Physics 2424 List of Assignments

Assignment #1 - Relativistic Kinematics

In your solution, indicate which measurements below to which frame. Indicate any proper times and proper lengths. Add an explanation to any calculation you do. Sketches are good! Q1-  Tipler 1.26 Q2 - Tipler 1.27  Q3 - Tipler 1.40 Q4. - An observer in a rocket moves toward a mirror at speed v = 0.65c relative to a stationary frame S, see figure below.  The mirror is stationary in S. A light pulse emitted by the rocket travels to the mirror and is reflected back to the rocket. The rocket is a distance d =  5  c·months, as measured in S, from the mirror when the light pulse is emitted. What is the total travel time of the pulse as measured by observers in (a) the S frame and (b) the front of the rocket?. Q5. - Two spaceships are nose to nose at t = t' = 0. Spaceship S is 100 m long as measured by it's pilot. At t = 9.75 ×10-7 s, the pilot of S detects that the tail of spaceship S' is at the tail of his ship S. S' is travelling at 0.65c with respect to S. (a) What is the length of  S' as measure in frame S? (b) What is the length of S' as measured by it's pilot? (c) At what time t' does S' measure when the spaceships are tail to tail? Q6. - Two spaceships are nose to nose in the x direction but vertically separated by 80 m at t = t' = 0. Spaceship S is 100 m long as measured by it's pilot. Spaceship S' is 125 m as measured by it's pilot and travelling at 0.75c. The pilot of S' simultaneously turns on beacon lights at the nose and tail of his ship at t' = 0. At what times would the pilot of S first see the beacon lights (remember light takes time to travel distances)? What times would the pilot of S deduce that the lights were fist turned on?




Assignment #3 - Paradoxes and Relativistic Dynamics

1. To derive the Law of Reflection, Huyghen's Construction is used. The diagrams below show how this works. A series of plane waves (i.e. they have a flat wavefront) of light approach a surface. Point A on the leading wavefront is absorbed and re-emitted by the surface. A little later, the part of the wavefront at B is absorbed and re-emitted by the surface. Finally point C of the wavefront arrives and is re-emitted. The total wavefront is found by drawing the line that is tangent to the circle that describes the reflected light at A (see figure b). This forms a right triangle. Note that the radius of that circle is exactly the same as the distance that point C travels more than A. A small amount of geometry should convince you that the direction of the reflected wave is 2θwith respect to the incident wave.
a) Confirm the Law of Reflection, i.e. that β = 2θ in figure c below.
b) If the surface was moving up with speed v, point C reaches the surface sooner. Find an expression for the reflected angle in this case. Hint what whould figure c look like?


(a)                                                          (b)

(c)

2. A 45° right prism is used to redirect starlight to a hole in the side of a box that holds the prism (see diagram (a) below). The whole appartaus is then sent hurtling toward the star so that γ = 2. An observer on earth says the prism is length contracted so that the reflected light misses the hole (see diagram b). An observer in the frame of the prism says nonsense, I would see no change so it does go through hole. Show that a proper analysis of the problem will lead to the light still passing through the hole. The results of Q4 will be helpful.



Tipler Chapter 1 - 55

Tipler Chapter 2 - 21, 23, 41, 49,and 53(a). Change! 53(b) just find an expression for the speed of M if E = 4mc². New! 53(c) Find expressions for the speeds of the decay particles in part (a) in the frame of a person with velocity opposite to the value found in  53(b). Recall u/c = pc/E.

Note for 2-21. Threshold kinetic energy is most easily defined in the zero-momentum frame (ZMF). The ZMF is the frame where the total intial momenum is zero. Consequently the created particles will also have zero momentum. The Threshold Energy is the KE just big enough to create the extra mass with no energy going into movement. You can always use a Lorentz Transform to find the threshold KE value in the lab frame.


Assignment #4 - Review 

Read Chapter 3 and 4
Tipler	Chapter 3 - 2, 48
The sun is 150 × 109 m from the earth. Assume that the sun is a blackbody (a) The peak in the sun's blackbody energy distribution is at 502 nm. What is the surface temperature of the sun? (a) The flux (or power radiated per unit area) of sunlight at the earth is 1.34 × 103 W/m2. Determine the total power emitted by the sun. The surface area of a sphere is 4πr2. (b) Calculate the radius of the sun. This is how the radius of nearby stars is calculated.
If you stand naked in a room, your skin and the walls of the room will exchange heat by radiation. Suppose the temperature of your skin is 33° C, the surface area of your skin is 1.5 m2, and the temperature of the walls is 15° C. Assume that your body and the walls act as blackbodies. (a) What is the rate at which your body radiates heat? (b) What is the rate at which your skin absorbs heat? (c) What is the net rate of your loss of heat? (d) How many Oh Henry! bars (1338 kJ per bar) would you have to eat in a day to survive?
How far away can you see a 100-W light bulb at night? Assume that the light emitted has a wavelength of 550 nm and the threshold for your eye to detect light is 25 photons per second passing through your pupil. The diameter of a dark-adapted pupil is about 8 mm.
A photon of initial wavelength 0.0400 nm suffers two successive collisions with two electrons. The deflection in the first collision is 90° and in the second collision is 60°. What is the is the final wavelength of the photon?
Tipler	Chapter 4 - 28
Use the Bohr model to predict the wavelengths of the Balmer series lines of the Hydrogen atom that falls in the visible region (400 nm to 700 nm). If a cloud of interstellar hydrogen is moving away from the Earth at 0.3c what wavelengths will be seen for the Balmer lines?

            Assignment #5 - Schrodinger's Equation I.

1. For the following potentials and energy levels, sketch the corresponding y(x). Be sure to explain all the features!
a.

b.


2. For the following graphs of y(x). Indicate the energy level n. Sketch the corresponding potential well. Be sure to explain all the features!
a.

b.

  

Assignment #7 - Barriers and Atoms (New!)

1.	A beam of electrons encounters the barrier below. Calculate the coefficient of transmission T (see eqn 6-75). Hint break the barrier up into simple steps, then T = T1 × T2 × T3 …. Take a = 0.150 nm and V = 1.0 eV.
2.	A 2-D simple harmonic oscillator has a potential .            (a) Show that the wavefunction is separable, i.e. that y(x,y) = y1(x)y2(y) solves the Schrodinger Equation into two independent parts.            (b) Obtain an expression for the energy.            (c) What is the groundstate wavefunction? Make sure it is correctly normalized.            (d) Find the selection rule for transitions.
3.	Find the peaks in the R30 hydrogen radial wavefunction. Evaluate <r>, <r2>, and Dr.
4.	Tipler 7-33.
5.	Tipler 7-65
6.	Tipler 7-68

Questions?mike.coombes@kpu.ca