Question

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?

Answer 1

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^@`