Resultant Force
In the below diagram, determine the resultant magnitude of the three forces.
Expand Hint
$$$R=\sqrt{{R_{x}}^{2}+{R_{y}}^{2}}$$$
Hint 2
We need to find the total forces both in the x and y directions.
$$$R_{x}=\sum F_{xi}$$$
$$$R_{y}=\sum F_{yi}$$$
$$$i=A,B,C$$$
First, let's find the hypotenuse for the two given triangles/slopes for the 220 N and 400 N vectors.
$$$H_{220}=\sqrt{4^2+3^2}=5$$$
$$$H_{400}=\sqrt{12^2+5^2}=13$$$
We need to find the total forces both in the x and y directions (watch out for +/- directions!):
$$$R_{x}=\sum F_{xi}$$$
$$$R_{y}=\sum F_{yi}$$$
$$$i=A,B,C$$$
$$$R_{x}=-3/5(220N)+12/13(400N)+0N=-132N+369.2N=237.2N$$$
$$$R_{y}=4/5(220N)+5/13(400N)-50N=176N+153.8N-50=279.8N$$$
Finally, to solve for the magnitude:
$$$R=\sqrt{{R_{x}}^{2}+{R_{y}}^{2}}=\sqrt{(237.2N)^{2}+(279.8N)^{2}}=\sqrt{134,552N^{2}}=367N$$$
367 N
Time Analysis
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