Question
Download Solution PDFTwo forces of equal magnitude (F) act at an angle of β to each other. The resultant of these forces will be given by:
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFConcept:
If two forces of equal magnitude (F) act at an angle of β to each other, then the resultant of these forces is given by
\({\bf{R}} = \sqrt {{{\bf{F}}^2} + {{\bf{F}}^2} + 2 \times {\bf{F}} \times {\bf{F}} \times {\bf{cosβ }}} \)
\( R= \sqrt {2{{\rm{F}}^2} + (2{{\rm{F}}^2} \times {\rm{cosβ )}}} \)
\(R = \sqrt {2{F^2}(1 + \cos \beta )} \)
\(\therefore {\bf{R}} = 2{\bf{Fcos}}\left( {\frac{{\bf{β }}}{2}} \right)\) \(\left( \because{1 + {\rm{cosβ }} = 2\cos^2 \left( {\frac{{\rm{β }}}{2}} \right)} \right)\)
Last updated on May 17, 2025
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