calculus-based physics 2 phys 002 (tip reviewer)

7/23/2019 Calculus-Based Physics 2 PHYS 002 (TIP Reviewer)

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Fluids

- is not just something liquid as common notion says

- is any substance that readily flows (free-flowing)

- liquids (water, wine) and gases (steam, smoke, wind)

Fluid Mechanics is the study of fluid's behavior

1. Hydrostatics (fluid statics) - fluid at rest, not moving

*fluid in container.

*the container exerts force against the fluid for it not to move

2. Hydrodynamics (fluid dynamics) - fluid in motion

*viscosity: internal friction of fluids, pagigingmalapot

Distance of molecules are farther in gases..

Gases move faster than liquids (Especially when heated).

Liquids are incompressible fluids, hence, volume can't be changed..

Gases are compressible fluids due to the big spaces in between their molecules, hence, volume can be changed (dry ice).

Liquids versus Gases

Pressure (Pascal's Principle)1.

Buoyancy (Archimedes' Principle)2.

Density3.

Surface Tension4.

Capillarity5.

Specific Gravity / Relative Density6.

Characteristics of Static Fluids (Fluids at rest)

Fluid Dynamics:

1. Rate of Flow; Continuity Principle

2. Bernoulli's Principle

3. Torriceli's Principle

Pressure in a fluid

- force per unit area

- amount of force exerted by the fluid

- the fluid exerts force against the container and the container also exerts force against the fluid- Force exerted by fluid = Force exerted by its container, due to Newton's 3rd Law of Motion

- Gauge Pressure - Pressure at Depth

Units of Pressure

2. Pascal (Pa)

4. Atm (atmosphere)5. Bar

6. Torr7. mmHg (milimeters of Mercury)

Note:

1 atm = 101.3kPa = 14.7 psi = 760 mmHg = 760 torr

Factors affecting the pressure of a fluid

a. External force

i. the forces a fluid exerts on the walls of its containers and vice versa, always acts perpendicular to the walls

ii. an external pressure exerted on a fluid is transmitted uniformly throughout the volume of the fluid*Net external force due to Force (pressure) on the other side will lift the vehice

P - Fluid Mechanics

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Pascal's principle

- pressure applied to an enclosed liquid is transmitted undiminished to every point in the fluid and to the walls of the container

*Kung equal yung force, di aangat yung vehicle. Forces should not be the same because the two points don't have equal surface areas.*For pressure to be equal, the surface area of point B has to be bigger. - Concept of Hydraulic lifts.

*Other examples: Which is more painful being stomped by a big basket ball player wearing sneakers or a small petite lady wearing a sharp

stiletto? Which is more painful: diving sidewards or full frontal dive?

ii. Pressure on a small surface in a liquid is the same regardless of the orientation of the surface*Pressure in not dependenton the shape of the container*Hydrostatic paradox: we expect that the narrow ones will be filled first

Buoyant Force (FB)

- upward force exerted by the fluid on an immersed object.

3 States of Buoyancy:

1. Positive Buoyancy = density of object < density of fluid (lulutang!)

2. Neutral Buoyancy = density of object = density of fluid (partially submerged!)

3. Negative Buoyancy = density of object > density of fluid (lulubog)

1. Laminar Flow - the motion of fluid is very orderly with all particle moving in straight line parallel to the pipe.

2. Turbulent Flow - irregular flow characterized by whirlpool like regions

Laminar Flow Low Velocity RE < 2000 Y > Internal Force

Turbulent Flow High Velocity RE > 4000 Y < Internal Force

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Temperature - property of substance that gives a sensation of hotness and coldness.

Thermodynamics - is the microscopic or large scale approach to the study of thermal properties of matter

involving the transfer of heat energy.

First Law of Thermodynamics - If two objects are each in thermal equilibrium with a third object, then these two

objects are in equilibrium with each other.

Thermal Equilibrium - When the 2 objects have the same temperature.

B. Thermal Expansion - The changes in the dimensions of solid, liquid and gas due to the change in temperature.

- Can be explained based on kinetic molecular theory.

- May occur as linear expansion, surface area expansion and bulk / volume expansion.

- only the length of the object changes due to the change in temperature.

- the length and the thickness, or the length and the width of the object changes due to the change in

temperature

- the length, width and height changed due to the change in temperature

P - Temperature:

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*Van de Graaff generator causes the individual hair on her head to become charged, hence, each strand exerts

repulsive force, resulting in the "stand up" hairdo.

23.1 Properties of Electric Charges

Experiments:

1. Rubbing a balloon on your hair on a dry day.

2. Vigorously rubbing your shoes on a wool rug.

3. Lightly touching (and starting) a friend.

*Works best on a dry day because an excessive amount of moisture in the air can cause any charge you build up to

leak from your body to the Earth)

1. Dichotomy: There are only two categories of Electric Charges.

Glass Rod - Positive

Rubber - Negative

Benjamin Franklin:

"Charges of the same sign repel one another and the charges with opposite signs attract one another."

2. Conservation : Electric charge is always conserved in an isolated system.

- Charge is not created, but transferred.

- One gains some amount of negative charge (becomes negative net charge) while the other gains an equal amoun

positive charge (positive net charge.)

3. Quantization - electric charge always occurs as integer multiples of e ( 1.60 x 10-19 C).

Electrons = -e

Protons = +e

23.2 Charging Objects by Induction

Classification of Materials according to the ability of electrons to move freely

1. Conductors: some electrons are not bound to atoms and can move relatively freely through the material (e.g. gl

rubber and dry wood)

2. Insulators: all electrons are bound to atoms and cannot move freely through the material (e.g copper, aluminum

and silver)

3. Semiconductors: electrical properties are somewhere between those of insulators and conductors (e.g Silicon an

Germanium)

Induction:

1) There is a neutral conducting sphere insulated from the ground, where there are equal number of electrons andprotons.

2.) When negatively charged rod is brought near (not touching), electrons escape through the other side and throu

the ground.

3) When rod is removed, sphere now is positively charge, while the rod loses nothing.

Conduction (Rubbing) in insulators: With the presence of a charged rod, they realign the side to attract the rod.

23.3 Coulomb's Law

Torsion balance by Charles Coulomb

M - Electric Fields

Tuesday, January 27, 2015 10:49 PM

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*Point Charge = charged particle of zero size.

Coulomb's Law

Q

where

k = 8.99 x 109 Nm/C2 = 1 / 40c

0

= 8.85 x 10-12 C2 / Nm

@

where G = 6.674 x 10-11 Nm2 / kg2

Torsion = w ma

23.4 Analysis Model: Particle in a Field (Electric)

*Field Forces - like gravitational force and electrical force, can act through space, producing an effect even when n

physical contact occurs between interacting objects.

Electric Field: is said to exist in the region of space around a charged object, the source charge when another objec(test charge - q

o

) enters this electric field, an electric force acts on it.

*Note that electric fields exist without the test charge and the test charge only serves as a detector.

*If test charge is positive, it goes with the direction of the field. Otherwise, it opposes the field when negative.

*Use superposition principle when dealing with more than one electric fields

Electric Dipole: a positive charge q and a negative charge -q separated by a distance 2a.

23.5 Electric Field of a Continuous Charge Distribution

*Continuous charge distribution: system of closely spaced charges is equivalent to a total charge that is continousl

distributed along some line, over some surface or throughout some volume.

Charge Densities:

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Electric Field Due to a Charged Rod:

P

*If the rod gets closer to P (a --> 0), E -->.

*If the rod gets farther from P (a >> l), l is negligible and the rod will look like a point charge. Hence, formula is sim

to point charge.

Electric field of a Uniform Ring of Charge:

*If P is in the center (x = 0), E = 0.

*If P goes far from the ring (x >> a), the ring will look like a point charge. Hence, formula is similar to a point charg

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23.6 Electric Field Lines

Electric Field Lines: convenient way of visualizing electric field patterns

1. The electric field vectors are tangent to the electric field lines at each point.

2. The number of lines per unit area through a surface perpendicular to the lines is proportional to the magnitude

the electric field in that region.

3. Electric fields are stronger when field lines are closer together.

4. Because the lines at different locations point in different directions, the field is nonuniform.

5. Electric field lines do not represent the part of a charged particlemoving in an electric field, but only represents

field at various locations.

6. Electric field lines are not real material objects but only a pictorial representation to provide a qualitative

description of the electrical field.

Rules for drawing electric field lines

1. The lines must begin on a positive charge and terminate on a negative charge.

2. The number of lines drawn leaving a positive charge or approaching a negative charge is proportional to the

magnitude of the charge.

3. No two field lines can cross.

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23.7 Motion of a Charged Particle in a Uniform Electric Field

*a

x

= 0 if electric field is vertical

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*Topic is a link of electromagnetism to energy.

*Potential energy is a conservative force (e.g gravitational force and electric force exerted by a spring).

*Conservative means that the path does not matter.

*Work done in an internal system is negative of the change in potential energy (U).

M

Potential Energy (U) = a scalar energy of the charge field system that is relative to the configuration of

that is defined as U = 0.

*Similar to electrostatic force but with d only.

*ds is the displacement vector, where d is the magnitude and vector s is the direction.

Electric Potential or Potential (V) - a scalar physical quantity that depends only on the source charge

distribution and has a value at every point in an electric field.

Potential Difference (

V) = change in electric potential energy of the system when charge q is moved

between two points a and b divided by the charge.

L

Units:

M - Electric Potential

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*The electric field is a measure of the rate of change of the electric potential with respect to position.

25.2 Potential Difference in a Uniform Electric Field

*Electric field lines always point in the direction of decreasing electric potential.

*If q is positive, U then is negative!

*A system consisting of a negative charge and an electric field gains electric potential energy when the

charge moves in the direction of the field.p

*All points in a plane perpendicular to a uniform electric field are at the same electric potential.

25.3 Electric Potential and Potential Energy due to Point Charges

*Electrostatic force, electric field, voltage difference

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25.4 Obtaining the Value of the Electric Field from the Electric Potential

*This result shows that the equipotential surfaces must always be perpendicular to the electric field lines

passing through them.

*Electric field is like the negative slope!

*The electric field points in the direction of decreasing electric potential.

Electric Potential due to a Uniformly Charged Ring:

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Electric Potential (V) =

Electric Potential due to a Uniformly Charged Disk

Electric Potential due line charge

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Electric Dipole:

25.6 Electric Potential due to a Charged Conductor:

*When a solid conductor in equilibrium carries a net charge, the charge resides on the conductor's outer

surface.

*The electric field just outside the conductor is perpendicular to the surface and the field inside is zero.

*The electric potential is constant inside the conductor and is equal to the potential at the surface.

*A charged conductor surface = equipotential surface!

* a cavity surrounded by conducting walls is a field-free region as long as no charges are inside the cavity.

*Corona Discharge - the observed glow often observed near a conductor such as a high-voltage power

line.

25.7 The Millikan Oil-Drop Experiment

*This experiment proved that charges are indeed quantized.

25.8 Applications

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25.8 Applications

1. Van de Graaf

2. Electrostatic Precipatators

1. E

2. D

3. C4. C

5. A,B,C=D

6. A, C

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Answers: I) Negative, II ) Positive

Answer: 4000 V / m

M - Electric Potential Problems

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26. 1 Definition of Capacitance:

Capacitors: devices that store charge, which is composed of two conductor plates with same magnitude

but different signs

Capacitance (C) - positive ratio of the magnitude of the charge on either conductors to the magnitude of

the potential difference between the conductors

26.2 Calculating Capacitance

*Capacitance of an isolated, single capacitor with radius a:

*Capacitance of a parallel plate capacitor with Areas A and distance d from each other:

*Capacitance of a cylindrical shaped capacitor:

*l is the height of the cylinder

*a is the radius of the smaller cylinder

*b is the radius of the bigger cylinder

Capacitance of a spherical shaped capacitor:

M - Capacitance and Dielectrics

Monday, February 16, 2015 12:24 AM

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*a is the radius of the smaller cylinder

*b is the radius of the bigger cylinder

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27.1 Electric Current:

Current (I) = the rate which charge flows through a cross sectional surface.

* n is number of charges per volume electrons / m3

* vd is drift speed m / s

* q is charge C

* A is cross sectional area m2

*Displacement = vdt

*Force and drift velocity have the same direction.

*Current is conventionally assigned to the flow of protons / positive charge and

opposite the flow of electrons.

*Force and drift velocity have the same direction.

* Avogadro's Number of Atoms (NA = 6.02 x 1023 / mol )

27.2 Resistance

F - Current Resistance

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*resistivity ohm meters

Resistor Codes:

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Kirchoff's Rules - follows the laws of conservation of energy and electric for isolated systems.

Circuits in Steady State = currents in the circuit are constant in magnitude and direction.

Direct Current = a current that is constant in direction.

Alternating Current = current changes direction periodically

28.1 Electromotive Force

*Battery = source of electromotive force (source of emf)

*The emf of a battery is the maximum possible voltage the battery can provide between its terminals. It is

equivalent to the open-circuit voltage (terminal voltage when current is zero)

*Internal Resistance = the resistance of real battery

*Load Resistance = the resistance outside the battery

*An Ideal battery has zero internal resistance.

*Terminal voltage (VAB) is the emf lessened by internal resistance = - IR

*It should be as low as possible. (a)

*Power delivered by the battery is equal to the sum of power delivered by both its load and internal

resistance. Or Emf * Current.

*Maximum power is achieved when load resistance R = internal resistance r.

28.2 Series and Parallel

Series Parallel

I

total

= I1 = I2 = I3 Itotal = I1 = I2 = I3

V

total

= V1 = V2 = V3 Vtotal = V1 = V2 = V3

R

total

= R1 + R2 + R3 Rtotal = [(1 /R1) + (1/R2)+ (1/R3)]-1

*In series, Rtotal is always higher than the individual resistances.*In series, if one device in the series fails (or creates an open circuit), all the devices are inoperative.

*In parallel, the Rtotal is always less than the smallest resistance in the group.

F - Direct-Current Circuits (Chapter 28)

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28.3 Kirchoff's Rules

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F - Potential DifferenceTuesday, March 03, 2015 9:20 AM

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Introduction

*Magnetite (Fe

3

O

4

) - attracts pieces of iron

*Every magnet, regardless of shape has two poles: north and south, which exerts force on one another.

*Same poles repel while different poles attract.

*A single magnetic pole cannot be isolated, because magnetic poles exist in pairs.

29.1 Analysis Model: Particle in a Field (Magnetic)

*The region of space surrounding any moving electric charge also contains a magnetic field.

*Geographic North Pole is magnetic south pole while Geographic South Pole is magnetic north pole.

Observations:

1. The magnetic force is proportional to the charge q, speed v and magnetic field vector B of the particle.

2. The magnetic force on a negative charge is directed opposite to the force on a positive charge moving

in the same direction.

3. If the velocity vector makes an angle with the magnetic field, the magnitude of the magnetic force is

proportional to sin .

4. When a charged particle moves parallel to the magnetic field vector, the magnetic force on the charge

is zero.

5. When a charged particle moves in a direction not parallel, the magnetic force acts in a direction

perpendicular to both v and B.

is the smaller angle between v and b.

Fb is zero when v is parallel or anti parallel to b.

and maximum when v is perpendicular to b.

F - Magnetic Fields (Chapter 29)

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3.

4. Specific Gravity:

Reviewer (Prelim - Fluid Mechanics:)

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Reviewer (Prelim - Temperature and Heat)

calculus-based physics 2 phys 002 (tip reviewer)

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