An object with a mass of #4 kg# is acted on by two forces. The first is #F_1= < -5 N , 2 N># and the second is #F_2 = < 1 N, 6 N>#. What is the object's rate and direction of acceleration?

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Answer 1 · 2017-02-18T16:56:23

The rate of acceleration is #=2.24ms^-2# in the direction #=116.6#º

The resultant force is

#vecF=vecF_1+vecF_2#

#= <-5,2>+<1,6>#

#=<-4,8>#

#vecF=m veca#

#veca =1/m*vecF#

#=1/4<-4,8> = <-1, 2>#

The magnitude of the acceleration is

#||veca||=||<-1,2>||#

#=sqrt((-1)^2+(2)^2)#

#=sqrt(1+4)#

#=sqrt5=2.24ms^-2#

The direction is #theta = arctan((2)/(-1))#

But the angle is in the 2nd quadrant

#theta=arctan(-2)=116.6#º