An object with a mass of #3 kg# is acted on by two forces. The first is #F_1= < -2 N , -3 N># and the second is #F_2 = < 7 N, 1 N>#. What is the object's rate and direction of acceleration?

1 Answer
Apr 28, 2016

The resultant force acting is #<5,-2>#. The magnitude of the force is #5.4# #N#, leading to an acceleration of #1.8# #ms^-2# in a direction #21^o# below the positive x axis.

Explanation:

First find the resultant force acting:

#F_1+F_2= <-2+7,-3+1> = <5,-2>#

The magnitude of the force is:

#F=sqrt(5^2+(-2)^2)=sqrt(25+4)~~5.4# #N#

The magnitude of the acceleration is given by Newton's Second Law:

#a=F/m=5.4/3=1.8# #ms^-2#

The direction of the acceleration will be given by:

#tan^-1((opp)/(adj))=tan^-1(-2/5)=-21^o#