1.
(50%) WeBWorK set # 4.
2.
(25%) The Stanford Linear Accelerator Center (SLAC), located
at Stanford University in Palo Alto, California, accelerates electrons
through a vacuum tube, 3-km long.
Electrons,
which are initially at rest, are subjected to a continuous force of
2 x 10-12 N along the entire 3-km length of the tube and
reach speeds very close to the speed of light. Using
the material discussed in Chapter 5,
a.
Calculate the final energy, momentum, and speed of the electron.
b.
Calculate the time required to go the 3-km distance.
3.
(25%) A particle with mass M and charge +e and its antiparticle (same mass M, charge -e) are initially at rest, far away from each other. The attract each other and move toward
each other.
a.
Make a graph of the dependence of the various energies that are involved
in this process (the potential energy, the particle energies - including
the rest energy -, and the total energy) as function of distance.
b.
When the particle and antiparticle collide, they annihilate and produce
a different particle with rest mass m (which
is much smaller than M)
and charge +e and its antiparticle (same rest mass m, charge -e). When these particles
have moved far away from each other, how fast are they going? Is this speed large or small compared
to the speed of light?
c.
Now take the specific case of a proton and antiproton colliding to
form a positive and negative pion. Each
pion has a rest mass of 2.5 x 10-28 kg. When
the pions have moved far away, how fast are they going?
4.
(Optional; 25% extra credit)
Write a program in VPython to determine the final speed of each electron,
and the time required to cover the length of the tube of the accelerator at SLAC (see Problem 2). You
can use the VPython program classicalMotion.py from the Physics
141 software area as a starting point. However,
since the electrons will move with velocities very close to the speed
of light, you can no longer assume that v = p/m and you have to make
sure you use the relativistically correct equations to simulate the
motion. Submit the actual programs or a link to your public area of glowscript and your answers to the questions in pdf format via email to Professor Wolfs (wolfs@pas.rochester.edu). The name of the file should be hw04p04XXYYYYYYYY.txt and hw04p04XXYYYYYYYY.pdf, where XX are your initials and YYYYYYYY is your student id number and the subject of your email should start with hw04p04XXYYYYYYYY.
5. (Optional; 25%
extra credit) Create a computer model of a metal bar of length L by considering N atoms of mass m connected
by interatomic springs in a straight line. You can use the VPython program modelMetalBar as a starting point. Give the first atom a sudden push and compare the motions of al the
atoms, one time step after another. Calculate all of the forces before using these forces to update the
momenta and positions of the atoms. After each time step, display the displacements of all the atoms away
from their equilibrium positions, and determine the speed of sound (the
distance between the first and last atom of the bar divided by the time it
takes for the last atom to feel a non-zero force). Compare your results with the prediction
that the speed of sound is
where D is L/N and k is the spring constant. How does the agreement change when you
change the number of atoms in your model?
Submit the actual programs or a link to your public area of glowscript and your answers to the questions in pdf format via email to Professor Wolfs (wolfs@pas.rochester.edu). The name of the file should be hw04p05XXYYYYYYYY.txt and hw04p05XXYYYYYYYY.pdf, where XX are your initials and YYYYYYYY is your student id number and the subject of your email should start with hw04p05XXYYYYYYYY.
