Answer to Question #3024 in Mechanics | Relativity for Madam noor

Question

Three force F1 , F2, F3 act on a 5.00 kg object . The angle between F1 and F2 is 60 degree the angle between F2 and F3 is 30 degree .Taking F1 = 20.0 N and F2 = 15.0 and F3 = 10.0 N
A )- Find the magnitude and direction of the net force acting on the object ?
B)- Find the magnitude and direction of the acceleration of the object ?

Answer 1

Let F2 has x direction. Then
F_x=20*cos(60)+15+10*cos(30)=25+5√(3)
F_y=20*sin(60)-10*sin(30)=10√(3)-5

Net force:
F=sqrt(F_x²+F_y²)=5sqrt(41+6*√(3))

Direction:
the angle between net force and F₂ is
arctg(F_y/F_x)=arctg((-1+√(3))/2)

acceleration has the same direction. its magnitude
a=F/m=√(41+6*√(3))