Three forces with magnitudes 300 Newtons, 180 Newtons, and 250 Newtons act on an object at angles −30◦ , 45◦ , and 135◦ with the positive x-
Question
Three forces with magnitudes 300 Newtons, 180 Newtons, and 250 Newtons act on an object at angles −30◦ , 45◦ , and 135◦ with the positive x-axis, respectively. Find the direction and magnitude of the resultant of these forces.
in progress
0
Math
3 months
2022-02-16T15:10:30+00:00
2022-02-16T15:10:30+00:00 1 Answer
0 views
0
Answers ( )
Answer:
261∠36° Newtons
Step-by-step explanation:
A straightforward way to find the resultant is to add the x- and y-components of the forces:
r = 300(cos(-30°), sin(-30°)) +180(cos(45°), sin(45°)) +250(cos(135°), sin(135°))
= (300√3/2 +180√2/2 -250√2/2, -300/2 +180√2/2 +250√2/2)
= (150√3 -35√2, -150 +215√2)
≈ (210.310, 154.056)
≈ 260.698∠36.22°
The resultant is approximately 261 Newtons at an angle of 36°.
_____
From components (x, y), the angle is found as arctan(y/x). The magnitude is found as √(x²+y²).