SOLUTION: Br resolving the forces horizontally and vertically, find the magnitude and direction of the resultant of the 4 forces shown below: 1. F1 : 10N 90 degrees from X-axis

Algebra ->  Trigonometry-basics -> SOLUTION: Br resolving the forces horizontally and vertically, find the magnitude and direction of the resultant of the 4 forces shown below: 1. F1 : 10N 90 degrees from X-axis       Log On


   

Question 1062536: Br resolving the forces horizontally and vertically, find the magnitude and direction of the resultant of the 4 forces shown below:


1. F1 : 10N 90 degrees from X-axis (In other words y/ direction-north)
2. F2 : 30N 30 degrees from X-axis (direction-NE)
3. F3 : 20N 10 degrees from X-axis (direction-NE)
4. F4 : 10N 30 degrees belowX-axis (direction-SW)
Answer by josgarithmetic(39623) About Me  (Show Source):
You can put this solution on YOUR website!
Those forces are like this: 
F1:  90 degrees, 10 Newtons
F2:  30 degrees, 30 N
F3:  10 degrees, 20 N
F4:  120 degrees, 10 N


Put them into components.
West-East Component
10%2Acos%2890%29%2B30%2Acos%2830%29%2B20%2Acos%2810%29%2B10%2Acos%28120%29
0%2B30sqrt%283%29%2F2%2B20%2Acos%2810%29%2B10%2A%28-sqrt%283%29%2F2%29
15%2Asqrt%283%29%2B20%2Acos%2810%29-5%2Asqrt%283%29
10%2Asqr%283%29%2B20%2Acos%2810%29
North-South Component
10%2Asin%2890%29%2B30%2Asin%2830%29%2B20%2Asin%2810%29%2B10%2Asin%28120%29
10%2B30%281%2F2%29%2B20%2Asin%2810%29-10%281%2F2%29
10%2B15-5%2B20%2Asin%2810%29
20%2B20%2Asin%2810%29

These forces make an EASTWARD component 10%2Asqrt%283%29%2B20%2Acos%2810%29, and a NORTHWARD component 20%2B20%2Asin%2810%29. Units are Newtons.
Decimal Approximations:
EASTWARD 37.017 Newtons
NORTHWARD 23.473 Newtons
-
Angle Direction?
tan%28p%29=23.473%2F37.017
tan%28p%29=0.63411
highlight%28p=32.4%2Adegrees%29
-
Magnitude?
sqrt%2837.017%5E2%2B23.473%5E2%29
highlight%2826.2%2Anewtons%29