Question

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?

Answer 1

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`