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

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Answer 1 · 2017-02-22T09:08:29

The net acceleration is #=3.64ms^-2# in the direction of #=15.9#º

The resultant force is

#vecF=vecF_1+vecF_2#

#= <5,6>+<2,-4>#

#=<7,2>#

#vecF=m veca#

#veca =1/m*vecF#

#=1/2<7,2> = <7/2, 1>#

The magnitude of the acceleration is

#||veca||=||<7/2,1>||#

#=sqrt((7/2)^2+(1)^2)#

#=sqrt(49/4+1)#

#=sqrt 53/2=3.64ms^-2#

The direction is #theta = arctan((1)/(7/2))#

The angle is in the 1st quadrant

#theta=arctan(2/7)=15.9#º