Question

An object with a mass of `4 kg` is acted on by two forces. The first is `F_1= < -1 N , 8 N>` and the second is `F_2 = < -2 N, 5 N>`. What is the object's rate and direction of acceleration?

Answer 1

The rate of acceleration is `=3.34ms^-2` in the direction `=103^@ " anticlockwise from the x- axis"`

Explanation:

The resultant force is

`vecF=vecF_1+vecF_2`

`= <-1,8> + <-2,5>`

`= <-3, 13>N`

The mass of the object is `m=4kg`

According to Newton's Second Law

`vecF=mveca`

Therefore,

The acceleration is

`veca=vecF/m=1/4 *<-3, 13> = <-3/4, 13/4>`

The rate of acceleration is

`||veca||= ||<-3/4, 13/4>||`

`=sqrt((-3/4)^2+(13/4)^2)`

`=3.34ms^-2`

The direction is

`theta=arctan(-13/3)=103^@ "in the direction anticlockwise from the x- axis"`