Respuesta :
Answer:
[tex]Magnitude=180.27 \ lbf \\ \\ Direction=63.69 \ degrees[/tex]
Step-by-step explanation:
We have two forces as follows:
First force:
Magnitude: 150 pounds
Angle: 30°
First force:
Magnitude: 100 pounds
Angle: 120°
So the components can be found as follows:
[tex]F_{1x}=150cos(30)=129.90 \ lbf\\F_{1y}=150sin(30) = 75 \ lbf \\ \\ F_{2x}=100cos(120)=-50 \ lbf\\F_{2y}=100sin(120) = 86.60 \ lbf[/tex]
So the components of the resultant force can be found by adding each component of the individual forces as follows:
[tex]R_{x}=\Sigma F_{x} \\ R_{y}=\Sigma F_{y} \\ \\ R_{x}=129.90-50=79.90 \ lbf \\ R_{y}=75+86.60=161.6 \ lbf[/tex]
Finally, the magnitude and direction of the resultant force is:
[tex]Magnitude \rightarrow R=\sqrt{R_{x}^2+R_{y}^2}=\sqrt{79.90^2+161.6^2}=180.27 \ lbf \\ \\ Direction \rightarrow \theta=tan^{-1}(\frac{R_{y}}{R_{x}})=tan^{-1}(\frac{161.6}{79.90})=63.69 \ degrees[/tex]
Answer:
Magnitude:
[tex]|R|=180.27756[/tex]
Direction:
[tex]\theta=63.69^{\circ \:}[/tex]
Step-by-step explanation:
Calculation of first force:
we are given
[tex]|F_1|=150[/tex]
[tex]\theta=30[/tex]
now, we can find components
[tex]x=|F_1|cos(\theta)[/tex]
[tex]x=150cos(30)[/tex]
[tex]x=75\sqrt{3}[/tex]
[tex]y=|F_1|sin(\theta)[/tex]
[tex]y=150sin(30)[/tex]
[tex]y=75[/tex]
now, we can find force
[tex]F_1=(75\sqrt{3},75)[/tex]
Calculation of Second force:
we are given
[tex]|F_2|=100[/tex]
[tex]\theta=120[/tex]
now, we can find components
[tex]x=|F_2|cos(\theta)[/tex]
[tex]x=100cos(120)[/tex]
[tex]x=-50[/tex]
[tex]y=|F_2|sin(\theta)[/tex]
[tex]y=100sin(120)[/tex]
[tex]y=50\sqrt{3}[/tex]
now, we can find force
[tex]F_2=(-50,50\sqrt{3})[/tex]
now, we can find resultant force
[tex]R=F_1+F_2[/tex]
[tex]R=(75\sqrt{3},75)+(-50,50\sqrt{3})[/tex]
[tex]R=(75\sqrt{3}-50,75+50\sqrt{3})[/tex]
[tex]R=(79.90381 ,161.60254)[/tex]
Magnitude of Resultant:
[tex]|R|=\sqrt{79.90381^2+161.60254^2}[/tex]
[tex]|R|=180.27756[/tex]
Direction of Resultant:
[tex]\theta=tan^{-1}(\frac{161.60254}{79.90381})[/tex]
[tex]\theta=63.69^{\circ \:}[/tex]
