A) Net force in component form: [tex]F=100.0i-300.0j[/tex]
B) Magnitude of the net force: 316.2, direction: [tex]-71.6^{\circ}[/tex]
Explanation:
A)
The three forces given in this problem are:
[tex]F_1=300i+500j[/tex]
[tex]F_2=-200i[/tex]
[tex]F_3=-800 j[/tex]
The three forces are given in component form, where the components with unit vector i is the component along the x-direction, while the components with unit vector j is the component along the y-direction.
In order to find the net force in component form, we just need to add the components of the three forces along each direction. Therefore:
- Along the x-direction:
[tex]F_x = F_{1x}+F_{2x}+F_{3x}=300+(-200)+0=100[/tex]
- Along the y-direction:
[tex]F_y=F_{1y}+F_{2y}+F_{3y}=500+0+(-800)=-300[/tex]
So, the net force in component form is
[tex]F=100.0i-300.0j[/tex]
B)
The magnitude of a vector F is given by Pythagorean's theorem:
[tex]|F|=\sqrt{F_x^2+F_y^2}[/tex]
where in this problem,
[tex]F_x=100[/tex] is the x-component
[tex]F_y=-300[/tex] is the y-component
Substituting,
[tex]|F|=\sqrt{(100)^2+(-300)^2}=316.2[/tex]
The direction instead is given by
[tex]\theta=tan^{-1}(\frac{F_y}{F_x})=tan^{-1}(\frac{-300}{100})=-71.6^{\circ}[/tex]
where the negative sign means the direction is below the positive x-axis.
Learn more about vector addition:
brainly.com/question/4945130
brainly.com/question/5892298
#LearnwithBrainly
