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Three forces (-63j , 32.14i + 38.3j) and (14i – 24.25j) act on a body…

Three forces (-63j , 32.14i + 38.3j) and (14i – 24.25j) act on a body of mass 5kg. Find, correct to one decimal place, the :

(a) magnitude of the resultant force ;

(b) acceleration of the body.

Explanation

(a) Resultant of forces, (R = -63j + (32.14i + 38.3j) + (14i – 24.25j))

= (46.14i – 48.95j)

Magnitude |R| = (sqrt{(46.14)^{2} + (-48.95)^{2}})

= (sqrt{2128.9 + 2396.1})

= (sqrt{4525})

= (67.268 approxeq 67.3N) (to 1 d.p)

(b) (a = frac{F}{m})

= (frac{67.268}{5} = 13.454 ms^{-2})

(approxeq 13.5 ms^{-2})