 # Suppose the 1 kg standard body accelerates at 4.00 m/s2at 160(degree) from the positive direction of an x axis due to two forces; one is F1 - (2.50N)i + (4.60N)i What is the otherforce (a) in unit-vector notation and as (b) a magnitude and(c) an angle?

12 years ago

accleration = 4

it makes 160o with +ve x axis so 20o from -ve x axis ...

now resolve accleration into two rectangular components ,

a = 4cos20o (-i) + 4sin20o (j)

net force = ma = 4cos20(-i) + 4sin20(j)

(sin20o similar to sin18o = 0.3  &

cos20o is similar to cos18o = 0.67 )

Fnet = -2.7(i) + 1.2 (j)           ...........1

force on particle (Fnet)  = F1 + F2

F1 = 2.5(i) + 4.6 (j)  so

F2 =  -5.2(i) - 3.4 (j)          ............2             ans a)

magnitude = (sum of squares of cofficient of x comp & y comp)1/2 = 6.2          (ansc)

unit vector = vector/magnitude

unit vector = -(5.2i + 3.4j)/6.2 = -0.83(i) - 0.55(j)           (ans b)

approve if u like my ans

12 years ago

reso;ve the forces into components and separately apply the newton's laws of motion...