Download Examples of questions asked on previous CORE`s. Caveat emptor

Examples of questions asked on previous CORE’s. Caveat emptor!
Mechanics
1. Given an Atwood’s machine with Ml > M2. Assume there is no friction. Derive algebraic
expressions for the magnitudes of the acceleration and the tension of the system.
2. Circular Motion. What keeps a satellite of the earth from “falling down”?
3. If a particular simple pendulum having a period T0 on earth were to be taken to a planet with the
same mass as the earth, but having a radius twice the earth’s, what would the period of the
pendulum be in terms of T0?
4.
Are all forces in nature conservative? Explain. Give examples of conservative and
non-conservative forces.
5. Oscillatory Motion
(a) Use Hooke’s Law with Newton’s Second Law to get a differential equation for the
mass/spring system, and discuss the nature of the motion. Derive a formula for the period
of the harmonic oscillator in terms of the spring constant k and the mass M.
(b) Compare the mechanical oscillator system with the LC (inductance/capacitance) oscillator
Derive a formula for the period of an LC circuit.
(c) What can you say about the quantum mechanical harmonic oscillator?
(d) Discuss resonance for any one of the above systems.
6. Discuss the motion of a simple pendulum of length L and mass M.
(a) Draw a free body diagram.
(b) Find the equation of motion.
(c) Derive the period of motion for small oscillations.
7. State Newton’s three laws of motion.
8. State Kepler’s three laws of planetary motion.
9. Tell how the Principle of Conservation of Energy is involved in various branches of physics.
Explain how energy conservation relates to the following: Work-Energy Theorem;
Conservation of Mechanical Energy; First Law of Thermodynamics; Kirchhoff’s Loop Rule;
Lenz’s Law; Einstein’s Mass/Energy Equation. Can you think of other examples?
10. Explain what is meant by “resonant frequency.” Give some examples from mechanics and
electricity.
11. What are the conditions for mechanical equilibrium?
12. A cylinder with radius Rand mass M is rolling along the floor without slipping. The speed of
the center of the cylinder with respect to the floor is “v”. Determine the kinetic energy of the
cylinder in terms of M, R, and v.
13. What is moment of inertia? Show how to calculate the moment of inertia of a solid cylinder of
mass M and radius R.
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14. A boy sits on the top of a frictionless
hemisphere of ice. He starts to slip. At what
angle will he leave the block of ice?
15. Consider a car going around a horizontal (un-banked) curve. Draw a free-body diagram of the
car showing all forces acting on it. What force is the centripetal force in this case? Is the
friction force static or kinetic friction? Discuss the case of a car going around a banked curve.
16. Give an example of a physical quantity that is a scalar (dot) product of two quantities that are
vector quantities. Give an example of a physical quantity which s the vector (cross) product of
two physical quantities which are vector quantities.
17. A ball is thrown at an angle. What can you say about its velocity at its highest point? Does this
depend on air resistance?
18. Consider a thin metal hoop rolling down an inclined plane without slipping
(a)
(b)
(c)
(d)
Find the equation of motion.
Show all forces acting on the hoop and on the plane.
Is there a frictional force? Does it do work?
Is energy conserved in this problem?
19. What is meant by the torque on a body? What is center of mass? What is center of gravity?
20. You are running around a circular track.
(a) What force causes you to move in a circle? What is the physical origin of that force?
(b) Why is it necessary for you to lean toward the center of the circle?
21. A mass is connected to two massless, horizontal rubber bands each of length L and each under
tension T. The mass is displaced a small vertical distance y. Assume the tension in the rubber
bands remains constant. Show that the mass will execute simple harmonic motion. Determine
the period of the motion.
22. Discuss the motion of a beer can floating on the surface of a lake after being vertically
displaced and then released.
23. Given two vectors in component form. Calculate the angle between them. Calculate their cross
product.
24. Define simple harmonic motion. Give an example of a system that moves in SHM. Write down
Newton’s laws for this system. Write down energy conservation for this system. Write down
the period of oscillation. What is the relation between period, frequency, and angular
frequency?
25. A particle of mass M is projected up an inclined plane (inclination ) with a speed v0 to a height
h above the starting point, where it comes to rest. If the coefficient at kinetic friction between
the particle and the surface of the inclined plane is , what is the work done by friction?
26. What is the “small angle approximation?” How small is “small?”
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27. What is phase velocity? What is group velocity?
28. Consider a barrel, height H, radius R, floating in water. The buoyant force is defined as the
density of water times the volume of the barrel under water, times the gravitational field
strength g.
(a) When the barrel is in equilibrium, what fraction will be under the water?
(b) If I push the barrel down slightly it will oscillate. Is this SHM? If so determine the
frequency.
29. What is the difference between a particle and a wave? Write down the expression for a wave
traveling in one dimension. Define the important quantities that describe a wave. What
determines the power carried by the wave? What determines the speed of the wave? Its
wavelength? Its frequency? What determines the speed of a particle in the wave?
30. When two waves come together, what can happen? Describe what is needed for: constructive
interference, beats, standing waves.
31. What are the Conservation Laws in Physics? Under what conditions are the laws true?
32. A rod of mass m1 is on a horizontal, icy surface (no friction) and is pivoted at one end. It
initially rotates clockwise with an angular speed . A small blob of putty,
of mass m2 is moving horizontally with an initial speed v0. The putty
collides and sticks to the rod. What is the final angular velocity of the rod
plus putty? Clearly explain your steps.
33. As in question 32, but now the putty is replaced with a perfectly elastic
ball.
34. As in question 32, but no there is no pivot. The putty still sticks to the rod.
35. As in question 32, but now there is no pivot, and the putty is replaced with a perfectly elastic
ball.
Electricity and Magnetism
1. State the Lorentz Force Law.
2. Discuss the Hall Effect and show how it can be used to determine the sign of the (majority)
charge carriers in a conductor. What other useful information can be determined using the Hall
Effect?
3. Given a charged particle, with mass M and charge q, which moves with a velocity v in a uniform
magnetic field B. Discuss the trajectory of the particle for each of the following cases.
(a) v is perpendicular to B
(b) v is parallel to B
(c) v has components which are both perpendicular and parallel to B
4. What is the magnetic field around along a long straight wire? (Use Ampere’s Law.)
5. Given two very long parallel wires with currents I1 = 20 A
and I2 = 5 A. The wires are separated by a distance of 6
P
I1
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meters.
(a)
(b)
(c)
(d)
Sketch and label the magnetic field contribution B1 at the point P due to I1.
Sketch and label the magnetic field contribution B2 at the point P due to I2.
Sketch and label the net magnetic field B at the point P
At what point along the x-axis is the net magnetic field equal to zero?
6. What atomic properly of iron is responsible for the magnetic field of a bar magnet?
7. In the diagram, the current I in the long wire at the top is
steady.
I
(a) Consider a point “a “ inside the rectangular wire loop.
a
What is the direction of the magnetic field at this point?
(b) On what physical quantities does the magnetic field in
the vicinity of a long, straight wire depend? What are the units of magnetic field?
(c) How would you calculate the magnetic flux through the loop?
(d) Suppose the current in the wire at the top decreases at a constant rate. What is the direction
of the induced current in the wire loop during the time the current in the long wire is
decreasing? Calculate the emf in the wire loop?
(e) Suppose I is constant but the loop moves. What is the direction of the induced current if the
loop moves parallel to the long wire (to the right), and if it moves radially away from the
long wire? (down)
8. Given a dipole on the y-axis. +Q is at y = a and -Q is at y = -a.
(a)
(b)
(c)
(d)
(e)
(f)
9.
Sketch the field lines and equipotential lines for a dipole charge distribution.
Construct an algebraic expression for the electric field on the y-axis for y > a.
Construct an algebraic expression for the potential on the y-axis for y > a.
Show that the electric field can be obtained from the potential function.
Is it possible for the potential to be zero and the electric field to be non-zero? (Where?)
Is it possible for the potential to non-zero and the electric field to be zero? (Where?)
Use Gauss’ Law to determine the magnitude of the field of a point charge.
10. Given an infinite sheet of charge with charge per unit area  Use Gauss’ Law to determine
the electric field at an arbitrary distance from the sheet of charge.
11. Given a parallel plate capacitor with charge Q, plate area A, and distance D between the plates.
(Hint: Use result from preceding question.)
(a) Determine the field between the plates.
(b) Determine the capacitance of the system.
(c) Sketch the field lines and equipotentials of the charged capacitor
12. Sketch the magnetic field lines of the earth. What do we mean when we say that the magnetic
field in Rochester is about “half of a Gauss.” Illustrate with a diagram.
13. Derive an expression for the radius of curvature of a charged particle (charge q, mass M) that
moves with velocity v perpendicular to a uniform magnetic field B at a given instant.
14. What is the physical interpretation of Gauss’ Law? Use Gauss’ Law to calculate the electric
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field at a distance r from a charge q.
15. Consider two long coaxial cylinders at length L with a uniformly distributed charge of +Q on
the inside cylinder and a uniformly distributed charge of -Q on the outside cylinder The radius
of the inner cylinder is r1 and the radius of the outer cylinder is r2.
(a) What is the electric field for r < r1?
(b) What is the electric field for r1 < r < r2?
(c) What is the electric field for r> r2?
(d) What is the capacitance of the system?
16. Why does a lightning rod work?
17. Given the following circuit. Let V1 be the potential
difference across R1 with the switch open. Let Vf
be the potential difference across R1 with the
switch closed. Determine which of the following
is true:
(a) V1 > Vf (b) V1 < Vf (c) V1 = Vf
18. Sketch the magnetic field lines of an ordinary iron bar magnet. What is the source of those field
lines?
19. If light is thought of as propagating E and B fields, how is the intensity of the light related to
this concept?
20. List Maxwell’s equations and tell what all the symbols mean.
21. What are the units of q, E, V, I, R, C, B, ? Be able to check units in an equation such as
=qvB
F
22. Consider a very long straight insulating rod of radius R. It is uniformly charged with a linear
charge density . Find the electric field a distance r from the rod for r > R and r < R.
23. A C-shaped rectangular armature has a height L. A thin wire of resistance R and mass m
completes the rectangle, and can move without friction on the armature. The wire is pulled to
the right at a constant velocity, magnitude v, and a uniform and constant magnetic field B points
into the paper.
(a) What do the words uniform and constant mean?
(b) What is the current induced in the circuit, and in what direction does it flow?
(c) What force (size and direction) must be applied to the wire to keep it moving at constant
velocity. Show that the units work out.
24. A long straight wire carries a constant current I from right to left. Find the magnetic field at a
distance r, outside the wire.
25. An electron is shot with an initial velocity v pointing horizontally to the right on paper.
(a) It enters a region where there is a uniform electric field E pointing down on the paper.
Describe the subsequent motion of the electron and tell how you would find the position of
the electron after some time t.
(b) No electric field, but now there is a uniform and constant magnetic field B pointing into the
paper. Describe the subsequent motion of the electron, being as specific as possible.
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(c) Finally both the electric and magnetic fields are acting. Is it possible for the electron to
move in a straight line, and if so, under what conditions?
26. A circuit with a battery, switch, resistor, and capacitor. Derive the voltage across the resistor as
a function of time.
27. A circuit with a battery and 4 identical light bulbs arranged as shown. Initially the switch S is
closed.
A
S
B
(a) Rank the bulbs in order of brightness.
(b) Now the switch is opened, Rank again.
(c) When the switch is opened, does bulb B get
brighter or dimmer? Repeat for each of the
other bulbs.
Thermo
C
D
1. Given an “ideal” gas.
(a) What are the characteristics of an “ideal” gas?
(b) From memory, what is the equation of state for an ideal gas?
(c) From memory, how is the temperature concept defined according to the kinetic theory of
gases?
(d) How would you write the total internal energy for an ideal gas in terms of the usual
thermodynamic variables?
2. What are the usual thermodynamic variables for a system?
3. State the First Law of Thermodynamics. Define each variable.
4. Given an “ideal” gas.
(a) Illustrate graphically the work done in compressing the gas isothermally from volume Vl to
volume V2.
(b) Show how you would calculate this work.
(c) If the work done on the system is -100 Joules, what is the heat absorbed?
5. (a) Illustrate how to conceptually perform a reversible, isothermal expansion with an ideal gas.
(b) Illustrate how to conceptually perform a reversible, isothermal compression of an ideal gas.
(c) How would you sketch the graph of the P-V curve for an isothermal process such as (a) or
(b)?
6. (a) Illustrate how to conceptually perform a reversible, adiabatic expansion with an ideal gas.
(b) Illustrate how to conceptually perform a reversible, adiabatic compression of an ideal gas.
(c) How would you sketch the graph of the P-V curve for an adiabatic process such as (a) or
(b)?
7. Discuss the P-V diagram of a heat engine operating in a Carnot cycle.
8. What is the work done in a thermodynamic process during a complete cycle?
9. Discuss the P-V diagram of a heat engine operating in a Carnot Cycle. State which equation
corresponds to each individuaI process of the cycle.
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10. State the 2nd Law of Thermodynamics. What do you mean by energy? Consider a cup of
coffee that is cooling. Is the entropy of the cup increasing or decreasing?
11. (a) Describe different mechanisms for heat transfer. Give examples where each is important.
(b) Consider conduction of heat through a solid wall made of one material. What factors
determine the rate of heat conduction? Write an equation for heat conduction. What are the
units of heat conductivity?
(c) Suppose a wall is made of two different materials, thickness L1 with conductivity k1, and
thickness L2 with conductivity k2. Temperatures on the left and right of the compound wall
are T0 and T2. Find the temperature T1 at the boundary between the two materials, and find
an expression for the heat transfer in terms of L1, L2, k1, k2, area A, T0 and T2.
12. Estimate the size of an aluminum atom given the density of 2.7 g/cm^3, atomic number 13, and
atomic mass number 27.
13. Consider an ideal gas in a cylinder.
(a) Sketch a PV diagram and show the following processes on the diagram: isothermal,
isobaric, isovolumic, adiabatic. What is the work done in isobaric and isovolumic
processes?
(b) Sketch a cycle on the PV graph for a heat engine. What is the work done in one cycle in
terms of the graph? Define the efficiency of the engine.
14. State the First Law of Thermodynamics (this is the Conservation of energy equation) and
define the terms.
15. How would we calculate heat transfer as a substance undergoes a change in temperature at a
constant pressure?
16. Define entropy. What is a reversible process and what happens to entropy in this type of
process? What is an irreversible process and what happens to entropy in this type of process?
Modern
1. (a) Describe an experiment that shows light acts like a wave. Discuss what happens as
wavelength changes.
(b) Describe an experiment that shows that light acts like a particle. What happens as
wavelength changes.
(c) Discuss the contradiction between (a) and (b) and explain the resolution of this
contradiction.
2. A muon is created in the upper atmosphere from the decay of a pion. It subsequently decays
producing an electron. The muon has a lifetime of about 2 microseconds. Suppose the muon is
created with a speed of v = 0.80 c in the laboratory frame of reference.
(a) How far would the muon go classically before it decays?
(b) How far would the muon go relativistically before it decays?
(c) Which distance is correct, (a) or (b)? Can you think of some actual naturally occurring
phenomena to prove your answer?
3. (a) How would you calculate the number of electrons per gram of a given material ? Use copper
(Z = 29 atomic mass Ma = 63.5) as an example.
(b) How does this number vary from material to material ?
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4. (a) Derive the Bohr model equation for the energy levels of the Hydrogen atom.
(b) What are the successes of the Bohr model?
(c) How is the Bohr model incorrect and what is the full theory?
5. In what way(s) does electromagnetic radiation interact with matter?
6. Discuss the photoelectric effect. What is a work function?
7. Discuss the Compton effect.
8. Sketch an energy level diagram for hydrogen and indicate the meaning of the following:
Balmer, Lyman, and Paschen Series; ionization energy (can you give its value?).
9. The ground state electron energy of the hydrogen atom is -13.6 eV. Calculate the energy levels
for atomic hydrogen. Sketch an energy level diagram for hydrogen.
10. The ground state electron energy of the hydrogen atom is -13.6 eV. Given the constants “h’
and “c’, show how to calculate the wavelengths of the Balmer emission spectra. Illustrate the
transitions which correspond to the four visible wavelengths. Do you remember their colors?
11. What is a “wave function” for a particle? How are its wavelength and frequency determined?
What is the Schroedinger equation?
12. What do we mean by the phrase “particle in a box.” Can you give an example of a ‘finite”
box? Can you give an example of an “infinite” box?
13. What experimental evidence is there that light behaves like a particle? Describe the experiment
and explain what is measured and how that shows the particle nature.
Optics
1. Write the mathematical condition for total internal reflection. Give a few examples of this
phenomenon. Why does a diamond “sparkle” more than a piece of glass?
2.
Young’s Experiment (a) Derive the “maxima” conditions for double slit interference. Let d be
the distance between slits,  be the wavelength, L be the distance from the slits to the screen,
and  denote the angular position of the interference maximum. (b) Find the “minima”
conditions. (c) Sketch the pattern seen on the screen. (d) What happens to the patterns if the
value of d is doubled? If wavelength is doubled? If the distance to the screen is doubled? If the
width of each slit is doubled?
3. Explain how a thin film antireflection coating works. Derive the appropriate equation.
4. What is a dispersive medium? Give an example.
5. (a) State the range of visible wavelengths in either nanometers or Angstroms.
(b) Calculate the corresponding range of visible frequencies.
(c) Give a typical wavelength for red, blue, and yellow light.
6. Light of wavelength 500 nm goes from air into glass with index 1.50. Calculate (a) the speed of
light, (b) the wavelength of light, and (c) the frequency of the light in the glass.
7. What is total internal reflection? Show how to calculate the critical angle between glass (n
=1.5) and air.
8. Tell me something about the nature of light ...
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9. What experimental evidence is there that light behaves like a wave? Describe the experiment
and derive the result.
10. You shine laser light of wavelength  through a pair of slits of width a, height h and separation
d. Sketch the pattern seen on a screen located a large distance D from the slits. What happens to the
pattern on the screen under the following changes (always compare to the first set-up.)
(a) Double the wavelength
(b) double the width
(c) double the separation
(d) double the distance to the screen
(e) Double the number of slits, keeping dimensions and spacing the same
(f) Reduce the number of slits to 1.
(g) I use a single wavelength obtained by using a color filter over a light bulb and pass it
through two slits. I do not get the pattern seen when I use laser light. Why?
11. What is a typical wavelength of visible light? Arrange the following in order of increasing
wavelength: blue light, gamma rays, microwaves, radio waves, red light, X-rays
12. What are the laws of reflection and refraction? What information does an index of refraction
give you?
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