Formulas:

∑F = ma

∑F = Net Forces; m = mass; a = acceleration

Frictions:

(Static Friction) Fs ≤ µ n (µ being the coefficient of static friction in this case)

(Kinetic Friction) Fk = µ n (µ being the coefficient of kinetic friction in this case)’

“µ” should be found on a table or be provided.

n = the force normal *(the force perpendicular to the surface contact)

Trigonometric Formulas:

O = Opposite; A = Adjacent; H = hypotenuse

a) Sinθ = O/H

b) Cosθ = A/H

c) Tanθ = O/A

d) sqr (O^2 + A^2) = H^2

Follow these rules when attempting to solve the problems:

1. Find a coordinate system that will work to help describe the forces directionally *(Often with the y-axis being gravity).
2. Draw out every force described in a picture (with θ); draw a free body diagram.
3. Use ∑F = ma and cancel out the forces (may need to calculate the base x and y components of  forces).
4. Solve for Unknowns!

Quick problem walk through:

In order to solve for ∑F it may be easier to break down every single force into x-axis and y-axis components, then canceling out the forces on each axis (a negative force on the x-axis will cancel with a positive force on the x-axis, same applies for the y-axis).

Once everything is canceled, all that need to be done is to think of the two remaining force vectors as two legs on a triangle (O and A from the Trigonometric Formulas), then use formula ‘d’ from the Trigonometric Formulas section (above) to get the magnitude of the ∑F. To obtain the net force vector you then must use formula ‘c’ from the Trigonometric Formulas section and obtain the θ. Then redraw the picture (to make sure it makes sense) and solve for unknowns.

Newton’s Laws:

1. If an object does not interact with other objects, it is possible to identify a reference frame in which the object has a zero acceleration. * Think of it as if there was a man in the train, if he stands up to walk to a car further up in the train to a person watching from the outside he is going the same velocity as the train PLUS his walking speed, but to those in the train he is only walking as fast as he is walking. This is because they are in the same frame of reference. In the absence of external forces and when viewed from an internal reference frame, and object at rest remains at rest and an object in motion continues in motion with a constant velocity. *An object will stay still or in motion unless a force acts upon it.
2.  When viewed from an inertial reference frame, the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass: ∑F = ma.
3. Any force that an object(a) exerts on object(b), object(b) also exerts on object(a). * Think of yourself pushing on a wall, the resistance of the wall you feel is the wall “pushing back” or resisting you.