Notes, summaries, assignments, exams, and problems for Physics

1) A wave has the form

When x = 0, the wavelength is

By applying continuity conditions at x = 0, find the amplitude A_x>0 (in terms of A) and phase Φ of the wave in the region x > 0. Use any variable or symbol stated above as necessary.

2) An electron is trapped in an infinite well of width L = 1.87nm. What are the three longest wavelengths permitted for the electron's de Broglie waves?

The wave function must be zero everywhere the potential is infinite. So the wave function is zero outside the well. Since the wave function must be continuous, the wave function inside the well must go to zero at the edges of the well. Thus, only certain discrete wavelengths are allowed.

3) A particle is described by the wave function ψ(x) = b(a² - x²) for

Matthew Arnold's Touchstone Method of Criticism was really a comparative system of criticism.  Arnold was mostly a classicist.  He admired the ancient Greek, Roman and French authors as the models to be followed by the modern English authors.  The old English like Shakespeare, Spenser or Milton were also to be taken as models.  Arnold took selected passages from the modern authors and compared them with selected passages from the ancient authors and thus decided their merits.  This method was called Arnold's Touchstone Method.             However, this system of judgement has its own limitations.  The method of comparing passage with a passage is not a sufficient test for determining the value of a work as a whole.  Arnold... Continue reading "dsf" »

Vocabulary

• Motion: An object’s change in position relative to a reference point.
• Frame of Reference: A system for specifying the precise location of objects in space and time.
• Displacement: The change in position of an object.
• Speed: The distance traveled divided by the time interval during which the motion occurred.
• Velocity: The speed of an object in a particular direction.
• Acceleration: The rate at which velocity changes over time; an object accelerates if its speed, direction, or both change.
• Force: An action exerted on a body in order to change the body’s state of rest or motion; force has magnitude and direction.
• Friction: A force that opposes motion between two surfaces that are in contact.
• Net Force: The combination of all forces acting

LASER = Light Amplification by Stimulated Emission of Radiation

A laser is actually an oscillator rather than a simple amplifier. The difference is that an oscillator has positive feedback in addition to the amplifier.

Light is understood in a general sense: electromagnetic radiation with a wavelength around 1 μm. Thus, one can have infrared, visible, or ultraviolet lasers.

The atomic medium with population inversion used in the laser is called the active medium. The positive optical feedback is obtained by placing the active medium between two mirrors. One of them (M1) totally reflects back the light (R1 = 1) to the active medium, while the other one (M2, called the output coupler) has a reflectivity less than unity (R2 < 1) and allows some... Continue reading "Introduction to LASER Technology: Types, Operation, and Applications" »

The 8 Thresholds of Increasing Complexity

• 1: The Big Bang: The origin of the universe.
• 2: The First Stars: Hydrogen fusion with helium; stars consist of hydrogen and helium, while dying stars create all other elements.
• 3: Creation of Heavy Chemical Elements: The synthesis of complex matter.
• 4: The First Planets: Chemical elements orbiting stars, bound together gravitationally and chemically.
• 5: Life: Complex molecules bound together chemically and physically, developing abilities for metabolism, homeostasis, reproduction, and adaptation.
• 6: Evolution of Homo Sapiens: Collective learning; language and teamwork drive progress.
• 7: Agriculture and the Birth of Civilization: Warmer climates led to the Neolithic Revolution, shifting from hunting and gathering

DEFINITIONS

DISTANCE

How much ground an object has covered/traveled.

DISPLACEMENT

The change in position of an object.

SCALAR QUANTITY

Quantity that only has magnitude and no direction.

VECTOR

Physical quantity that has both magnitude and direction.

CONSTANT SPEED

Speed that does not change.

VELOCITY

Speed in a given direction.

FRAME OF REFERENCE

A background used to judge motion/speed (precise location of an object).

INSTANTANEOUS SPEED

Speed at a given moment.

ENERGY

The capacity/power to do work/move an object by applying force.

MATTER

Anything that has mass and takes up space (how much matter).

WEIGHT

Measure of how gravity pulls matter.

SPEED

Amount of distance traveled in a certain amount of time.

AVERAGE SPEED

Total distance divided by total time.

TIME DISTANCE

Reading Section

1. C  11. B  21. C  31. A  41. D  51. A
2. B  12. C  22. D  32. C  42. ?
3. A  13. A  23. C  33. B  43. C
4. A  14. B  24. A  34. B  44. A
5. C  15. B  25. C  35. D  45. C
6. D  16. C  26. D  36. B  46. A
7. A  17. C  27. D  37. D  47. D
8. A  18. B  28. D  38. C  48. C
9. C  19. C  29. D  39. A  49. D
10. A 20. B  30. D  40. D  50. A

Writing and Language Section

1. D  11. B  21. C  31. C  41. C
2. C  12. A  22. B  32. A  42. ?
3. C  13. D  23. B  33. B  43. ?
4. B  14. A  24. D  34. D  44. ?
5. A  15. B  25. A  35. C
6. D  16. D  26. D  36. B
7. B  17. D  27. B  37. A
8. B  18. A  28. A  38. C
9. A  19. C  29. D  39. C
10. A 20. D  30. D  40. C

Math Sections

Math Section 3

1. C   11. B
2. D   12. A
3. B   13. A
4. D   14. C
5. A

Application of Atomic Structure to Static Electricity

• All material objects are composed of atoms.
• An atom consists of a nucleus and a vast region of space outside the nucleus.
• The nucleus of the atom contains positively charged protons and neutral neutrons.

Charging by Friction

The frictional charging process results in a transfer of electrons between the two objects which are rubbed together.

Triboelectric Series: materiales ordenados según la capacidad de tendencia de atraer electrones.

Electrizar: cargar una sustancia/cuerpo que era neutra.

Charging by Induction

Is a method used to charge an object without actually touching the object to any other charged object.

The Electroscope

An electroscope is a device which is capable of detecting the presence... Continue reading "Static Electricity and Fundamental Electric Principles" »

Understanding Waves and Energy Transfer

A wave is a disturbance that travels a distance, carrying the energy which generated it. When the wave travels through a medium, like water or air, it does not displace the particles of the medium.

Characteristics of a Wave

• Wavelength: This is defined as the distance between two adjacent peaks or troughs of the wave. It is expressed in metres (m).
• Frequency: This is the number of oscillations or complete movements that a wave produces in one second. Its unit in SI is the Hertz (Hz).
• Speed of Propagation: This is the distance, e, that the wave travels divided by the time taken, t. It is expressed in m/s.

  Waves travel at a constant speed. Therefore:

  V_wave = e/t

  Which implies:

  e = V_wave · t

• Amplitude: This is the