An object with a mass of #2 kg# is acted on by two forces. The first is #F_1= < 3 N , 5 N># and the second is #F_2 = < 7 N, -6 N>#. What is the object's rate and direction of acceleration?

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Answer 1 · 2017-05-17T14:22:08

The rate of acceleration is #=5.02ms^-2# in the direction of #5.71º# clockwise from the x-axis

The resultant force is

#vecF=vecF_1+vecF_2#

#= <3,5>+<7,-6>#

#=<10,-1>#

#vecF=m veca#

Mass, #m=2kg#

#veca =1/m*vecF#

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

The magnitude of the acceleration is

#||veca||=||<5,-1/2>||#

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

#=sqrt(25.25)=5.02ms^-2#

The direction is #theta = arctan((-1/2)/(5))#

The angle is

#theta=arctan(1/10)=5.71º# clockwise from the x-axis