Question

An object with a mass of `2 kg` is acted on by two forces. The first is `F_1= < 2 N , 5 N>` and the second is `F_2 = < 1 N, -6 N>`. What is the object's rate and direction of acceleration?

Answer 1

The rate of acceleration is `=sqrt10/2ms^-2` in the direction `=18.4^@` clockwise from the x-axis.

Explanation:

The resultant force is

`vecF=vecF_1+vecF_2=<2,5> + <1,-6> = <3,-1>`

The mass is `m=2kg`

According to Newton's Second Law of motion

`vecF=mveca`

The acceleration is

`veca=1/mvecF=1/2 <3,-1> = <3/2,-1/2>`

The rate of acceleration is

`||veca|| =| |<3/2,-1/2>|| = sqrt((3/2)^2+(1/2)^2)=sqrt(9/4+1/4)=sqrt10/2ms^-2`

The direction of acceleration is

`theta = arctan((-1/2)/(3/2))=arctan(-1/3)=18.4^@` clockwise from the x-axis.