How Do You Calculate Net Force from Multiple Vector Forces?

[anna sung]

Homework Statement

calculate the net force if the following three forces are all being applied at the same time:
40N, 60N[N], and 30N[N35degreeE].

Homework Equations

When cacluating vector forces do you always have to draw out to scale?
if not, then how would you get the direction of the resultant force

the answer on the book is 50N [E70degreeN]

The Attempt at a Solution

60[N]-40[N] = 20[N]
30Cos(35)=24.57
30Sin(35)=17.2
20[N]+24.57=44.57
$$\sqrt{}17.2^2+44.57^2$$=47.7 N
how come its off by 3 N . ?
finding the angle
tan-1(44.57/17.2)=68.88
how would you get the direction. ??
please help me

 

[cepheid]

Homework Statement

calculate the net force if the following three forces are all being applied at the same time:
40N, 60N[N], and 30N[N35degreeE].

Homework Equations

When cacluating vector forces do you always have to draw out to scale?

No, not unless if you want to get the resultant by measuring what you've drawn with a ruler and protractor (which is unnecessary)

if not, then how would you get the direction of the resultant force

By doing what you've done in your attempt below.

the answer on the book is 50N [E70degreeN]

The Attempt at a Solution

60[N]-40[N] = 20[N]
30Cos(35)=24.57
30Sin(35)=17.2
20[N]+24.57=44.57
$$\sqrt{}17.2^2+44.57^2$$=47.7 N
how come its off by 3 N . ?

Assuming that "[N35degreeE]" means "35 degrees east of north", then I don't see anything wrong with what you've done. I'm not sure why the book answer rounds it to 50.

finding the angle
tan-1(44.57/17.2)=68.88
how would you get the direction. ??
please help me

You just did. Draw a picture. If the tangent is given by 44.57/17.2, (vertical component/horizontal component), then this corresponds to an angle of 68 degrees FROM THE HORIZONTAL AXIS, which is 68 degrees north of east, since the positive vertical direction is north, and the positive horizontal direction is east.

 

[anna sung]

oh thank you so much!

 

[pongo38]

You don't have to draw it to scale, but I always do, to check for errors. In my experience, people very often confuse sin and cos etc.