Physics Day 1Units, Vectors, and Kinematics

Units

Velocity and Acceleration

t

xv

units are

s

m

t

va

units are

2s

m

Force (Newtons)

maF 22 s

mkg

s

mkgN

Energy/Work (Joules)

FdW 2

2

s

mkgmNJ

2

2

1mvKE

2

22

s

mkg

s

mkgJ

mghPE 2

2

2 s

mkgm

s

mkgJ

Power (Watts)

t

WP

3

22

2

s

mkg

s

s

mkg

s

J

Density

V

m units are

3m

kg

Pressure (Pascal)

A

FP

22 sm

kg

m

NPa

gDP fluid 223 sm

kgm

s

m

m

kgPa

SI Units

Length m

Mass kg

Time s

Electric current A

Temperature K

Luminous intensity Cd (candela)

Derived Units

Volume m3

Force N

Energy/Work J

Power W

Pressure Pa

Charge C

Resistance Capacitance F

Electric Field Strength

qEF so q

FE units are

C

N (not usually broken down further but could be)

Potential/Voltage (Volts)

qVPE so q

PEV

3

23

2

sA

mkg

A

s

mkg

A

W

C

sW

C

JVolts

Current (Ampere)

t

qI

s

CAmps

Resistance (Ohms)

IRV so I

VR

32

2

32

22

2

2

2 sA

mkg

sC

mkgs

sC

mkg

C

sJ

s

CC

J

A

V

(a little tricky)

Capacitance

V

QC

2

42

22

42

2

22

2

2

22

mkg

sA

mkgs

sC

mkg

sC

s

mkg

C

J

C

C

J

C

V

CF

(a little tricky)

Magnetic Field Strength (Tesla)

sinqvBF so sinqv

FB

sC

kg

mC

ss

mkg

mC

sN

s

mC

NT

2

sinBIF so sinI

FB

sC

kg

mC

ss

mkg

mC

sN

ms

C

N

mA

NT

2

Vectors

Kinematics

Displacement = x (change in position) or d (Difference from Distance)

Velocity t

xv

vavg =

2

fi vv (Difference from Speed)

Acceleration t

va

-acceleration due to gravity

-acceleration while moving along a curve

-signs () are important when displacement, velocity, and acceleration dont all point in the same direction

vtd (no acceleration)

tvd avg (constant acceleration)

2

2

1attvd i (constant acceleration)

2

2

1atd when starting from rest

advv if 222 (constant acceleration) used when no time information is available

1. A car accelerates from 40mph to 60 mph in 4 seconds. What is its acceleration?

2. A car travels north at 60mph for 5 hours. What is its total displacement?

3. From rest a car accelerates at 3m/s2. What is the cars velocity after 6s? How far has it traveled?

4. A penny is dropped from the roof of a building and takes 4s to reach the ground. From what height was the

penny dropped? (Ignore air resistance and use g=10m/s2)

5. A penny is dropped from the roof of a 100m tall building. How long does it take for the penny to reach the

ground? (Ignore air resistance and use g=10m/s2)

6. A penny is dropped from a building. Its final velocity just before it reaches the ground is 40m/s. From what height was the penny dropped?

Graphs

7.

Projectile Motion

time to max height (tup) g

vt

yi

up

0 g = gravity

max height (ymax) upyi

upyavg tv

tvy2

max

total time (ttotal) uptotal tt 2

horizontal displacement (x) totalxtvx

8. A potato is fired from a potato gun with an initial velocity of 100m/s 30 above the horizontal. What is the time of flight of the potato? What is its maximum height during flight? What is the distance between where it

was fired and where it lands?

0

v

t

at

vslope

area = d

Area = d 0

x

t

vt

xslope

Graph A Graph B

Physics Day 2Mechanics Newtons Laws 1

st Law An objects velocity remains constant unless a net force is acting upon it.

If F=0, then v=constant

2nd

Law F=ma

3rd

Law For every force exerted by one object on a second object, there is an equal but opposite force by the second object on the first.

1221 FF

1. Two astronauts of masses 100kg and 150kg are at rest floating in space. The larger pushes the smaller so that

they are moving away from each other. The 100 kg astronaut has a resulting acceleration of 2m/s. What was

the force of the larger astronaut on the smaller astronaut? What was the resulting acceleration of the larger

astronaut?

Gravity

W = mg 2

21

r

mmGFg 2

2111067.6

kg

mNxG

For an object on the surface of the earth, mgr

mMGF

E

Eg 2 , so 22 8.9 s

m

r

MGg

E

E

2. A new planet with twice the mass and a radius that is three times greater than that of earth has been

discovered. How will its gravitational acceleration compare to that of earth?

Normal Force Perpendicular component of the contact force that a surface exerts on an object.

Friction

Nkf FF kinetic

Nsf FF max static

3. A 100kg man is on an elevator that is accelerating upward 2m/s2. What is his apparent weight?

4. A 10 kg object is being pulled horizontally along a surface with a force of 200N resulting in a net

acceleration of 18m/s2. What is the coefficient of kinetic friction between the object and the surface?

Inclines

5. A 10 kg object is at rest on a plane inclined 30 above the horizontal. What is the force of friction acting upon the

object? What is the coefficient of friction (Be careful!)?

6. A 10 kg object slides down a frictionless plane inclined 30 above the horizontal. What is its acceleration?

7. An object slides down a 45 incline at constant velocity? What is the coefficient of kinetic friction between the object and the incline?

Pulleys

8. For pulley 1, what is the tension in the rope if the mass is suspended at

rest?

9. For pulley 2, what is the acceleration of the 7.5kg mass?

10. For pulley 3, what is the acceleration of the 7.5kg mass?

Centripetal Force/Acceleration

r

vac

2

cmar

mvF

2

11. A boy is twirling a 100g yoyo with a 600cm radius horizontally in a circle

above his head with a speed of 2m/s. What is the maximum centripetal force

acting on the yoyo?

12. Give an expression for the radius of a satellite in a stable orbit around the Earth in terms of the gravitational

constant G, the mass of the Earth ME, and the velocity v of the satellite.

13. A roller coaster car completes a loop-d-loop on its track. Is the normal force acting on the car by the track greater at the top or bottom of the loop-d-loop? By how much (answer in terms of m, v, r, and g)?

Work and Energy

FdW (only force component in the direction of motion)

14. How much work is performed by an Alaskan husky pulling a dog sled 10m across the snow with a pulling

force of 300N.

Mechanical Energy

PEKEE 2

2

1mvKE mghPE (gravitational)

Conservation of Mechanical Energy ( 0E )

ffii mghmvmghmv 22

2

1

2

1 (if no work is done by nonconservative forces)

EWNC (work performed by nonconservative forces; when mechanical energy is not conserved)

Work-Energy Theorem

KEW (work performed by a net force)

15. A ball is dropped from a 45m cliff. What is the velocity of the ball just before it reaches the ground (ignore

air resistance)?

16. A 1.5m long pendulum is released from an angle of 60 from the vertical. What is the maximum velocity achieved by the pendulum?

17. A 1kg ball is dropped from a 45m cliff. Its velocity just before it reaches the ground is 20m/s. How much

work is done by air resistance on the ball?

Power Fvt

WP

18. If John can do twice as much work as Bill in half the time, how much greater power is John providing?

Momentum and Impulse

Momentum mvp

Impulse-Momentum Theorem mvtF

19. A 1kg baseball traveling at 40m/s towards home is sent in the opposite direction at 30m/s after being hit

with a baseball bat. If the bat is in contact with the ball for 0.05s, with what force was the ball struck by the

bat?

Collisions

Elastic Collisions Perfectly Inelastic Collisions

(objects stick together)

p = 0 ...... 22212211 ffii vmvmvmvm p = 0 ...... 22212211 ffii vmvmvmvm

KE = 0 ...2

1

2

1...

2

1

2

1 222

2

11

2

22

2

11 ffii vmvmvmvm KE 0 (some mechanical energy is lost)

20. A 2kg ball heading west at 5m/s across a frictionless surface collides head-on with a 4kg ball that had also

been moving. After the collision, the two balls are stuck together and are moving with a velocity of 5m/s

directly east. What was the original velocity of the 4kg ball?

21. A stationery bomb explodes into 3 fragments. The 1st fragment weighing 2kg is moving directly north with

a velocity of 100m/s after the explosion. The 2nd

fragment weighing 4kg is moving directly west with a

velocity of 50m/s after the explosion. What is the velocity of the 3rd

fragment (weighing 2kg) immediately

after the explosion?

Impulse

Physics Day 3-Rotational Kinematics/Dynamics and Fluids Rotational Kinematics

Angular Displacement = or rd

Angular Velocity t

rv

Angular Acceleration t

ra

Rotational Kinematics Eqns Analagous Translational Kinematics Eqns

t vtd (no acceleration)

tavg tvd avg (constant acceleration)

2

2

1tti

2

2

1attvd i (constant acceleration)

222

if advv if 222 (constant acceleration)

1. A fly is sitting on the edge of a record with a radius of 0.2m spinning at constant velocity. If the fly

completes 6 revolutions in 30s, what is the angular velocity of the record? What is the translational velocity

of the fly?

2. A boy is riding a horse on a carousel located 2m from its center, while his father is sitting on a bench on the

carousel located 5m from its center. How much greater is the angular velocity of the boy compared to his

father? How much greater is the translational velocity of the boy compared to his father?

Rotational Dynamics

Center of Mass ...

...

21

2211

mm

xmxmxCM

Torque F lever arm

I (just like F=ma)

Inertia 2mrI (for point masses about an axis)

Angular Momentum IL

Rotational KE2

2

1I

Rotational/

Angular

Translational

d

v

a

I m

F

2

2

1IKE 2

2

1mvKE

W FdW IL mvp

3. Where would a fulcrum need to be placed for the following bar to be balanced perfectly?

4. A 20kg sign is hanging on the end of a 50kg boom that is suspended by a wire attached to the wall as in the

following figure. What is the tension in the cable?

5. A solid cylinder and a hollow cylinder of equal mass and radius roll down an incline. Which one reaches the

bottom first?

6. A wheel with a moment of inertia of 100kg.m

2 is accelerated from rest by a motor to an angular velocity of

80rad/s. How much work is performed by the motor?

Hydrostatics

Density: V

m Specific Gravity

OH2

31000

2 m

kgOH

Pressure

A

FP 1atm = 760torr = 760mmHg ~ 100,000Pa

1. The applied force is tripled and the area over which it is applied is cut in half. What is the affect on the

pressure?

Hydrostatic Pressure (Gauge Pressure)

gDP fluid where D=depth

2. A snorkeler dives to a depth of 25m in a freshwater lake. What is the total pressure at this depth? What is

the hydrostatic pressure?

Manometers

Buoyancy Force (Archimedes Principle)

gVWF submergedfluiddisplacedfluidB _

objectB WF (if the object is floating)

% submerged 100fluid

object

3. A large piece of Styrofoam with a mass of 2kg and a specific gravity of 0.05 is floating in a pool of water.

What volume of the piece of Styrofoam is submerged below the surface?

4. If an object normally weighs 500N and while submerged in water it has an apparent weight of 300N, what is

the density of the object?

5. A block of wood having a specific gravity of 0.6 is floating in a pool of water. What percentage of the block

of wood is above the surface?

Every 10m depth in H2O is ~1 atm pressure

Hydraulic Jack

2

2

1

1

A

F

A

F 2211 dAdA

6. For the following hydraulic jack, how much force must be applied to the small side of the jack in order to lift

a 250kg engine on the large side?

Hydrodynamics

Laminar flow vs Turbulent flow

Flow Rate: Avf A = cross-sectional area velocityv

2211 vAvA

Bernoullis Equation

2

2

221

2

112

1

2

1gyvPgyvP

7. If the radius of the larger portion of the pipe is 3 times larger than the radius of the smaller end of the pipe, in

which portion of the pipe is the velocity of an ideal fluid undergoing steady flow higher and how much higher?

Where is the pressure higher?

8. For an ideal fluid undergoing steady flow, in which region of the pipe is the pressure higher? Region 1?

Region 2? Not enough information given to determine?

2

1

Physics Day 4 Waves and Periodic Motion, Sound, and Solids Simple Harmonic Motion

tAx cos or tAx sin A=Amplitude =frequency factor

)cos( tAx = phase shift or phase angle

Av max 2

max Aa

Tf

22

Tf

1 f = frequency T = period

Spring Pendulum

m

k

L

g (for small angles)

1. A spring with a 1kg mass attached obeying simple harmonice motion follows the following equation of

motion: tcmx 5cos)100( . What is the velocity of the mass as it passes through the equilibrium position?

What are the frequency and period of oscillation?

2. A mass on a spring undergoing simple harmonic motion has another mass glued to the original mass while in

motion effectively quadrupling the mass. What is the effect on the period of oscillation?

3. If the length of a pendulum is increased by a factor of 10 and the mass of the bob is doubled, what will be the

effect on the frequency of oscillation?

Springs

kxF k=spring constant x=displacement from equilibrium position

2

2

1.. kxEP

4. If a 50N force displaces a spring 2cm from its equilibrium position, what displacement would a 10N force

result in?

5. A spring with a spring constant of 800N/m and a 2kg mass on the end is stretched 10cm from its equilibrium

position. What is the velocity of the mass on the end of the spring as it passes through the equilibrium position?

Sound

Longitudinal waves, not transverse waves

vf smvsound /343~

Sound generally travels faster in solids than in liquids than in gases.

The speed of sound in solids/liquids is inversely related to its density.

Speed of sound in gases:

Pv P = pressure = density

6. The wavelength of a sound wave in air is 1.70m. What is its frequency? (vsound=340m/s)

7. A ship on the surface of the water uses sonar to detect a submarine that is below it. If the sonar pulse takes 3s

to return to the ship on the surface, what is the depth of the submarine? (vsound=1500m/s in water)

Standing Waves

n

Ln

2 (pipe open at both ends)

n

Ln

4 #oddn (pipe open at one end)

n=1 is first harmonic or fundamental frequency

Beat Frequency difference between two frequencies of two different sound waves

Same as rope with both ends fixed

8. What is the fundamental frequency of a 0.25m pipe that is open at both ends? (vsound=340m/s)

9. After the fundamental frequency, what is the next harmonic of a 0.75m pipe that is open at one end?

(vsound=340m/s)

Intensity

24 r

P

A

PI

0

log10I

I

2

12

0 10m

WI

10. If the intensity level of a siren is 80dB at a distance of 10m from a fire truck, what is the intensity level at a

distance of 100m?

Doppler Effect

S

O

SOvv

vvff

11. You are moving in a car toward a stationery ambulance with a velocity of 32m/s. Is the frequency of the

ambulances siren you observe higher or lower than the actual emitted frequency? By what percentage is the frequency you observe different from the actual frequency?

12. A bat is moving with a velocity of 15m/s toward a moth flying directly toward the bat also with a velocity

of 15m/s. If the bat sends out a sound wave of 20kHz, what is the observed frequency (by the bat) of this sound

wave after its reflected off of the moth?

SO ff if, relatively, object and source are moving towards each other

SO ff if, relatively, object and source are moving away from each other

Elasticity of Solids

Stress = Modulus x Strain

Stretching/Compression

0L

LY

A

F

Shear Deformation

0L

XS

A

F

Volume Deformation

0V

VBP

13. A stretching force of 100N is applied to a 100cm length of wire of radius 1mm resulting in an elongation of

5mm. What is the Youngs modulus of the wire?

14. A solid piece of metal with a bulk modulus of 1.0x1011

is dropped to a depth of 1000m. What is the

fractional change in the volume of this piece of metal?

Stress Modulus Strain

Youngs Modulus Stretching/Compression A

F=

Y

0L

L

Shear Modulus

Shear Deformation A

F=

S

0L

X

Bulk Modulus

Volume Deformation

P = B

0V

V

Physics Day 5-Electricity and Magnetism Electric Forces and Fields

qEF

2

21

r

qqkF k = 9x109 N.m2/C2 Coulombs Law

2r

qkE Electric Field due to a point charge

r

qkV Potential (voltage)

qVPE Potential Energy

1. Two point charges of +2C are 1mm apart. What are the magnitudes of the force and the electric field experienced by either of the point charges? (k=8.99x10

9 N

.m

2/C

2)

2. For the following arrangement of point charges, at what location is the electric field zero?

3. An electron (q=1.6x10-19

C, m=9.11x10-31

kg) is accelerated from rest through a potential difference of

1x10-6

V. What is its final velocity?

Electric Circuits

IRV V = potential I = current R = resistance Ohms Law

Current

t

qI

Resistance

A

LR = resistivity L = length A = cross-sectional area

...21 RRReq Resistors in Series

...111

21

RRReq

Resistors in Parallel

R

VRIVIP

22 Power

+9C -1C

10mm

Charge on an electron

e=1.6x10-19

C

4. A piece of copper wire of resistance R is replaced with a new piece of copper wire that is twice as long and

has a radius that is 3 times larger. What is the resistance of the second piece of wire?

5. If the resistance of 3 resistors hooked up in parallel are each doubled, what is the effect on the equivalent

resistance of the circuit?

6. What is the equivalent resistance in the following circuit?

What is the total current in the circuit?

What is the potential across R1?

What is the current through R4?

What is the power dissipated through R4?

Alternating Current

2

maxVVrms 2

maxII rms

7. The peak voltage in an AC circuit is 280V. What is the rms voltage?

Capacitance

V

QC

Parralel Plate Capacitor

d

AC 0 EdV

d

AC 0 ( dielectric constant)

2

2

1.. CVEP (stored in a capacitor)

...111

21

CCCeq

Capacitors in Series

...21 CCCeq Capacitors in Parallel

8. When a parallel plate capacitor is fully charged in a circuit with a 16V battery, there are 1x1012

excess

electrons on one of the two plates. What is the capacitance of the capacitor. When fully charged how much

energy is stored on this capacitor?

9. The lengths of the sides of each of the plates of a square parallel plate capacitor are doubled and so is the

distance of separation between the two plates. What is the effect on its capacitance?

Magnetism and Electricity

Charged Particle Moving through a Magnetic Field

sinqvBF velocityv B=magnetic field

Current-carrying Wire in a Magnetic Field

sinBIF

Magnetic Field Due to a Current Carrying Wire

r

IB

2

0

Right Hand Rule thumb=v

Fingers=B

Palm=force

Right Hand Rule thumb=I

Fingers=B

Palm=force

Right Hand Rule thumb=I

Fingers (curled)=B

Imax

t

I

CHARGING

Qmax

t

Q

Vmax

t

V

Imax

t

I

DISCHARGING

Qmax

t

Q

Vmax

t

V

10. When the electron in the diagram below enters the magnetic field, it permanently starts moving in a

repeating circular pattern. Give an expression for the radius of the electrons circular motion and state whether the motion is clockwise or counterclockwise.

11. Is the force between the following two wires attractive or repulsive?

What would be the effect of doubling the current in both wires on the force between the two wires?

12. The charged particle in the field below is experiencing a force in the upward direction due to the magnetic

field created by the current in the wire. Which direction does the current in the wire point?

I

I

I?

+e

Physics Day 6 Light and Optics Light

vf

hchfE photon smc /100.3

8 sJh 341063.6

Law of Reflection

Angle of incidence = Angle of reflection

Snells Law of Refraction

2211 sinsin nn

v

cn Index of Refraction (Frequency of light doesnt change from medium to medium)

1

2sinn

ncritical Total Internal Reflection

Dispersion

The index of refraction is different for different wavelengths.

1. If the angle of incidence of a flashlights beam into a lake is 60, what is the angle of reflection? (nair=1, nwater=1.33)

2. Light passes from air (n=1) into a glass block (n=1.5). Is the angle of refraction larger or smaller than the

angle of incidence? What is the speed of light in the glass block?

Electromagnetic Spectrum

Violet

Indigo

Blue

Green

Yellow

Orange

Red

Gamma Rays

X-rays

UV

VIS

IR

Microwaves

Radio Waves E f

Interference

Double Slit Interference

Bright Fringes: md sin m 0, 1, 2, d = distance between slits

Dark Fringes:

2

1sin md m 0, 1, 2, d = distance between slits

Diffraction Grating

Bright Fringes: md sin m 0, 1, 2, d = slit separation

Single Slit Diffraction

Dark Fringes: ma sin ,...2.1,0 m a = slit width

Thin Films

Reflected rays are inverted when going from smaller to larger index of refraction.

filmmt

2

12 m 0, 1, 2, (No phase shift) t = thickness of film

filmmt 2 m 1, 2, (Phase shift between reflected rays)

3. What is the minimum thickness of a layer of gasoline (n=1.40) floating on water (n=1.33) if green light (air = 565nm) is eliminated from the reflected light by destructive interference?

X-Ray Diffraction Diffraction of x-rays by atoms can be used to determine a substances crystal structure

Optics Mirrors and Lenses

fdd io

111 od distance to object id distance to image f focal length

o

i

o

i

h

h

d

dm m magnification ih height of image oh height of object

Rf2

1 R radius of curvature

Lens Strength = f

1 (unit is Diopters; f must be in meters)

Mirror Type di do f

Concave + (do>f)

- (dof)

- (do0 real image (and inverted)

di0 upright

m

4. If an object is placed 6cm in front of a concave mirror (f=2cm), what will be the magnification of the image?

Is it real or virtual, upright or inverted?

5. If an object is placed 6cm from a diverging lens (f=2cm), what is the magnification of the image? Is it real or

virtual, upright or inverted?

6. If an object is placed 6cm from a converging lens (f=4cm), where will the image appear? Will the image be

real or virtual, upright or inverted?