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Dot Product A · B
A · B = [A][B]cosθ
You get a scalar product.

Cross Product A x B
A x B = [A][B]sinθ
You get a vector product.

Displacement vs Distance
 Displacement: includes the magnitude and direction of only the net change from start to finish
 Distance: a scalar quantity that takes into account to length traveled

Velocity vs Speed
 Velocity: magnitude of measured rate of change of displacement per unit of time (vector quantity)
 Speed: rate of actual distance traveled divided by a given unit of time

Instantaneous Velocity
v = lim(as Δt → 0) Δx/Δt


Net Force
Newton's second law of thermodynamics
 F = ma
 m: mass
 a: acceleration

Gravity
F _{g }= (Gm _{1}m _{2})/(r ^{2})
 G: 6.67x10^{11} N·m^{2}/kg^{2}
 r: distance between the two object of m_{1} and m_{2}

Static Friction
Exists between two objects at rest. It is an equal and opposite force acting on object.
0 ≤ f _{s} ≤ μ _{s}N
 μ_{s}: coefficient if static friction
 N: normal force (component of force perpendicular to the plan between object on at rest and surface)

Kinetic Friction
Exists between two objects sliding along a surface.
f _{k} = μ _{f}N
 μ_{f}: coefficient if kinetc friction
 N: normal force (component of force perpendicular to the plan between object on at rest and surface)

Relate coefficient of static friction to kinetic friction
μ_{s} > μ_{k}

Weight
A measure of gravitational on an objects mass.
F_{g} = mg
g: 9.8 m/s^{2}


Average Acceleration
A = Δv / Δt

Linear Motion Equation
(no x value)
v = v_{0} + at

Linear Motion Equation
(no v value)
x = v_{0}t + at^{2}/2

'Linear Motion Equation
(no t value)
v^{2} = v_{0}^{2} + 2ax

Linear Motion Equation
(no v_{0} or a value)
x = vt

Two gravity equation for an inclined plane
 F_{g,ll} = mgsinθ = ma
 F_{g,(perpendicular)} = mgcosθ = N

Centripetal Force
F _{c} = mv ^{2}/r
(centripetal acceleration)
 Note:
 Centrifugal force is antiparrallel to centripetal force

Translational equilibrium
Exists only when the vector sum of all forces is 0

Fulcrum
Fixed pivot point

Torque
Application of force at some distance from the fulcrum.
τ = r x F = (r)(F)sinθ
r: distance of applied force from fulcrum

τ sign when rotated clockwise / counterclockwise
 Counterclockwise ()
 Clockwise (+)

Normal force exerted by fulcrum
 n = F_{g,seesaw + blocks}
 N = (m_{seesaw} + m_{1} + m_{2})g

Equation for kinetic energy
Kinetic Energy: energy of motion
K = (1/2)mv^{2}

How is kinetic energy related to speed and velocity?
It is NOT related to velocity, but it IS related to speed.
The faster something is, the more kinetic energy it has, hense K = (1/2)mv^{2}

Potential Energy Equation
Potential Energy: energy with the potential to do work of stationary objects
U = (1/2)mgh

Elastic Potential Energy
When a spring is stretched from it's equilibrium length, the spring has spring potential energy determined by the following equation:
U = (1/2)kx ^{2}
 k: spring constant (high k means spring is stiffer)
 x: magnitude of displacement from the equilibrium length

Total Mechanical Energy
The sum of the objects potential and kinetic energy.
E = U + K
This is if the system is conserved (no energy leaves system due to things like friction, heat, light)

Two commonly encountered conservative forces
 Conservative Forces: those that are path independent and do not dissipate energy
 gravitational
 electrostatic
If the net change is 0, then the forces are conserved.

Nonconservative Forces
 Forces that dissipate mechanical energy as thermal or chemical energy:
 friction
 air resistance

Equation for conservation of energy when work done by nonconservative forces is 0
ΔE = ΔU + ΔK = 0 = W
(work is measured in J)

Work done by nonconservative forces
W_{nonconservative} = ΔE = ΔU + ΔK
(work is measured in J)

Work Equation when something exerts forces on something else
Work: it is not a form of energy, but the process by which energy is transferred from one system to another
W = F · d = Fdcosθ
θ: the angle between force vector and displacement vector
(work is measured in J)

Isovolumetric or Isochoric process
In a P vs V diagram, this is when no work is done. This means volume does not change, ONLY pressure.

Calculating work in a Isobaric process
Isobaric: when pressure is constant, and only volume changes.
W = PΔV
The area under a P vs. V line is work.
(work is measured in J)

How would you calculate work when P and volume is not constant?
It would be the area under the curve. Try cutting it up into shapes who's areas you know and calculating the area.
(work is measured in J)

What does it mean to have (+) work? () work?
 (+): work is done by a system
 (): work is done on a system
(work is measured in J)

Power Equation
Power: rate at which energy is transferred from one system to another.
P = W/t = ΔE/t
(work is measured in J)

WorkEnergy Theorum
Mechanical application for relating energy and work. The net work done by forces acting on an object result in equal change in the objects kinetic energy:
 W_{net} = ΔK = K_{f}  K_{i}
 Knowing the magnitude of forces acting on an object allows you to calculate the work.
(work is measured in J)

Mechanical Advantage
Mechanical Advantage: ratio of magnitudes of the force exerted on an object by a simple machine (F_{out}) to the force applied on a simple machine (F_{in}).
Mechanical Advantage = F_{out}/F_{in}

Calculating Efficiency of a Pulley
Efficiency = W _{out}/W _{in} = [(load)(load distance)]/[(effort)(effort distance)]
 load: weight (mass x gravity)
 load distance: object height lifted
 effort: force required to lift crate
 effort distance: how much rope must be pulled (height raised x number of pulleys)
You don't always get 100% efficiency because of nonconservative forces.

What are the six simple machines?
 Inclined plane
 Wedge
 Pulley
 Liver
 Wheel and axle
 Screw

How can you calculate the force being used to pull a weight on a pulley, given a mass and acceleration?
The force used to pull up the pulley is F = ma. The tensions on the pulley cancel force done by gravity if it was still but increase as tension increases, giving:
F_{net} = ma = xT  mg
x: number of ropes used

