Question

An object with a mass of `5 kg` is acted on by two forces. The first is `F_1= <10 N , 6 N>` and the second is `F_2 = <4 N, 16 N>`. What is the objects rate and direction of acceleration?

Answer 1

The rate of acceleration is `=5.21ms^-2` in the derection `=57.5^@ "in the direction anticlockwise from the x- axis"`

Explanation:

The resultant force is

`vecF=vecF_1+vecF_2`

`= <10,6> + <4,16>`

`= <14, 22>N`

The mass of the object is `m=5kg`

According to Newton's Second Law

`vecF=mveca`

Therefore,

The acceleration is

`veca=vecF/m=1/5 *<14, 22>= <14/5, 22/5>`

The rate of acceleration is

`||veca||= ||<14/5, 22/5>||`

`=sqrt((14/5)^2+(22/5)^2)`

`=5.21ms^-2`

The direction is

`theta=arctan(22/14)=57.5^@ "in the direction anticlockwise from the x- axis"`