An object with a mass of #4 kg# is acted on by two forces. The first is #F_1= <1 N , 8 N># and the second is #F_2 = < 7 N, -8 N>#. What is the object's rate and direction of acceleration?

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Answer 1 · 2017-03-07T09:38:26

The rate of acceleration is #=2ms^-2# in the direction #=0#º

The resultant force is

#vecF=vecF_1+vecF_2#

#= <1,8>+<7,-8>#

#=<8,0>#

#vecF=m veca#

#veca =1/m*vecF#

#=1/4<8,0> = <2, 0>#

The magnitude of the acceleration is

#||veca||=||<2,0>||#

#=sqrt((2)^2+(0)^2)#

#=sqrt(4)=2ms^-2#

The direction is #theta = arctan((0)/(2))#

The angle is in the 1st quadrant

#theta=arctan(0)= 0#º