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Answer to Question #115556 in Mechanics | Relativity for isaac

Question #115556
forces 5N, 12N and 13N acting on a body are in equilibrum. What is the angle between the forces 5N and 12N
1
2020-05-14T09:18:19-0400

Solution.

"F_1=5N;"

"F_2=12N;"

"F_3=13N;"

"\\overrightarrow{F_1}+\\overrightarrow{F_2}+\\overrightarrow{F_3}=0;"

"\\overrightarrow{F_1}+\\overrightarrow{F_2}=\\overrightarrow{F_3};"

f the forces are perpendicular, then we find the equivalent of the two forces by Pythagoras' theorem, otherwise we will use the cosine theorem.

"\\overrightarrow{F_{12}}=\\overrightarrow{F_1}+\\overrightarrow{F_2};"

First, check whether the forces are perpendicular:

"F_{12}=\\sqrt{F_1^2+F_2^2};"

"F_{12}=\\sqrt{(5N)^2+(12N)^2}=13N;"

"F_{12}=F_3;"

Therefore, the forces 5N and 12N form an angle of 90o;

Answer: the forces 5N and 12N form an angle of 90o.

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