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Suppose the 1 kg standard body accelerates at 4.00 m/s2 at 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 other force (a) in unit-vector notation and as (b) a magnitude and (c) an angle?

Suppose the 1 kg standard body accelerates at 4.00 m/s2
at 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 other
force (a) in unit-vector notation and as (b) a magnitude and
(c) an angle?


 

Grade:11

2 Answers

vikas askiitian expert
509 Points
10 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

akhil mahajan
36 Points
10 years ago

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

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