help me with physics?

Question

how do i find the concurrent forces of the ff:
given: F(sub 1)= 5 Newton,north; F(sub 2) 7 N at 30degreeof W; F(sub 3)= 10 N at 75 degree W of S

determine:1. F(sub 1) +F(sub 2) 2. F(sub 2)- F(sub 3) 3. F(sub3)+F(sub1)-F(sub 2)

what will i do...i dont know if its only a ordinary addition or substraction???please kindly help me with this

Answer 1

First, break each force into its north-south and east-west components. Since these components will be orthogonal (perpendicular), you'll be able to add the components normally. After you add them and then calculate the angle and magnitude of the resultant force.

That is, (notice the NEGATIVE signs) (I ASSUME that F_2 is 30 degrees NORTH of west)

F_1_NORTH = 5 Newtons
F_1_EAST = 0 Newtons

F_2_NORTH = (7 Newtons)*sin( (180-30) degrees ) = 3.5 Newtons
F_2_EAST = (7 Newtons)*cos( (180-30) degrees ) = -3.5*sqrt(3) Newtons = -6.06218 Newtons

F_3_NORTH = (10 Newtons)*sin( (270-75) degrees ) = -5*(sqrt(3)-1)*sqrt(2)/2 Newtons = -9.65926 Newtons
F_3_EAST = (10 Newtons)*cos( (270-75) degrees ) = -5*(sqrt(3)+1)*sqrt(2)/2 Newtons = -2.58819 Newtons

So now . . .

F_1_NORTH + F_2_NORTH = 8.5 Newtons
F_1_EAST + F_2_EAST = -6.06218 Newtons

So F_1 + F_2 is now:

sqrt((8.5 Newtons)^2 + (6.06218 Newtons)^2)) = 10.4403 Newtons

at

arctan( 8.5/-6.06218 ) = -54.5036 degrees

HOWEVER, since we're taking the arctan, we need to remember that this is in the SECOND quadrant, so this represents the angle NORTH of WEST.

In other words, F_1 + F_2 is 10.4403 Newtons at 54.5036 degrees NORTH of WEST.

This intuitively makes sense. F_1 is going entirely in the north direction, so when you add it to F_2, you simply increase it's north component. The result is that if it was originally going 30 degrees north of west, it's now goignt o go 54.5036 degrees north of west. Additionally, the magnitude is greater than both. We haven't taken away from any component. We've only added to both components, so the total magnitude is sure to increase.

Follow the same procedure for the other two. Deal with the COMPONENTS and then recombine later.

Answer 2

Draw a scale model of the problem. That should get you started.