An object with a mass of 3 kg is acted on by two forces. The first is F_1= < -6 N , -5 N> and the second is F_2 = < 3 N, 3 N>. What is the object's rate and direction of acceleration?

1 Answer
Apr 19, 2018

The rate of acceleration is =1.20ms^-2 in the direction =213.7^@ anticlockwise from the x-axis

Explanation:

The resultant force is

vecF=vecF_1+vecF_2

vecF= <-6,-5> + <3,3> = <-6+3, -5+3>

= <-3,-2> N

The mass of the object is m=3kg

According to Newton's Second Law

vecF=mxx veca

Therefore,

veca=1/m*vecF= 1/3* <-3,-2>

= <-1, -2/3> ms^-2

The rate of acceleration is

||veca|| = || <-1,-2/3> || = sqrt ((-1)^2+(-2/3)^2)

=sqrt(1+4/9)= sqrt13/3=1.20ms^-2

The direction is

theta=arctan((-2/3)/(-1)) = 180^@+arctan(2/3)=213.7^@ anticlockwise from the x-axis