An object with a mass of #9 kg# is acted on by two forces. The first is #F_1= < -2 N , -1 N># and the second is #F_2 = < 8 N, -5 N>#. What is the object's rate and direction of acceleration?

1 Answer
Jan 23, 2017

The object is accelerating at a rate of #1.602m/s^2#
at an angle of #-33.69^@#

Explanation:

The total force acting upon an object is the sum of all the forces acting on that object.

#F_"tot"=sumF_i#

In this case

#F_"tot"=F_1+F_2#

Then adding algebraically we get

#F_"tot"= <-2N,1N> + <8N,-5N>#

# = <6N,-4N>#

and by Newton's 2nd Law

#F=ma#

Then we divide by #m=9kg#

#F_"tot"=9kg*<2/3m/s^2,-4/9m/s^2> #

Then

#a=<2/3m/s^2,-4/9m/s^2>#

The rate of acceleration is the magnitude of a.

#|a|=sqrt((2/3)^2+(-4/9)^2)=sqrt(4/9+16/81)=sqrt(36/81+16/81)=sqrt(52/81)=(4sqrt(13))/9approx1.602m/s^2#

The direction is down and to the right and the angle #theta#

#theta=arctan(-2/3)approx.-0.588 radapprox-33.69^@#