SOHCAHTOA

What’s the difference between distance and displacement?

Distance is the total amount an object has traveled.

Displacement is the object’s change in position

• A rock is thrown straight upward from the edge of a 30 m cliff, rising 10 m then falling all the way down to the base of the cliff. Find the rock’s displacement.

• An infant crawls 5 m east, then 3 m north, then 1 m. What is the infant’s DISTANCE and DISPLACEMENT

• An athlete runs exactly once around the track, a total distance of 500 m. Find the runner’s displacement for the race

S = d/t, or V = x/t

• If the infant in the previous example takes 20 seconds to complete his journey, find the magnitude of his average velocity.

• Is it possible to move with constant speed but not constant velocity? Is it possible to mov e with constant velocity but not constant speed?

a = v/t

A car is traveling in a straight line along a highway at a constant speed of 80 miles per hour for 10 seconds. Find its acceleration.

Spotting a police car ahead, a driver of a car slows from 32 m/s to 20 m/s in 2 seconds. Find the car’s average acceleration

tvvx o 21

221 attvx o

atvv o

axvv o 222

• An object with an initial velocity of 4 m/s moves along a straight axis under constant acceleration. Three seconds later, its velocity is 14 m/s. How far did it travel during this time? 27m

• A car that’s initially traveling at 10 m/s accelerates uniformly for 4 seconds at a rate of 2 m/s2 in a straight line. How far does the car travel during this time? 56m

• A rock is dropped off a cliff that’s 80 m high. If it strikes the ground with an impact velocity of 40 m/s, what acceleration did it experience during its descent? 10 m/s2

The area under a velocity vs. time graph equals the displacement.

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Gravity is 10 m/s2

y = ½ at2

• A rock is dropped from an 80 m cliff. How long does it take to reach the ground? 4s

• A baseball is thrown straight upward with an initial speed of 20 m/s. How high will it go? 20m

• One second after being thrown straight down, an object is falling with a speed of 20 m/s. How fast will it be falling 2 seconds later? -40 m/s

• If an object is thrown straight upward with an initial speed of 8 m/s and takes 3 seconds to strike the ground, from what height was the object thrown? 21m

X-motion is INDEPENDENT of Y-motion

• An object is thrown horizontally with an initial speed of 10 m/s. It hits the ground 4 seconds later. How far did it drop in 4 seconds? -80m

• From a height of 100 m, a ball is thrown horizontally with an initial speed of 15 m/s. How far does it travel horizontally in the first 2 seconds? 30m

• A rolling ball falls off a lab desk with a velocity of 2 m/s. The height of the lab desk is 1 m. How far away does the ball land?

• Any push or pull is called a force (N)

- Tension- Gravitational force- Air resistance- Normal force- Frictional force- Electrostatic force- Nuclear forces

Law of Inertia – A body at rest wants to stay at rest or a body in motion wants to stay in motion unless acted upon by an outside force

F = ma

Force is measure in Newtons (kg●m/s2)

For every action, there is an equal but opposite reaction

• What net force is required to maintain a 5000 kg object moving at a constant velocity of magnitude 7500 m/s?

• How much force is required to cause an object of mass 2 kg to have an acceleration of 4 m/s2? 8 N

• An object feels two forces; one of strength 8 N pulling to the left and one of strength 20 N pulling to the right. If the object’s mass is 4 kg, what is its acceleration? 3 m/s2

• A book whose mass is 2 kg rests on a table. Find the magnitude of the force exerted by the table on the book. 20 N

A can of paint with a mass of 6 kg hangs from a rope. If the can is to be pulled up to a rooftop with a constant velocity of 1 m/s , what must the tension in the rope be? 60 N

What force must be exerted to lift a 50 N object with an acceleration of 10 m/s2? 100 N

The force that is perpendicular to the surface

A book whose mass is 2 kg rests on a table. Find the magnitude of the normal force exerted by the table on the book. 20 N

• Parallel to the surface and opposite the direction of the intended motion

1)Static friction – the force that resists movement Fs = μsFN

2)Kinetic friction – the force that acts on a moving objectFk = μkFN

A crate of mass 20 kg is sliding across a wooden floor. The coefficient of kinetic friction between the crate and the floor is 0.3◦ Determine the strength of the friction force acting

on the crate. 60 N◦ If the crate is being pulled by a force of 90 N

(parallel to the floor), find the acceleration of the crate. 1.5 m/s2

• A block slides down a frictionless, inclined plane that makes a 30 degree angle with the horizontal. Find the acceleration of this block. 5 m/s2

• Suppose the same block slides down the same inclined plane with a coefficient of kinetic friction of 0.3. Find the acceleration of the block

• Ac = v2/r• Fc = mv2/r• Anything pointing towards the center of the

circle is positive, anything pointing away is negative

• An object of mass 5 kg moves at a constant speed of 6 m/s in a circular path of radius 2 m. Find the object’s acceleration and the net force responsible for its motion. 18 m/s2 ; 90 N

• An athlete who weighs 800 N is running around a curve at a speed of 5.0 m/s with a radius of 5.0 m. Find the centripetal force acting on him & what provides the centripetal force? 400 N & static friction

• A roller-coaster car enters the circular loop portion of the ride. At the very top of the circle, the speed of the car is 15 m/s, and the acceleration points straight down. If the diameter of the loop is 40 m and the total mass of the car is 1200 kg, find the magnitude of the normal force exerted by the track on the car at this point. 1500 N

• How would the normal force change if the car was at the bottom of the circle? 25,500 N

τ = FrsinθCounterclockwise – Torque is positiveClockwise – Torque is negative

What is the net torque in the following picture? 5.6 N●m

W = Fdcosθ

A crate is moved along a horizontal floor by a worker who’s pulling on it with a rope that makes a 30 degree angle with the horizontal. The tension in the rope is 69 N and the crate slides a distance of 10 m. How much work is done on the crate by the worker? 600 J

• A box slides down an inclined plane with an angle of 37 degrees. The mass of the block is 35 kg, the coefficient of kinetic friction is 0.3, and the length of the ramp is 8 m.

1.How much work is done by gravity? 1690 J2.How much work is done by the normal

force? 0 N3.How much work is done by friction? -671 J4.What is the total work done?

• KE = ½ mv2

• The energy an object possesses due to its motion

• A pool cue striking a stationary billiard ball (m = 0.25 kg) gives the ball a speed of 2 m/s. If the average force of the cue on the ball was 200 N, over what distance does this force act? 0.0025 m

PE = mgh The energy an object possesses due to its

position

A 60 kg stuntwoman scales a 40 m tall rock. What is her gravitational potential energy? If she were to jump off the cliff, what would her final velocity be? 24,000 J; 28 m/s

• Ei = Ef

• KEi + PEi = KEf + Pef

• A ball of mass 2 kg is gently pushed off the edge of a table that is 5 m above the floor. Find the speed of the ball as it strikes the floor. 10 m/s

• A box is projected up a long ramp with an incline of 37 degrees with an initial speed of 10 m/s. If the surface of the ramp is frictionless, how high up the ramp will the box go? What distance along the ramp will it slide?

A skydiver jumps from a hovering helicopter that’s 3000 m above the ground. If air resistance can be ignored, how fast will he be falling when his altitude is 2000 m? 140 m/s

Wile E. Coyote (m = 40 kg) falls off a 50 m high cliff. On the way down, the force of air resistance has an average strength of 100 N. Find the speed with which he crashes into the ground. 27 m/s

• The rate at which work is done• P = W/t or P = Fv

• A mover pushes a large crate (m = 75 kg) from the inside of the truck to the back end (distance of 6 m), exerting a steady push of 300 N. If he moves the crate this distance in 20 s, what is his power output? 90 W

• What must be the power output of an elevator motor that can lift a total mass of 1000 kg and give the elevator a constant speed of 8.0 m/s? 80,000 W or 80 kW

• p = mv• F = ∆p/∆t = ∆mv/∆t• Momentum is also conserved

• A golfer strikes a golf ball of mass 0.05 kg and the time of impact between the golf club and the ball is 1 ms. If the ball acquires a velocity of magnitude 70 m/s, calculate the average force on the ball. 3500 N

• J = F∆t

• An 80 kg stuntman jumps out of a window that’s 45 m above the ground.

1. How fast is he falling when he reaches the ground? 30 m/s

2. He lands on an air bag, coming to rest in 1.5s. What average force does he feel while coming to rest? -1600 N

3. What if he had instead landed on the ground (impact time 10 ms)? -240,000 N

• Elastic Collisions – Kinetic Energy is conserved• Inelastic Collisions – Kinetic Energy is not

conserved.

• Two balls roll toward each other. The red ball has a mass of 0.5 kg and a speed of 4 m/s just before impact. The green ball has a mass of 0.2 kg and a speed of 2 m/s. After the head-on collision, the red ball continues forward with a speed of 2 m/s. Find the speed of the green ball after the collision. Was the collision elastic? 3.0 m/s; no

F = Gm1m2 / r2

G = 6.67 x 10-11 N ● m2 / kg2 Given that the radius of the earth is 6.37 x

106m, determine the mass of the earth. 6.1 x 1024 kg

An artificial satellite of mass m travels at a constant speed in a circular orbit of radius R around the earth (mass M). What is the speed of the satellite? √GM/R

F = -kx The stiffer the spring, the greater the k Force and acceleration are greatest when

displacement is greatest.

A 12 cm long spring has a spring constant of 400 N/m. How much force is required to stretch the spring to a length of 14 cm? 8 N

PEelastic = ½ kx2 PE is maximized when spring is at the

endpoints, KE is minimum PE is 0 when spring is passing through x=0

(equilibrium) and KE is maximum

A 0.05 kg block oscillates on a spring whose force (spring) constant is 500 N/m. The amplitude of the oscillations is 4.0 cm. Calculate the maximum speed of the block. 4 m/s

A 2.0 kg block is attached to an ideal spring with a force constant of 500 N/m. The amplitude is 8.0 cm. Determine the total energy of the oscillator and the speed of the block when it’s 4.0 cm from equilibrium. 1.6 J; 1.1 m/s

T = 1/f T = 2∏√m/k w = 2∏f, 2∏/T, √k/m

A block oscillating on the end of a spring moves from is position of maximum stretch to maximum compression in 0.25 s. Determine the period and frequency. 0.5 s; 2 Hz

A student observing an oscillating block counts 45.5 cycles in one minute. Determine its frequency and period. .758 Hz; 1.32s

A 2.0 kg block is attached to a spring whose spring constant is 300 N/m. Calculate the frequency and period. 1.9 Hz; 0.51 s

A block is attached to a spring and set into oscillatory motion and its frequency is measured. If this block were removed and replaced by a second block with ¼ the mass of the first block, how would the frequency of the oscillations compare? f increases by a factor of 2

KE is maximum at the equilibrium position Frequency nor period depends on the

amplitude for any object in SHM

L

g

T

2

A simple pendulum has a period of 1s on Earth. What would its period be on the moon, where g is 1/6th of the earth’s value?2.4s

p = m/v specific gravity = psubstance / pwater (1000

kg/m3)

A cork has a volume of 4 cm3 and weighs .01 N. What is the specific gravity of the rock? 0.25

P = F/A 1 atm = 101,300 Pa (1.013 x 105 Pa)

A vertical column made of cement has a base area of 0.5 m2. If the height is 2 m, and the sp. Gravity of cement is 3, how much pressure does this column exert on the ground? 6 x 104 Pa

Fg = pvg Pliquid = pgh (depends only on density and

depth) Ptotal = Patm + Pliquid

What is the gauge pressure of a swimming pool at a point 1 m below the surface? 1 x104 Pa

What happens to the gauge pressure if we double the depth below the surface of a liquid? What happens to the total pressure? Gauge pressure increases by a factor of 2; Total pressure increases by less than a factor of 2

A flat piece of wood of area 0.5 m2 is lying at the bottom of a lake. If the depth of the lake is 30 m, what is the force on the wood due to the pressure? 2 x 105 N

The net upward force of an object in a liquid is called the buoyant force.

Archimedes Principle - The strength of the buoyant force is equal to the weight of the fluid displaced by the object.FB = pvg

Vsub = pobject

Vtotal pfluid

If pobject < pfluid , then the object will float

A brick with a specific gravity of 2 and volume of 1.5 x 10-3 m3, is dropped into a swimming pool full of water. Explain why the brick will sink. When the brick is lying on the bottom of the pool, what is the magnitude of the normal force on the brick? Specific gravity is greater than 1; 15 N

A glass sphere of specific gravity 2.5 and volume of 10-3 m3 is completely submerged in a large container of water. What is the apparent weight of the sphere while immersed? 15 N

f = Av A1v1 = A2v2 (flow speed increases when the

pipe narrows or inversely proportional)

A pipe carries water. At one point in the pipe, the radius is 2 cm and the flow speed is 6 m/s. What is the flow rate? What is the flow speed where the pipe’s radius changes to 1 cm? 7.5 x 10-3 m3/s; 24 m/s

If the diameter of the pipe increases from 4 cm to 12 cm, what will happen to the flow speed? 1/9 the flowrate

States that energy is conserved for fluid flowP1 + pgy1 + ½ pv1

2 = P2 + pgy2 + ½ pv2

The pressure is lower where the flow speed is greater (airplanes, hurricanes).

Celsius to Fahrenheit9/5C + 32 = F

Fahrenheit to Celsius(F-32)5/9 = C

Celsius to KelvinC + 273 = K

Q = mc∆T (how much heat is added of removed in the system to change the temperature)

Q = mL (changing phases) Sp. Heat of water = 4186 J/kg ·C

Rate of heat transfer L

TkA

t

Q

TLL o • A brass rod 5 m long and 0.01 m in diameter increases in length by 0.05 m when its temperature is increased by 500°C. A similar brass rod of length 10 m has a diameter of 0.02 m. By how much will this rod’s diameter increase if its temperature is increased by 1000°C? 4 x 10-4 m

An aluminum rod (p = 2.7 x 103 kg/m3 has a radius of 0.01 m and an initial length of 2 m at a temperature of 20°C. Heat is added to raise its temperature to 90°C. Its coefficient of linear expansion is = 25 x 10-6/°C, the specific heat is 900 J/kg°C, and a thermal conductivity of k = 200 J/s m°C.◦ What is the mass of the aluminum rod? 1.7 kg◦ What is the amount of heat added to the rod?

107,100 J◦ What is the new length of the rod? 0.0035 m◦ If we were to use this rod to transfer heat between

two objects one side being at 20°C and the other side at 90°C, what would the rate of heat transfer be? 2.2 J/s

P = F/A (Pa)

Pv = nRT Speed of molecules of a gas

In order for the average speed of the molecules in a given sample of gas to double, what must happen to the temperature? Since v is proportional to square root of T, the temperature must quadruple

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3 M

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A cylindrical container of radius 15 cm and height 30 cm contains 0.6 mole of gas at 433 K. How much force does the confined gas exert on the lid of the container? 35 N

Zeroth Law – Heat flows from the warmer object to the cooler one until they reach thermal equilibrium.

First Law

◦ W = -P∆V Work is positive when work is done ON the system

(volume id decreaseing Work is positive when work is done ON the

surroundings (volume is increasing)

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THE SECOND LAW OF THERMODYNAMICS: THE LAW OF ENTROPY

Heat flows spontaneously from a substance at a higher temperature to a substance at a lower temperature and does not flow spontaneously in the reverse direction.

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Q

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A heat engine draws 800 J of heat from its high temperature source and discards 450 J of exhaust heat into its cold-temperature reservoir. How much work does this engine perform and what is its thermal efficiency? 350 J; 44%

An inventor proposes a design for a heat engine that operates between a heat source at 500°C and a cold reservoir at 25°C with an efficiency of 2/3. What’s your reaction to the inventor’s claim?

4 types of thermal processes

An isobaric process is a process that occurs at constant pressure.

An isochoric process is a process that occurs at constant volume.

An isothermal process is a process that occurs at constant temperature.

An adiabatic process is a process during which no energy is transferred to or from the system as heatat.

Consider two small spheres, one carrying a charge of +1.5nC and the other a charge -2.0 nC, separated by a distance of 1.5 cm. Find the electric force between them. -1.2 x 10-4 N

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It is the surrounding charges that create the electric field at a given point.

The electrostatic force points in the direction of attraction

The electric field always points away from the positive charge and towards the negative charge.

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FE

Electric field does not depend on the sign of the test charge

2r

qkE

A charge q = +3.0 nC is placed at a location at which the electric field strength is 400 N/C. Find the force felt by charge q. 1.2 x 10-6 N

A dipole is formed by two point charges, each of magnitude 4.0 nC, separated by a distance of 6.0 cm. What is the strength of the electric field at a point midway between them? 8.0 x 104 N/C

An object of mass 5g is placed at a distance of 2 cm above a charged plate. If the strength of the electric field is 106 N/C, how much charge would the object need to have in order for the electrical repulsion to balance the gravitational pull? 5 x 10-8 C

Electric Field Lines Never Cross Always perpendicular to the surface and

point AWAY from the positive TOWARD the negative

Conductors permit the flow of excess charge; they conduct electricity well (metals)◦ There can be no electrostatic field within the body

of a conductor. Why? Insulators do not conduct electricity well.

Electrons do not flow well

A solid sphere of copper is given a negative charge. Discuss the electric field inside and outside the sphere.

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A positive charge q1 = 2 + 10-6 C is held stationary, while a negative charge q2 = -1 x 10-8 C, is released from rest at a distance of 10 cm from q1. Find the kinetic energy change of charge q2 when it’s 1 cm from q1. 0.016 J

Let Q = 2 x 10-8 C. What is the potential at a Point P that is 2 cm from Q? 900 V

How much work is done as a charge moves along an equipotential surface? 0

BAo

ABAB r

kq

r

kq

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r

kqV

Capacitors are storage devices for electricity.

q = CV Parallel plate capacitors

d

AC o

A 10 nF parallel plate capactior holds a charge of 50μC on each plate. What is the electric potential difference between the plates? If the plates are separated by a distance of 0.2 mm, what is the area of each plate? 5000 V; 0.23 m2

Amount of voltage the battery produces

I = q/t (Amps, A) The direction of the current is taken to be

the direction that a positive charge would move

Resistors are devices that control current R = V/I (Ohm’s Law) Notice that if the current is large, the

resistance is low. If the current is small, the resistance is high.

Resistivity:A

LR

resistivity in units of ohm·meter

A wire of radius 1mm and length 2 m is made of platinum (resistivity = 1 x 10-7 Ω•m). If a voltage of 9 V is applied between the ends of the wire, what will be the resulting current? 140 A

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Combining Resistors ◦ Series (one after the other):

Add as normal

◦ Parallel (side by side): Add as inverse

Same voltage applied across each device

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1111

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Calculate the equivalent resistance in the circuit

Combining Capacitors ◦ Series (one after the other):

Add as inverse

◦ Parallel (side by side): Add as normal

C = q/V

321 CCCCP

321

1111

CCCCS

Field lines travel away from the North poles and travel toward the South poles.

X X X X X ● ● ● ● ●X X X X X ● ● ● ● ●X X X X X ● ● ● ● ●X X X X X ● ● ● ● ●

(into the page) (out of the page)

The magnetic force always remains perpendicular to the velocity and is directed toward the center of the circular path.

sinvq

FB

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Right Hand Rule #1 (for positive charges)◦ Thumb – Direction particle is traveling◦ Index – Direction of Magnetic Field◦ Middle – Direction of Magnetic Force

If the charge is NEGATIVE, the force is the opposite direction

Page 249

Page 251 sinILBF

Pg 255

r

IB o

2

AmT104 7 o

In the drawing, one cycle is shaded in color.

The amplitude A is the maximum excursion of a particle of the medium fromthe particles undisturbed position.

The wavelength is the horizontal length of one cycle of the wave.

The period is the time required for one complete cycle.

The frequency is related to the period and has units of Hz, or s-1.

Tf

1

Sound travels faster through solids, then liquids, then gases.

f

Tv

Lm

Fv

LONGITUDINAL SOUND WAVES

The area of condensation is the region of compression with increased air pressure

The area of rarefaction is the region behind the condensation with decreased air pressure

c = 3.00 x 108 m/s (speed of light)

Pg 313

Law of Reflection◦ Incident angle is the same as the reflected angle

n = c/v Snell’s Law – relates the angle of

incidence and the angle of refraction

If n2<n1, light bends AWAY from the normal. If n2>n1, light bends TOWARD the normal.

2211 sinsin nn

A beam of light in air is incident upon a piece of glass striking the surface at an angle of 30 degrees. If the index of refraction of the glass is 1.5, what are the angles of reflection and refraction? 60°; 35°

Critical Angle - The angle of incidence at which the angle of refraction is 90°. No light is refracted out and the beam is refracted along the surface.◦ If the angle of incidence is greater than the

critical angle, no beams of light are refracted.

211

2 sin nnn

nc

Page 319

Focal length = R/2

Concave Mirrors1. An incident ray parallel to the axis that is reflected

through the focal point2. An incident ray that passes through the focal point and

reflected parallel3. An incident ray that strikes the vertex is reflected at an

equal angle to the axis Convex Mirrors

1. An incident ray parallel to the axis is reflected away from the focal point

2. An incident ray directed towards the focal point is reflected parallel to the axis

3. An incident ray that strikes the vertex is reflected at an equal angle to the axis

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Page 324

Mirror Equation

Magnification Equation

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i

o

i

d

d

h

hm

Summary of Sign Conventions for Spherical Mirrors

mirror. concave afor is f

mirror.convex afor is f

mirror. theoffront in isobject theif is od

mirror. thebehind isobject theif is od

image). (realmirror theoffront in isobject theif is id

image). (virtualmirror thebehind isobject theif is id

object.upright an for is m

object. invertedan for is m

An object of height 4 cm is placed 30 cm in front of a concave mirror whose focal length is 10 cm.◦ Where’s the image? 15 cm◦ Is it real or virtual? real◦ Is it upright or inverted? inverted◦ What the height? -2cm

An object of height 4 cm is placed in front of a convex mirror whose focal length is -30cm.◦ Where’s the image? – 12 cm◦ Is it real or virtual? virtual◦ Is it upright or inverted? upright◦ What’s the height of the image? 2.4 cm

Converging lenses cause rays of light to converge to a focal point.

Diverging lenses cause rays of light to diverge away from the focal point

Converging Lenses◦ Incident ray parallel to the axis is refracted

through the focal point.◦ Incident rays pass through the center point of the

lens. Diverging Lenses

◦ An incident ray parallel to the axis is reflected away from the focal point

◦ Incident rays pass through the center point of the lens.

Page 330

Page 331

Summary of Sign Conventions for Lenses (page 827)

lens. converging afor is f

lens. diverging afor is f

lens. theofleft the toisobject theif is od

lens. theofright the toisobject theif is od

image). (real lens theofright the toformed imagean for is id

image). (virtual lens theofleft the toformed imagean for is id

image.upright an for is m

image. invertedan for is m

An object of height 11 cm is placed 44 cm in front of a converging lens with a focal length of 24 cm◦ Where’s the image? 53 cm◦ Is it real or virtual? real◦ Is it upright or inverted? inverted◦ What’s the height of the image? -13 cm

An object of height 11 cm is placed 48 cm in front of a diverging lens with a focal length of -24.5 cm.◦ Where’s the image? -16 cm◦ Is it real or virtual? virtual◦ Is it upright or inverted? upright◦ What’s the height of the image? 3.7 cm