An object with a mass of 8 kg is acted on by two forces. The first is F_1= < -9 N , 2 N> and the second is F_2 = < -4 N, -3 N>. What is the object's magnitude and direction of acceleration?

1 Answer
Feb 12, 2018

The magnitude of acceleration is sqrt(170)/8
And it makes an angle theta = pi - arctan(1/13) with the positive x-axis

Explanation:

The net force in x-direction is : ((-9) + (-4))N = -13 N
The net force in y-direction is : ((+2) + (-3))N = -1 N

The magnitude of the net force: F = sqrt((13)^2 + (1)^2) = sqrt(170)/8

Thus the force makes an angle phi = arctan(1/13) with the negative x-axis. Which can be written as it makes an angle theta = pi - arctan(1/13) with the positive x-axis

Hence the magnitude of acceleration: a= F/m =sqrt(170)/8
And the direction will be same as that of the net force.