Question

An object with a mass of `4 kg` is acted on by two forces. The first is `F_1= < -7 N , 4 N>` and the second is `F_2 = < -3 N, -2 N>`. What is the object's rate and direction of acceleration?

Answer 1

The first force vector acting on the object of mass `m=4kg` is given by `vecF_1=(-7hati+4hatj)N`

The 2nd force vector acting on the object of mass `m=4kg` is given by `vecF_2=(-3hati-2hatj)N`
So the resultant force
`vecF=vecF_1+vecF_2=((-7-3)hati+(4-2)hatj)N=(-10hati+2hatj)N`

So the acceleration
`veca=vecF/m=1/4(-10hati+2hatj)m/s^2` `=1/2*(-5hati+hatj)m/s^2`

Hence the magnitude of acceleration is
`a=sqrt((-5/2)^2+(1/2)^2)=sqrt26/2m/s^2`

And its direction is `tan^-1(-1/5)` with the X-axis.