Essay questions on light scattering

by Quirino Sugon Jr.

1.  Why is the sky blue?  

The atmosphere around the Earth is largely made up of two colorless gases: oxygen and nitrogen. Red and blue light reacts very different from each other to oxygen. Because the wavelength of blue light is roughly the size of an atom of oxygen, blue light interacts with the oxygen and is scattered by it, while red light, with its longer wavelength, goes right pass the oxygen atoms. If the Earth had no atmosphere, the sun’s light would travel directly from the Sun in a straight line towards our eyes and we would see the Sun as a very bright star in sea of blackness. But because the Sun’s blue light is scattered by the oxygen in the atmosphere, blue light from the Sun enters our eyes from all sorts of different angles and we see the entire sky as blue. The atmosphere scatters violet light even more effectively, but our eyes are more sensitive to blue. Wherever we look towards the sky, some light is bouncing off an oxygen atom and entering our eyes, making the sky appear to be blue. (Skywatch)

2.  Why are sunrises and sunsets red?

Read the same article in Question 1.

3.  Why is the sea blue?

Visible white light is made up of a spectrum of all the colors-red, orange, yellow, green, blue, indigo, and violet. When we look at an object and see it as blue, we are seeing the blue light of the spectrum reflected from the object. All other colors are absorbed and cannot be seen. In the case of the sea, red light is absorbed as soon as it breaks through the water’s surface. And by a depth of about 25 feet virtually all the red light discernible to the human eye is gone; a bright red air tank on a diver, for example, would seem a dull dark brown. At a depth of 75 feet a yellow air tank looks more greenish blue, because the discernable yellow light has been absorbed by the water. The still shorter rays of light are almost all absorbed by 100 feet. All that remains are the shortest rays: blue, indigo, and violet. Below 100 feet or so, all light appears a monochromatic blue. So, when the sea is pure and clear, as often is the case in the open ocean, the least-absorbed shade of the spectrum blue, is reflected to our eyes. (marine-surveyor)

4.  Why is the sea sometimes bluish green or brown or even red?

Read the same reference in Question 3.

5.  How do rainbows form?

Read the Wikipedia article on rainbow.  What causes the dispersion of light?  What must be the angle formed by the sun, the water droplet, and the eye of the beholder? What is the Alexander’s band?  What does Newton have to do with rainbows? Why do you think rainbows formed after the Great Flood of Noah?

Problems for electricity and magnetism

by Quirino Sugon Jr.

1. An electron is under a 2T magnetic field pointing out of the paper and the electron has a speed of one-tenth the speed of light and is initially moving towards the right.  What is the magnitude and direction of the  magnetic force on the electron?  What will be the orbital radius of the electron?  Is it clockwise or counterclockwise?
2. In a Hydrogen atom, what is the ratio between the electric force and the gravitational force on the electron due to the proton?
3. Prove  the rules for equivalent resistance of two resistors connected in series and parallel using Kirchoff’s voltage law.  Hint: resistors in series requires only a single loop; the resistors in parallel requires two loops.
4. Three charges are connected in 30-60-90 degree triangle with the longest side equal to 1 m.  The charge on the right angle is 1 C, the charge on the 60 deg angle is 2 C, and the charge on the 30 deg angle is 3 C.  What is the net electric force on the 2C charge? Hint: use Coulomb’s law.

Essay questions for electricity and magnetism

by Quirino Sugon Jr.

1. Why do auroras or northern lights occur? Hint: magnetic force on charges
2. Why are the wires of plugs tied together? Hint: Ampere’s law.
3. Why is iron attracted to magnets? Hint: magnetic domains.
4. How does a metal detector work? Hint: magnetic induction and eddy currents.
5. How do some birds and fishes know where the North Pole is?
6. Compare and contrast electric and magnetic forces.
7. State Gauss’s Law
8. State Ampere’s Law
9. State Faraday’s Law

Interrelated conceptual questions for electromagnetic induction: How to light a bulb by moving a magnet towards a coil of wire

Choose a word or phrase inside the parenthesis that makes the statement true.  Write your answer on the space provided before each number.

1. Draw a circle on a sheet of paper.  The normal vector to the circular area points (downward, upward),
2. so that the corresponding path direction around the circular area is (clockwise, counterclockwise).
3. Let that circle represent a wire loop.  If you hold a bar magnet vertically above the circle, with the South pole below and the North pole above, then the magnetic field flowing through the circular area points (downward, upward).
4. Since the direction of this magnetic field is (parallel, opposite) to the positive reference sense for the area’s normal vector,
5. then the magnetic field flowing through the circular area is (negative, positive).
6. This means that the flux of the magnetic field through the area, which is the dot product of the magnetic field and the area’s normal vector,  is (negative, positive).
7. If you do not move the magnet, the magnetic flux through the area will (decrease, remain constant, increase) in time,
8. and (a, no) current will be induced in the wire.
9. On the other hand, if you move the magnet upward, the magnitude of the magnetic field flowing through the circular area will (decrease, remain constant, increase) in time,
10. so that the flux of the magnetic field through the area will (decrease, remain constant, increase) in time.
11. Therefore, the change in the magnetic flux per change in time will be (negative, zero, positive).
12. According to (Ampere’s, Faraday’s) law,
13. the electromotive force along the circular wire is (same as, opposite to) the change in the magnetic flux through the circular wire.
14. This electromotive force is equal to the product of the component of the electric field along the circular path and the total length of the path which is the path’s circumference.  By convention, the path length is always (negative, positive ).
15. Thus, by the law stated in (12), the electric field must be (negative, positive) with respect to the circular path,
16. which means that the electric field must be pointing (clockwise, counterclockwise) along the circular path.
17. In the wire the free charges that can move are (electrons, protons).
18. The electric force on the free charges points (clockwise, counterclockwise).
19. By Newton’s (First, Second, Third) Law,
20. the resulting acceleration of the free charges is (clockwise, counterclockwise).
21. Without friction due to collisions with the nuclei in the wire’s molecular structure, the speed of the free charges would be (decreasing, remain constant, increasing) in time.
22. But because of friction, the free charges move at a (decreasing, constant, increasing) speed around the wire.
23. Since current is proportional to the product of the number of free charges, the charge of the free charges, and the drift velocity of the free charges, then the induced current in the wire is (negative, positive).
24. This means that induced current is flowing (clockwise, counterclockwise) around the circular wire.
25. If the wire is connected to a light bulb, the bulb (will, will not) light.
26. The stronger the induced current, the (dimmer, brighter) is the light.
27. One way to make the induced current stronger is to move the magnet (slower, faster).
28.  Now, by (Ampere’s, Faraday’s) law,
29. the induced magnetic field inside the circular loop points (into, out of) the paper,
30. while the induced magnetic field outside the circular loop points (into, out of) the paper.
31. This means that the induced magnetic field has its North pole (below, above) the circular area
32. and its South pole (below, above) the circular area.
33. Thus, since like poles (attract, repel)
34. and unlike poles (attract, repel),
35. then the original magnet and the induced magnet will attract repel.

Answers:

1. Upward.  It doesn’t matter whether you choose upward or downward because it is simply reference direction for electromagnetic quantities, but all your other answers will depend on this choice.
2. Counterclockwise.  If your answer in no. 1 is upward, put your thumb pointing out of the paper and look at the curl of your right hand fingers.  They should curl counterclockwise.  That is the path direction.  But if your answer in no. 1 is downward, then your answer in no. 2 should be clockwise.
3. Upward.  Magnetic field lines flow from the North pole to the South pole.  Since the South pole is directly above the circle in the paper, then the magnetic field lines are going towards the South pole.  This means that the magnetic field flowing through the circular loop is pointing upward.
4. Positive.  The magnetic field lines flowing through the wire loop are pointing upward according to no. 3.  Since the reference direction for the area vector is also upward by no. 1, then the magnetic field is positive with respect to the area vector.
5. Positive.  Since the magnetic field and the area vector are both pointing upward according to nos. 1 and 3, then the angle between them is 0 degrees, so that the dot product of the two vectors is positive.
6. Positive.  Since flux is defined as the dot product of the magnetic field and the area vector, then whatever your answer in no. 5 should be the same as your answer in no. 6.
7. Remain constant.  Since you do not move the magnet, the magnetic field flowing through the area will be constant, so that the flux will be constant.
8. No.  According to Faraday’s law, the electric field (which will drive the current in the wire) will only be induced in the wire if the magnetic flux is changing in time
9. Decrease.  The further you are from the magnetic pole, the lesser becomes the magnetic field strength.
10. Decrease.  If you move the magnet upward, the angle between the magnetic field and the area vector remain the same, then the magnetic flux will still be positive after moving the magnet upwards, but it is a smaller positive flux compared to what was before in no. 6.  Therefore the flux decreases.
11. Negative.  Since the flux decreases by no. 10, then the change in flux is negative.
12. Faraday’s. No. 13 is a statement of Faraday’s law.
13. Opposite.  The negative sign  in Faraday’s law means opposite.
14. Positive.  This is the convention, but you must note that the positive direction for the path is defined by no.2.
15. Positive.  The change in magnetic flux through the circular area is negative by no. 11.  Opposite or negative of no. 11 is  positive.  Since the path is positive by no. 14, then the electric field must be positive.
16.  Counterclockwise.  By no. 2, the positive direction for the path is counterclockwise.  Since the electric field is positive by no. 15, then the electric field must also point counterclockwise in the wire loop.
17. Electrons.  The electrons are free to move in a metal.  The protons are locked in the metal’s crystal lattice bonds.
18. Clockwise.  The electric field is pointing counterclockwise by no. 16.  Since the charge of electrons is negative, then the magnetic force, which is the product of the charge and electric field, must be negative counterclockwise.  That is, clockwise.
19. Second.  No. 20 is a statement of Newton’s second law of motion.
20. Clockwise.  The electric force points clockwise by no. 18.  Therefore, the charges will accelerate in the direction of the force, and that is clockwise.
21. Increasing.  Without friction in the air, a raindrop will fall faster and faster because the gravitational force is pulling them down.  In the same way, charges will move faster and faster due to the continuous pull of the electric force, as long a friction is not present.
22. Constant.  Friction causes the raindrops to fall at constant velocity called terminal velocity.  In the same way, friction causes charges to move along the wire at constant speed called drift speed (or velocity).  The motion of the charges will be clockwise by no. 20.
23. Counterclockwise.  Number of charges is always positive.  Since the charges that are moving are electrons, then their charge is negative.  Since the motion of the charges is clockwise by no. 20, then the product of these three factors–which is the current–is negative clockwise.  That is, counterclockwise.
24. Counterclockwise.  This is just a restatement of no. 23 just to know if you are awake.
25. Light.  If you connect the wire to a light bulb in such a way that a close loop is preserved, then current will flow in the bulb and it will light.
26. Brighter.  The sentence explains itself.
27. Faster.  Moving the magnet faster means making the change in the magnetic field flowing in the wire loop bigger.  If the change in the magnetic field is bigger, then the change in the magnetic flux will also be bigger, resulting to bigger currents induced in the wire.
28. Ampere’s .  Ampere’s law is for the generation of magnetic fields by currents.
29. Into.  By no. 23 or 24, the current is flowing counterclockwise.  Now, put your right hand thumb along the wire in the direction of the current.  Outside the area inside the wire loop, the curl of your right hand fingers point downward (or into the paper); inside the wire loop, the curl of your right hand fingers point upward (out of the paper).
30. Out of.   See explanation in no. 29.
31. Above.  The magnetic dipole representation of the wire loop will depend only on the magnetic field direction inside the area of the loop.  Since the direction of the magnetic field in this area points out of the paper by no. 29, then the North pole must be above the paper and the South pole below.
32. Below.  See explanation in no. 31.
33. Repel.  Like poles repel.
34. Attract.  Unlike poles attract.
35. Attract.  The original magnet has its South Pole directly above the wire loop.  The induced magnet has its North pole directly above the wire loop.  The two poles will attract.  (You can use similar analysis why a magnet will float in a superconductor, but that is another story.)

Essay questions for dynamics: Laws of motion and gravitation

by Quirino Sugon Jr.

I.  Physical Laws.  State the following laws in one sentence.

1. Law of universal gravitation
2. Gauss’s law for gravitation
3. Newton’s first law of motion
4. Newton’s second law of motion
5. Newton’s third law of motion

II.  Application.  Answer the following questions in at most two sentences.

1. Why are there high tides and low tides?
2. If you drill a hole from the North Pole to the South Pole and you drop the stone on the hole, what will happen to the stone?  Describe its motion.
3. If you are in a supermarket and you wish to buy meat, how do you estimate the force constant of the spring in the weighing scale?
4. Are the geostationary satellites not moving?
5.  You are standing on  top of a weighing scale while in an elevator.  If the elevator’s cables snap and the elevator falls freely, what happens to your weight and mass?  Why?
6. How do you measure the mass of the earth?
7. How did Cavendish measure the gravitational constant?
8. What is dark matter and why do scientists believe such matter exist?

Identification questions for dynamics: Laws of motion, gravitation, rotations, and oscillations

by Quirino Sugon Jr.

Read Hewitt, 9th ed., Chapters 2, 3, 5 (Newton’s laws), 9 (Gravity), 10 (Projectile and Satellite Motion), 19 (Vibrations and Waves)

I.  Identification.  Identify the word or phrase described.  Write your answer on the space provided before each number.

1. A state when the net force acting on an object is zero
2. Push or pull
3. Property of things to resist changes in motion
4. Quantity of matter in an object
5. Force of gravity on an object
6. A law relating the intensity of an effect to the inverse square of the distance from the cause
7. a condition encountered in free fall wherein a support force is lacking
8. The influence that a massive body extends into space around itself, producing a force on another massive body.
9. A concentration of mass resulting from gravitational collapse, near which gravity is so intense that not even light can escape.
10. The primordial explosion that is thought to have resulted in the expanding universe
11. The speed that a projectile, space probe, or similar object must reach to escape the gravitational influence of the Earth or celestial body to which it is attracted.
12. Maximum displacement in a sinusoidal motion
13. Number of vibrations per unit time
14. Time for one complete oscillation

II.  Symbols.  Identify the symbol or group of symbols described.  Write your answer on the space provided before each number.

1. Force
2. Net force
3. Component of a force along the x-direction
4. Component of acceleration along the y-direction
5. Amplitude
6. Angular velocity
7. Frequency
8. Period
9. Phase angle
10. Unit for frequency
11. Unit for angular frequency
12. Gravitational constant
13. Unit for force equal to
14. Orbital radius
15. Volume
16. Volume of a sphere
17. Area of a circle
18. Surface area of a sphere
19. Product of the masses
20. Square of the distance
21. Force constant of a spring
22. Opposite

Conceptual questions for dynamics of orbital motion: Gravitational and Coulomb forces

Fig. 1. Orbital motion of mass m around mass M at a radius r

A.  Gravitational Force.  Choose the word or phrase inside the parenthesis that makes the statement true. Write your answer on the space provided before each number.

1. According to Newton’s law of Gravitation, the gravitational force between two objects is directly proportional to the (sum, product) of their masses
2. and inversely proportional to the (distance, square of the distance) between them.
3. Thus, if one of the masses becomes twice that of the other mass, then the gravitational force is (2, 3)  times the force when the masses are the same.
4. On the other hand, if the distance between the masses is halved, the force between the masses is (1/2, 1, 2, 4) times the original force.
5. Now the gravitational force is (attactive, repulsive),
6. so that the force on mass m due to mass M points  (up, down, left, right).
7. This force is (centripetal, centrifugal).
8. By Newton’s (First, Second, Third) Law of Motion, the acceleration of mass m points (away, toward) mass M.
9. This acceleration is proportional to the (speed, square of the speed) of mass m
10. and inversely proportional to the (distance, square of the distance).
11. If the mass m is orbiting in a counterclockwise motion, then at point A, the velocity of mass m is pointing (up, down, left, right).
12. The orbital speed of the mass m is (), where is the mass’s orbital period.

B.  Coulomb Force.  Choose the word or phrase inside the parenthesis that makes the statement true. Write your answer on the space provided before each number.

1. The Coulomb force between two objects is proportional to the (sum, product) of the charges
2. and inversely proportional to the (distance, square of the distance) between them.
3. In a hydrogen atom, the mass M represents the proton with (negative, positive) charge
4. and mass m represents the electron with (negative, positive) charge.
5. Since the magnitude of the charges of the electron and proton are the same, then the force between the electron and the proton is (attractive, zero, repulsive).
6. Thus, when the electron is at point B, the force of the proton on the electron points (up, down, left right),
7. while the force of the electron on the proton points (up, down, left, right),
8. by Newton’s (First, Second, Third) law of motion.
9. If the electron is replaced by a proton, then the force between the two protons is (repulsive, attractive).
10. If the central proton is fixed in space, then an incoming electron would move in a (linear, parabolic, circular, hyperbolic) motion.
11. This is the principle behind (Coulomb’s, Rutherford’s) alpha particle scattering experiment to probe the structure of the atom.
12. On the other hand, the force between the proton and the neutron is (repulsive, zero, attractive).
13. So if the proton is fixed in space, then an incoming neutron would move in a (linear, parabolic, circular, hyperbolic) motion.
14. Inside the nucleus of an heavy atoms are several protons and neutrons.  By Coulomb’s law, the nucleus will (be stable, split).
15. Thus, there must be a nuclear force that is (stronger, weaker) than the Coulomb force in order to keep the nucleus intact.

Conceptual questions for a mass sliding on an inclined plane

by Quirino Sugon Jr.

Fig. 1. Mass on top of an inclined plane

Choose a word or phrase inside the parenthesis that makes the statement true.  Write your answer on the space provided before each number.

1. Gravitational force on an object on the plane is pointing (down, up).
2. By Newton’s (First, Second, Third) Law,
3. the normal force on the object is pointing (parallel, perpendicular) to the inclined plane.
4. If we assume that the object is only moving along the plane and the angle of inclination of the plane is with respect to the horizontal, then the magnitude of the normal force on the object is .
5. Since the only force acting on the object is (parallel, perpendicular) to the inclined plane,
6. then by Newton’s (First, Second, Third)
7. the acceleration of the object is (parallel, perpendicular) to the inclined plane.
8. Specifically, since the net force on the object is (down, up) the plane,
9. then the acceleration of the object is therefore (down, up) the plane.
10. The magnitude of the acceleration is ().
11. One way to check your answer is to make the inclined plane perpendicular to the ground, so that is ().
12. This gives an acceleration of magnitude ().
13. The other way to check your answer is to make the inclined plane parallel to the ground, so that is (.
14. This gives an acceleration of .
15. This means that if the object is initially at rest, then the object will (remain at rest, move with constant velocity, accelerate)
16. by Newton’s (First, Second, Third)  law.

Ps 1: Essay questions on Ancient Greek physics and astronomy

Answer the following questions in not more than two sentences.

1. Name the four 5 elements in Aristotle and relate them to our modern understanding of the states of matter.
2. What are the natural motions of the four elements and relate them to the Aristotelian concept of immovable earth. (Hewitt)
3. How did Aristarchus measure the distance of a moon? (Hewitt)
4. How did Eratosthenes measure the size of the earth? (Hewitt)
5. How did Aristarchus measure the size of the moon? (Hewitt)
6. How did Aristarchus measure the distance of the sun? (Hewitt)
7. Describe the planetary orbits of the Ptolemaic and Copernican models and compare their accuracy.
8. What does Aristotle say about the speeds of the objects in relation to their masses and how did Galileo disprove Aristotle’s theory? (Hewitt)

Ps 1: Conceptual questions for kinematics of circular motion

by Quirino Sugon Jr.

Conceptual Analysis.  Choose a word or phrase in inside the parenthesis that makes the statement true.  Write your answer on the space provided before each number.

1. A particle is rotating on a horizontal plane while being tied to a string to a fixed point.  The particle is rotating counterclockwise.  If the position of the particle is towards the North with respect to the fixed point, then the velocity of the particle is towards the (North, South, East, West)
2. and its acceleration is towards the (North, South, East, West).
3. If the position of the particle is towards the South, then the velocity of the particle is towards the (North, South, East, West)
4. and its acceleration is towards the (North, South, East, West).
5. If the position of the particle is towards the East, then the velocity of the particle is towards the (North, South, East, West)
6. and its acceleration is towards the (North, South, East, West).
7. And if the position of the particle is towards the West, then the velocity of the particle is towards the (North, South, East, West).
8. Assume that the rotating particle is David’s slingshot.  If Goliath is standing towards the North with respect to David, then David must release his sling stone when its position with respect to David is (North, South, East, West).
9. The ratio of the magnitude of velocity and the length of the sling is (half, same as, double, square of) the angular velocity of the string.
10. Thus, the faster the rotation of the slingshot, the (smaller, greater) in magnitude is the angular velocity of the sling stone.
11. Actually, the sling stone also has gravitational acceleration pointing (downward, upward),
12. so the effective radius of the sling is (smaller, same as, bigger) than the length of the sling.
13. The sling would then trace a (circular plane, cone) as the sling stone orbits in space.