Draw a diagram of the problem, labeling a few quantities
Create a free body diagram with the main forces (IMPORTANT) and define your axes. A good set up is positive in the direction of acceleration.
Create a FBD with the component (optional)
Create your \(F = ma\) equation with individual axes (one for the x-axis, one for the y-axis), keeping in mind the signs. Remember that some forces only have a component acting in a given axis.
Don’t group up forces in the same direction (ex: \(mg-(\mu N + T) = ma\))as you may forget to distribute the sign. Instead, individually assign each force a sign (ex: \(mg-\mu N - T = ma\))
Substitute the known expressions for the quantities that have them (\(F_g=mg, f=\mu N\); etc)
Solve for the necessary quantities. You may need to solve both equations or only one.
Misc. Tips
The friction force can be of any magnitude equal to or less than \(\mu N\), even 0 if the object is not moving
The direction of friction on a moving object depends on the object’s velocity not acceleration
The magnitude of static friction (the force needed to get an object moving) is always larger than that of kinetic friction (the force needed to keep an object from slowing down)
Don’t remember the sine and cosine components as only vertical or horizontal, etc. Try to figure them out in every problem as they can mean different quanitities depending on the angle and direction given.