Question

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?

Answer 1

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.