"Forces of 10.6 N north, 19.1 N east, and 16.0 N south are simultaneously applied to a 3.62 kg mass as it rests on an air table. What's the direction of acceleration in degrees (Take east to be 0 degrees and counterclockwise to be positive.) "
Using components, I already figured out the magnitude of acceleration.
Fnet=19.8N --> broken into components: F(x)=19.1N, F(y)=-5.4N
Trig ratios for sin and cos
The Attempt at a Solution
Using components, I figured out the total force in the x and y directions, and then used the pythagorean theorem to calculate the Fnet.
To find acceleration, I then isolated for a = Fnet/m = 5.48m/s/s
However, I'm having a lot of trouble figuring out the direction of the acceleration, and I don't know why! It's simple trig ratios.
cos(thetha) = F(x)/Fnet = 19.1/19.8
(theta) = 15.3 degrees
Its positive because the counterclockwise direction is positive.
Am I doing it wrong because they are asking for the direction of accleration, and I'm using the direction of Fnet? I don't see how I can use acceleration in the trig ratios though, since acceleration is only in the direction of Fnet... not the components on the x and y axis.