An object with a mass of #14 kg# is acted on by two forces. The first is #F_1= < 5 N , 6 N># and the second is #F_2 = < -9 N, 4 N>#. What is the object's rate and direction of acceleration?

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Answer 1 · 2017-07-23T18:07:17

#veca= <-2/7,5/7>#

#|veca|=sqrt29/7m/s^2#

#theta=111.8^o#

Let's find the sum of the forces :

#vec(F_1)+vec(F_2)=<5,6>+<-9,4> =<-4,10>#

Now from the #2^"nd" Law of Newton :#

#ΣvecF=mveca=>veca=(ΣvecF)/m=1/14*<-4,10> =#

#<-2/7,5/7>#

So #veca= <-2/7,5/7>#

The magnitude is #|veca|=sqrt(4/49+25/49)=sqrt29/7m/s^2#

The angle with the horizontal is #theta=arctan((5/7)/(-2/7))=#

#arctan(-5/2)=111.8^o#