An object with a mass of #9 kg# is acted on by two forces. The first is #F_1= < -7 N , 1 N># and the second is #F_2 = < 4 N, -5 N>#. What is the objects rate and direction of acceleration?
We're asked to find the acceleration (magnitude and direction) of an object with a known mass and two forces that act on it.
We can use the famous equation
to help solve this problem. In component form, this becomes
We therefore need to find the components of the net force acting on the object.
The net force components are the vector sums of the components of the individual forces:
The components of the acceleration are
The magnitude of the acceleration is thus
The direction of the acceleration is