An object with a mass of #2 kg# is acted on by two forces. The first is #F_1= <-3 N , -5 N># and the second is #F_2 = < 6 N, 7 N>#. What is the object's rate and direction of acceleration?
Adding the vectors gives a magnitude of
Using Newton's Second Law:
First we find the resultant force acting on the object, by adding the components of the force vectors:
So the resultant force vector is 3 in the x direction and 2 in the y direction. We can use Pythagoras' theorem to find the magnitude of the resultant:
To find the direction, we use trig: 3 and 2 are the opposite and adjacent sides of a right-angled triangle, so:
Using Newton's Second Law, the acceleration is given by: