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Two forces 12 N and 16 N are acting upon...

Two forces 12 N and 16 N are acting upon a body, what can be the maximum and minimum resultant force on the body ?

Text Solution

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Here : `A = 10 N, B=15 N:R = sqrt( A^2 +B^2 + 2AB cos theta )`
(a) R will be maximum ic `cos theta =1`
then ` R =A +B =10 +15 = 25 N`
In the direction of ` vecA and vecB `
(b) R will be manimum if ` cos theta =-1`
Then `R =A -B or B -A `
` therefore R = 15 - 10 = 5N `
in the direction of ` vecB `
* vector additions obeys
` (1) ` commutative law ` vecA + vecB = vecB +vecA `
(2) distributive law `m ( vecA + vecB ) = m vecA + m vecB `
(3) Associative law ` vecA + ( vecB + vecC ) = ( vecA + vecB ) + vecC `
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