NEWTONIAN MECHANICS. Kinematic equations Frictional Force

NEWTONIAN MECHANICS

Kinematic equations

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2

1

22

20

oo

o

o

xxavv

attvxx

atvv

Frictional Force

force normal

NF

FFfric

Centripetal acceleration:

The acceleration of an object due to it’s changing direction as it moves at a constant speed in a circular path. Always directed toward the center of the circle

r

vac

2

Torque:

A force applied at a distance from the pivot to produce a rotation.

sinrF

momentum:

The product of the mass and velocity.

impulse:

The product of the average force applied and the time is equal to the change in momentum

of mvmvptF

mvp

kinetic energy – Energy of motion

gravitational potential energy – Energy due to position in a gravitational field

Elastic potential energy – energy due to a stretch or compression

2

2

2

1

2

1

kxU

mghU

mvK

s

g

Work:

A force applied through a distance that changes the energy of the system

Power:

The rate of doing work

cos

cos

Fvt

WP

rFW

Hooke’s law:

The force due to a stretch or compression.

kxFs

Period of a pendulum

Period of a mass on a spring

The period is the inverse of the frequency

fT

k

mT

g

LT

s

p

1

2

2

Gravitational Force:

The force between two masses

Gravitational potential energy:

The potential energy between two masses

r

mGmU

r

mGmF

G

G

21

221

ELECTRICITY

Coulomb’s Law:

The force between two point charges.

221

r

qkqF

The Electric Field:

The force per unit charge at a point in space due to a the distribution of charges.

2r

kq

q

FE

The electric potential energy between two point charges

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UE =kq1q2

r

The Electric Potential (Voltage):

The electrical potential energy per unit charge at a position in an electric field.

C

JV 11

.....321

r

q

r

q

r

qkV

EdV

q

UV E

Capacitance: Charge stored on two parallel metal plates due to a potential difference between the plates. The capacitance is directly proportional to the Area of the plates and inversely proportional to the distance between the plates.

d

AC

V

QC

o

Energy Stored on a Capacitor

2

2

1

2

1CVQVUC

Current – The rate at which charge flows in a circuit

t

QI

The resistance of a wire is directly proportional to the resistivity and length of the wire and inversely proportional to the cross sectional area.

A

LR

Ohm’s Law: The relationship between the voltage, current and resistance. Current is directly proportional to the voltage and inversely proportional to the resistance.

IRV

Power – The rate at which electrical energy is dissapated.

IVP

As resistors are added in series the total resistance goes up.

As resistors are added in parallel the total resistance goes down.

.......1111

...........

321

321

RRRR

RRRR

p

s

Capacitors are just the opposite

.......1111

...........

321

321

CCCC

CCCC

s

s

MAGNETISM

The magnetic force on a moving charge in a magnetic field

sinqvBFB

The magnetic force on a current carrying wire in a magnetic field

sinBILFB

The magnetic field around a current carrying wire

r

IB o

2

Magnetic Flux:

The strength of a magnetic field passing through a loop of wire.

cosBAm

The induced EMF (voltage) is the rate of change of the flux with respect to time.

tm

avg

Motional EMF:

The EMF induced in a wire as it cuts across a magnetic field.

BLv

FLUIDS

Density:

The mass per unit volume

V

m

The pressure in a fluid is the sum of the absolute pressure and the gauge pressure.

ghPP o

Buoyancy Force:

The buoyant force depends on the density of the fluid, the volume and the gravitational field.

VgFB

Flow continuity:

If the volume of fluid flowing through a pipe is the same then the product of the fluid velocity and cross sectional area of the pipe must be constant

2211 vAvA

Bernoulli’s principle: Fast moving fluids result in low pressure.

constant2

1 2 vghP

THERMODYNAMICS

Pressure is the Force per unit area measured in N/m2 = Pa

A

FP

Ideal gas law:

Assumes all the internal energy is kinetic energy. Forces between particles are negligible.

2

22

1

11

T

VP

T

VP

nRTPV

1st Law of thermodynamics:

Heat added to a system (gas) is equal to the work done by the gas plus its change in internal energy

Work is done by the gas when the volume increases. Work is done on the gas when the volume decreases.

VPW

UWQ

Efficiency – The ratio of the work done to the input heat (energy)

The maximum efficiency of a heat engine is given by the Carnot equation.

H

CHc

H

T

TTe

Q

We

WAVES AND OPTICS

The wave equation:

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v = fλ

Waves slow down in different mediums. The ratio of the speed in a vacuum to the speed in the medium is the index of refraction

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n =c

v=λ

λ n

Refraction:

The bending of light when it travels from one medium to another. The angle of incidence is related to the angle of refraction by snell’s law

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n1 sinθ1 = n2 sinθ 2

Total internal reflection occurs when light travels between two mediums where n1>n2. If the angle of incidence is greater than the critical angle, total internal reflection occurs.

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sinθ c =n2

n1

The lens and mirror equation gives the relationship between the image distance, object distance and focal length

€

1

di+

1

do=

1

f

Magnification:

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M =−dido

=hiho

Double slit interference:

Evidence that light is a wave.

θ is angle to the nth order bright spot and xm is the distance. L is the distance to the screen and d is the slit separation

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d sinθ = mλ

xm =mλL

d

The same equation work for single slit diffraction except they give the dark spots.

Thin film interference:

The thickness of the film determines whether constructive or destructive interference occurs.

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constructive : d =λ n2

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destructive : d =λ n4

λn is the wavelength in the thin film

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λn =λ

n

ATOMIC AND NUCLEAR

The Energy of a photon

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E photon = hf =hc

λ= pc

The Photoelectric Effect:

Evidence for the particle theory of light. Photons incident on a metal eject electrons from the metal with a maximum kinetic energy that depends on the frequency (f) and work function of the metal (ϕ)

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Kmax = hf −φThe slope of the graph is plank’s constant and the y intercept is the work function. The x intercept is the threshold frequency

DeBroglie wavelength equation relates the wavelength to the momentum of a particle.

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λ h

p

Energy – Mass equivalence:

In a nuclear reaction mass is converted to energy. The mass defect Δm is related to energy by the square of the speed of light.

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E = Δm( )c 2

Alpha particle:

+ Beta particle:

-Beta particle:

Neutron:

Proton:

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α = 24He

Β+ = +10e

Β− = −10e

01n

11p = 1

1H