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})