)〗^2 )

As we see ; we have two equation and two unknown so we can get the magnitude and direction of f1