An object with a mass of #9 kg# is acted on by two forces. The first is #F_1= << -7 N , 1 N >># and the second is #F_2 = << 4 N, -3 N >>#. What is the objects rate and direction of acceleration?

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Answer 1 · 2017-06-08T04:48:13

The rate of acceleration is #=0.4ms^-1# in the direction of #=213.7º# anticlockwise from the x-axis

The resultant force is

#vecF=vecF_1+vecF_2#

#= <-7,1>+<4,-3>#

#=<-3,-2>#

#vecF=m veca#

Mass, #m=9kg#

#veca =1/m*vecF#

#=1/9<-3,-2> = <-1/3, -2/9>#

The magnitude of the acceleration is

#||veca||=||<-1/3,-2/9>||#

#=sqrt((-1/3)^2+(-2/9)^2)#

#=sqrt(0.16049)=0.4ms^-2#

The direction is #theta = arctan((2)/(3))#

The angle lies in the 3rd quadrant

#theta=arctan(2/3)=180+33.7º=213.7º# anticlockwise from the x-axis