An object with a mass of $6 kg$ is acted on by two forces. The first is $F_1= < -6 N , 2 N>$ and the second is $F_2 = < 1 N, 3 N>$ . What is the object's rate and direction of acceleration?

Question

1776 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-11-07T13:43:48

The rate of acceleration is $=1.18ms^-1$ in the direction $=135^@$ anticlockwise from the x-axis.

The resultant force is

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

The mass is $m=6kg$

According to Newton's Second Law of motion

$vecF=mveca$

The acceleration is

$veca=1/mvecF=1/6<-5,5> = <-5/6,5/6>$

The rate of acceleration is

$||veca|| =| |<-5/6,5/6>|| = sqrt((-5/6)^2+(5/6)^2)=sqrt(25/36+25/36)=sqrt50/6=1.18ms^-2$

The direction of acceleration is

$theta = arctan((5/6)/(-5/6))=arctan(-1)=135^@$ antilockwise from the x-axis.

An object with a mass of 6 kg6 kg is acted on by two forces. The first is F_1= < -6 N , 2 N>F_1= < -6 N , 2 N> and the second is F_2 = < 1 N, 3 N>F_2 = < 1 N, 3 N>. What is the object's rate and direction of acceleration?