Download Super Quick Mechanics Review Sheet

Super Quick Mechanics Review Sheet
Velocity = vector
Speed = scalar
use displ / time
use dist / time
v = average velocity
needs a direction
vi vf = instantaneous
Acceleration = change velocity 
v = (vi + vf) / 2
direction changes = centripetal acceleration
magnitude changes = linear (tangential) velocity
Same sign v & a = speed up
Opposite signs v & a = slow down
D-T curve
V-T curve
(flat lines = 0 v)
(flat line = const v)
(slope = velocity)
(slope = accel.)
(never add v’s)
(curve lines = accelerate)
(distance = areas) ( v = (vi + vf)/2)
Free Fall – any time moving in air and only gravity acts
 a = -9.81 m/s2 ALWAYS, no exceptions
 break up and down trip in half so time = t/2
vtop = 0  (vI down = 0, vf up = 0)
Vectors
– always draw to a rough scale
- draw head to tail, don’t assume right triangle
- draw exactly what is explained in the problem, don’t hesitate
- Always find the angle to describe direction of any vector quantity
 velocity, acceleration, force, momentum
Projectiles -
do the same thing everytime.
list x info and y info separately
ay = -9.81 m/s2, viy = 0 if initially moving horizontally  in this case Vx = Vi
if launched at an angle, find Viy and Vx (Vx remains the same throughout)
Always start with x direction. ONLY USE Vx = dx / t (NOTHING else for x direction).
After solving, or if you cant solve for anything move to the y direction.
Solve for whatever you can in y direction. You are either now done or need to return to
the x direction with the results you found.
If launched at angle, break the trip in half so that Vy top = 0 and time = t/2
Newtons Laws
- know the three laws and think about them when answering questions
- Force units = newtons N, a vector quantity that needs a direction
- Action – reaction forces ALWAYS are equal, even if you think one should be greater.
The action force and reaction force always act on separate objects
When solving a problem
- Always draw a NEAT AND CLEAR FBD and don’t forget friction if applicable
- Only draw Normal force if something is pushed against a surface
- Be aware that FN does not necessarily = Fg
- Look for “constant speed”  means a = 0 and forces must balance each other
- When specific materials are listed (wood, etc), look up the friction coeff’s on ref table.
- Forces at angles must be broken into x and y components
- Always draw Fgx and Fgy when on an incline. Review notes of how to draw these.
- start problems by listing “m” and Fg
- Do Fnet(y) = may and replace Fnet(y) with the y direction forces
(be careful to include all y direction forces)
- Do Fnet(x) = max and replace Fnet(x) with the x direction forces
(include all x direction force and look to use f = μFn if possible)
Work = Force x Distance
units of J (Joules)
- negative work when force is opposite the direction of motion (i.e. friction)
- use parallel part of work when force is at angles (Fx d if moving in x direction)
- forces that are perpendicular to direction of motion do ZERO work
- Work causes changes in energy of some form
(Non conservative work causes mechanical energy to be lost to “Q”,)
(Conservative work causes KE and PE to transfer between each other)
Power – the rate at which work is done and energy is used. Be aware of the multiple
equations that can be used to find Power.
Units = W Watts.
Energy
PE = stored energy
spring and gravity type
KE = motion energy
ME = KE + PEspring + PEgrav
Etot = ME + Q (internal energy)
Springs
Fsp = kΔx
k = stiffness (N/m) Δx = change in length
- Force in the spring is not constant but varies depending on how much Δx is. Force
always acts to pull or push the spring back to its rest (equilibrium) position.
Work – Energy
- conservative force (The path taken has no effect on the amount of work done)
- non-conservative force (The amount of work done depends on the path taken)
The function of work is to change energy. It transfers energy from one form to another.
- In a conservative situation (no friction) – the amount work done gives the amount that
PE, KE and PEspring switch forms between one another.
- In Non-conservative situations (friction) – the amount of work done by friction gives
the amount of ME removed. There is a loss in ME (PE+KE) and this loss is equal to the
work of friction and is transferred to heat.
Since Etotal = PE + KE + Q, in any situation (both conservative and non-conservative) total
energy is always conserved since it simply transfers from one form to another.
Problem Methods
1) Frictionless Problems - If only conservative forces are acting (meaning no friction, or
pushing forces), ME is conserved and the work done by the conservative forces causes
energy to be transferred among different ME types. We solve this problem type by
equating energy at two points.
MEi = MEf
KEi + PEi + PEsp(i) = KEf + PEf + PEsp(i)
2) Problems with non-conservative forces, (like Friction) - If non-conservative forces are
acting (there is friction), ME is changed and goes to Q. The work done by the nonconservative force removes ME and transfers it to Q. These problems can be solved
simply by finding the amount of work done by friction and understanding that this will be
the amount of ME lost. Sometimes, there is a pushing force, which would cause a gain in
ME (ex: a force compressing a spring). In this case, the work done adds ME. In either
case, the net result is that you can either add or subtract the work done from whatever
initial type of energy you have to find out what happens.
Pushed spring example: When springs are being pushed, there is an input of work and the
function of this work is to store energy in the spring. The work (Fd) done as the force
pushes the spring is equal to the amount of energy put into the spring (PEsp) once the
pushing is completed. (Note: You can not use F=kΔx in this situation because we are
analyzing the spring in motion over a given distance with a force that changes. You can
only use F=kΔx is you have a spring being held in place with a known force)
Impulse (unit Ns) – Momentum (unit kg m/s)
#1 most important thing  opposite directions = make one of the velocities “-“
J = Ft
Jnet
= Δp
= mvf - mvi
(use this when you have F’s, t’s, m’s, and v’s)
In collisions only, always start with
∑pi(tot) = ∑pf(tot)
and work from there. Fill in a “mv” term for each
item that has momentum
Elastic (ME & p conserved),
Inelastic and Perfect Inelastic (only p conserved)
Gravity – Fg = G m m / r2
be aware of #’s on ref table for planets
Satellite orbits are created by giving something a certain velocity tangent to the planet
such that the object continually “falls” around the planet. Fg provides the centripetal
force in this case.
Geosynchronous – satellite always stays in the same place when it orbits (it therefore
must orbit in 24 hrs to match the earths rotation rate)
Centripetal
- Centripetal force and acceleration always act towards the center
- Velocity is always tangent to the circular path at a given spot
(things that leave the circle follow the tangent line)
- Things are moving in circles, so in 1 revolution, d=2πr  v = 2πr / T
- ac is caused by direction changes, a is caused by speed changes
- Fc is not its own force, rather it is the name given to a force that makes a circle happen
(ex: friction can be called a centripetal force if it makes things go in circles)
- Fc does not push you out from circle center rather it pushes in to the center to make
the circle happen; inertia makes you “feel like” you are pushed to the outside
Fc = mac
ac = v2 / r

Fc = mv2 / r
Factors that effect Fc - (m, v and r) – simply look at the formula and decide what
happens. If v is increased, so is Fc, and so forth.