An object with a mass of #4 kg# is acted on by two forces. The first is #F_1= < -5 N , 7 N># and the second is #F_2 = < 4 N, 3 N>#. What is the object's rate and direction of acceleration?

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Answer 1 · 2017-06-11T11:53:54

The rate of acceleration is #=2.61ms^-2# in the direction #=106.7º# anticlockwise from the x-axis

The resultant force is

#vecF=vecF_1+vecF_2#

#= <-5,7>+<4,3>#

#=<-3,10>#

#vecF=m veca#

Mass, #m=4kg#

#veca =1/m*vecF#

#=1/4<-3,10> = <-3/4, 5/2>#

The magnitude of the acceleration is

#||veca||=||<-3/4,5/2>||#

#=sqrt((-3/4)^2+(5/2)^2)#

#=sqrt(6.8125)=2.61ms^-2#

The direction is #theta = arctan(-(10)/(3))#

The angle lies in the 2nd quadrant

#theta=arctan(2/3)=180-73.3º=106.7º# anticlockwise from the x-axis