An object with a mass of #5 kg# is acted on by two forces. The first is #F_1= < 1 N , 4 N># and the second is #F_2 = < 5 N, -3 N>#. What is the object's rate and direction of acceleration?

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Answer 1 · 2017-02-26T07:38:26

The rate of acceleration is #=1.22ms^-2# in the direction of #9.46#º

The resultant force is

#vecF=vecF_1+vecF_2#

#= <1,4>+<5,-3>#

#=<6,1>#

#vecF=m veca#

#veca =1/m*vecF#

#=1/5<6,1> = <6/5, 1/5>#

The magnitude of the acceleration is

#||veca||=||<6/5,1/5>||#

#=sqrt((6/5)^2+(1/5)^2)#

#=sqrt(36/25+1/25)#

#=sqrt 37/5=1.22ms^-2#

The direction is #theta = arctan((1/5)/(6/5))#

The angle is in the 1st quadrant

#theta=arctan(1/6)= 9.46#º