Review of Physics 201 - PowerPoint Presentation

Slide1

Review of Physics 201Slide2

Free Falling Objects

A free falling object is one that moves under the influence of gravity. The term

free fall includes objects that are initially at rest OR have initial upward/downward velocity. Acceleration due to gravity, g, is approximately 9.8 m/s2.

The motion of an object tossed up and allowed to fall. Slide3

Projectile Motion

Projectile motion

occurs when an object is given an initial velocity and then follows a path determined entirely by the effect of gravity. There is no horizontal acceleration and . The trajectory as functions of time is given by:

A projectile moves in a vertical plan that contains the initial velocity vector, v

0

.

Its trajectory depends only on v

0

and on the acceleration due to gravitySlide4

Free body diagrams

To help identify relevant forces, draw a

free-body diagram. Be careful to include all the forces acting on the object, but be equally careful not to include any forces that the object exerts on any other object.A free-body diagram of a man dragging a crate. The diagram shows all the forces acting on the man, and only forces acting on the man.Slide5

Contact forces and Friction

The

contact force between two objects can always be represented in terms of normal component n perpendicular to the surface of interaction and a friction component f parallel to the surface. When sliding occurs, the kinetic-friction force fk is often approximately proportional to n. Then the proportionality constant is μk, the coefficient of kinetic friction: fk= μkn. When there is no relative motion, the maximum possible friction force is approximately proportional to the normal force, and the proportionality constant is μs, the coefficient of static friction, with the equation The actual static-friction force may be anything from zero to the maximum value given by the equation, depending on the situation.  Slide6

Newton’s Law of Gravitation & Weight

Newton’s Law of Gravitation

Two particles with masses m1 and m2, a distance r apart, attract each other gravitationally with forces of magnitude:These forces form an action-reaction pair. If the objects cannot be treated as particles but are spherically symmetric, this law is still valid; then r is the distance between their centers.WeightThe weight w of a body is the total gravitational force exerted on it by all other bodies in the universe. Near the surface of the earth, an object’s weight is very nearly equal to the gravitational force exerted by the earth alone.Newton’s Law of GravitationWeightSlide7

Satellite motion

When a satellite moves in a circular orbit, the centripetal acceleration is provided by the gravitational attraction of the astronomical body it orbits. If the satellite orbits the earth in an orbit of radius

r, its speed v and period T are: Slide8

Conservation of energy

When only conservative forces act on an object, the total mechanical energy is constant; that is,

Where U may include both gravitational and elastic potential energies. IF some of the forces are nonconservative, we label their work as Wother. The change in total energy of an object, during any motion, is equal to the work Wother done by the nonconservative forces. Nonconservative forces include friction, which usually acts to decrease the total mechanical energy of a system. Slide9

Collisions

Collisions can be classified according to energy relationships and final velocities. In an

elastic collision between two objects, kinetic energy is conserved and the initial and final relative velocities have the same magnitude. In an inelastic two-object collision, the final kinetic energy is less than the initial kinetic energy; if the two objects have the same final velocity (they stick together), the collision is completely inelastic.Elastic:K conservedInelastic:Some K lostCompletely inelastic:Objects have same  Slide10

Impulse and Center of Mass

Impulse

The impulse of a constant force acting over a time interval Δt is the vector quantity (Δt)The change in momentum of a particle during any time interval equals the total force acting on the particleCenter of massCenter of mass (xcm, ycm) is given by:

Impulse

Center of massSlide11

Rotation about a moving axis

When a rigid body undergoes both motion of its center of mass and rotation about an axis through the center of mass, the total kinetic energy is given by:

For the special case of rolling motion, such as a rolling bicycle wheel, , where R is the radius of the wheel. Slide12

Torque and Angular Momentum

When a force

acts on a body, the torque τ of that force is given by . Using the convention that a torque causing counterclockwise rotation is a positive torque.The angular momentum L, with respect to an axis through O of a particle with mass m and velocity v is L=mvl. When a rigid body with moment of inertia I rotates with angular velocity ω about a stationary axis, the angular momentum with respect to that axis is L=Iω. The basic dynamic relationship is given by:If a system consists of bodies that interact with each other but not with anything else, or the total external torque is zero, then the total angular momentum is conserved:Slide13

Stress, strain, and elastic deformation

Forces that tend to stretch, squeeze, or twist an object constitute

stress. The resulting deformation is called strain. For small deformations, Hooke’s law states that stress and strain may be directly proportional: stress/strain = constantTensile and compressive stresses stretch and compress an object, respectively.Slide14

Superposition

The principle of

superposition states that when two waves overlap, the resulting displacement at any point is obtained by vector addition of the displacements that would be caused by the two individual waves. When a sinusoidal wave is reflected at a stationary or free end, the original and reflected waves combine to make a standing wave. At the nodes of a standing wave, the displacement is always zero; the antinodes are the points of maximum displacement.Slide15

Density and Archimedes' Principle

Density

Density is mass per unit volume. If a mass m of material has volume V, its density is . Specific Gravity is the ratio of material density to the density of water.Archimedes’ principle: buoyancyArchimedes’ principle states that when an object is immersed in a fluid, the fluid exerts an upward buoyant force on the object equal in magnitude to the weight of the fluid the object displaces. DensityArchimedes’ principle: buoyancyArchimedes’ principle states that when an object is immersed in a fluid, the fluid exerts an upward buoyant force on the object equal in magnitude to the weight of the fluid the object displaces. Because the fluid is in equilibrium, the vector sum of the vertical forces on the volume element must be zero: p2A-p1A-w=0The forces on the fluid element due to pressure must sum to a buoyancy force equal in magnitude to the element’s weight.Slide16

Thermal Expansion

The change

ΔL in any linear dimension L0 of a solid object with a temperature change ΔT is approximately:Where α is the coefficient of linear expansion. The net change in ΔV in the volume V0 of any solid or liquid material with a temperature change ΔT is approximately:

Where

β

is the

coefficient of volume expansion.

 Slide17

Heat and Phase changes

Heat is energy transferred from one object to another as a result of temperature difference. The quantity of heat

Q required to raise the temperature of a mass m of a material by a small amount ΔT isWhere c is the specific heat of the material.To change a mass m of a material to a different phase at the same temperature requires the addition or subtraction of a quantity of heat Q given byWhere L is the latent heat of fusion, latent heat of vaporization, or heat of sublimation. Slide18

Molar heat capacity

Molar mass

Specific heat capacity

Specific heat capacity (previous chapter)

 c=specific heat capacity [J/

kg.K

] (

)

Molar heat capacity (novel fundamental level)

Related to specific heat capacity c (small letter) by comparison with;

Change in translational kinetic energy

Energy gas (mono-atomic)

Diatomic:



A diatomic molecule can move in three ways: translation, rotation, and vibration. At lower temperature; only translation and rotation degrees are active and not vibration

Poly-atomic:

more degrees of freedom

Heat capacitiesSlide19

Work done during volume changes

s

The work W done is equal

to the area under the

PV curve

Thermodynamic system

= exchanges heat with environment

Thermodynamics is the study of

Energy,

and

(sign convection)

Work done during volume changes

When gas expands, it pushes on the boundary surfaces and does positive work.

Assume p is constant;

But usually it is not constant;

 Slide20

Work done in a cyclic process

15.39

note: For a constant volume process: W=0 For a constant pressure process: W=p.ΔV1 atm = 1.013x105

Pa, 1Liter=10-3

m3

The work done is positive when the volume increases and negative when the volume decreases.

Find

W

for each process in the cycle;

1

2:

23:

since

34:

41:

since

The area enclosed by the cycle (energy) is;

 Slide21

Thermodynamic processes

4 processes:

No heat transfer = Adiabatic Constant volume = isochoric Constant pressure = isobaric Constant temperature = isothermalIsothermal:

Adiabatic:

 Q=0

Expanding system

W>0,

Δ

U<0

Compressing

system

W<0

,

Δ

U>0

Increasing internal energy is often happen with increasing temperature

T

Example: combustion engine;

isochoric

 constant volume

All the energy added as heat increases energy

U

Example: heating a gas in a closed volume contains;

isobaric

 constant

pressure

All three quantities

Δ

U

1

,

W

1

, and

Q

change.

Constant pressure

isobaric



constant temperature: none of the

quantities

Δ

U

1

,

W

1

, and

Q

is zero.

Note that in some special case the internal energy

U

depends only on

T



,

(Example 15.9)

 Slide22

Fundamental laws of thermodynamics

Zeroth Law

Two systems that are each in thermal equilibrium with a third system are in thermal equilibrium with each other.First LawIf Q is added and W is done then the U will change by: ΔU = Q-WSecond LawEngine statementIt is impossible for any heat engine to undergo a cyclic process in which it absorbs heat from a reservoir at a single temperature and converts the heat completely into mechanical workSlide23

pV

- diagrams of engines

Otto or gasoline engineDiesel engineCarnot engineThe Carnot cycle operates between two heat reservoirs at temperatures Th and Tc and uses only reversible processes. Its thermal efficiency isNo engine operating between the same two temperatures can be more efficient than a Carnot engine.Otto or gasoline engineDiesel engineCarnot engineSlide24

Entropy and Disorder

Entropy provides a quantitative measure of disorder

Consider an infinitesimal isothermal expansion of an ideal gas, in that process we add heat Q, such that the temperature remains constant. Then all Q is converted to W.

The gas is in a more disorder state after the expansion since the molecules move in a larger volume and have more random mass in position.

Special most simple case

In a reversible isothermal process the entropy change

unit [

]

 Slide25

Nature Favors Decrease in Order – Increase in Entropy

The cream spontaneously mixes with the coffee, never the opposite.

© 2016 Pearson Education, Inc.Slide26

If you mix cold milk with hot coffee in an insulated Styrofoam cup, which of the following things happen?

(There may be more than one correct

answer)The entropy of the milk increasesThe entropy of the coffee decreases by the same amount that the entropy of the milk increased.The net entropy of the coffee-milk mixture does not change, because no heat was added to the system.The entropy of the coffee-milk mixture increases.Clicker - QuestionsSlide27

Entropy and the Coffee

Creamer

does disperse in coffee, never the opposite.Rooms become dirty.A house of cards naturally will fall.A pressurized gas will spontaneously expand.© 2016 Pearson Education, Inc.Slide28

An insulated box has a barrier that confines a gas to only one side of the box. The barrier springs a leak, allowing the gas to flow and occupy both sides of the box. Which statement best describes the entropy of this system?

The entropy is greater in the first state, with all the gas on one side of the box.

The entropy is greater in the second state, with all the gas on both sides of the box.The entropy is same in both states, since no heat was added to the gas and its temperature did not change.Clicker - QuestionsSlide29

© 2016 Pearson Education, Inc.

Free expansion=Irreversible process

Isothermal expansion=reversible processQ=0, W=0, U=0 in spite of this as we can see that entropy increases in a) and b)  Entropy change depends only on initial and final state. Since both processes have the same endpoints =same

Example 16.7Slide30

E

xample 16.4: Entropy change in melting ice

Compute the change in entropy of 1kg ice at 0oC when it is melted and converted to water at 0oC.

 Slide31

To access course evaluations:

Beginning December 7th at 8:00 A.M., visit the evaluation web site (

http://evaluation.tamu.edu/) and sign in with the Central Authentication System (CAS). You will be presented with a list of your PHYS/ASTR courses. Select PHYS 201 and complete your evaluation. You will receive an email in your TAMU Mail account on or before December 7th. The email will include direct links to each enrolled course. Click on a link to complete an evaluation for that course. The links in the email do not require you to sign-in.OR