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the directions of 3 forces 10N,20N,30N acting at a point are parallel to the sides of an equilateral triangle taken in order. magnitude of their resultant is

the directions of 3 forces 10N,20N,30N acting at a point are parallel to the sides of an equilateral triangle taken in order. magnitude of their resultant is
 

Grade:11

2 Answers

Arun
25763 Points
3 years ago
Forces A,B,C are 30N,20N,10N respectively. Let force A act along+ve x-axis then Force A = 30i Force B = (20cos120°)i + (20sin120°)j Force C= (10cos240°)i +(10sin240°)j So, Force A = 30i Force B= -10i +10√3j Force C= -5i -5√3j Resultant force(Position)=15i +5√3j Magnitude of resultant = 10√3 Direction of resultant = Resultant force vector/magnitude= (√3/2)i + (1/2)j
Amogh Vaishnav
11 Points
2 years ago
Let's put an x-axis on the direction of the 10N force 
and a perpendicular y-axis. 

The x-coord. of the resultant : 10 - 20cos60° - 30cos60° = -15 
The y-coord. of the resultant : 20sin60° - 30sin60° = -5sqrt(3) 
size of the resultant : sqrt(15² + 5²x3) = sqrt(300) = 10sqrt(3)

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