Physics
141, Midterm Exam #2
Tuesday November
17, 2009
8.00 am –
9.30 am
Do not turn the
pages of the exam until you are instructed to do so.
Exam rules: You may
use only a writing instrument while
taking this test. You may not consult any calculators, computers,
books, nor each other.
1. Answer the multiple-choice questions (problems 1 – 10) by marking your answer on the scantron form. For each multiple-choice question (problems 1 – 10), select only one answer. Questions with more than one answer selected will be considered incorrect. If your student ID is not listed properly on the Scantron form (in the bubbles on the top-left corner), the form will not be processed and you loose points for all multiple-choice questions.
2. Problems 11, 12, and 13 must be answered in the blue exam booklets (answer questions 11 and 12 in booklet 1 and question 13 in booklet 2.) The answers need to be well motivated and expressed in terms of the variables used in the problem. You will receive partial credit where appropriate, but only when we can read your solution. Answers that are not motivated will not receive any credit, even if correct.
At the end of the exam, you need
to hand in your exam, the blue exam booklets, and the scantron form. All items must be clearly labeled with
your name, your student ID number, and the day/time of your recitation. If any of these items are missing, we
will not grade your exam, and you will receive a score of 0 points.
Name: __________________________________________________
ID number:
______________________________________________
Recitation Day/Time: ______________________________________
Useful Relations:
The
typical energy level spacing of a set of states is 10 -2 eV. What type of states are we dealing
with?
1. Hadronic states.
2. Nuclear states.
3. Electronic states in atoms.
4. Vibrational states in molecules.
5. Rotational states in molecules.
Problem 2 (2.5 points)
Some of the properties of diatomic molecules NO and HCl can be described in terms of a simple model in which the two atoms are connected by a spring. Experiments show that the spacing between allowed vibrational energy levels in NO is 0.23 eV and the spacing between levels in HCl is 0.35 eV. The NO and HCl molecules have nearly the same mass. Which molecule has the greater bond stiffness (spring constant)?
1. NO.
2. HCl.
3. They have approximately the same bond stiffness.
Problem 3 (2.5 points)
You are given two carts, A and B. They look identical, and you are told that they are made of the same material. You place A at rest on an air track and give B a constant velocity directed to the right so that it collides elastically with A. After the collision, both carts move to the right, the velocity of B being smaller than what it was before the collision. What do you conclude?
1. Cart A is hollow.
2. The two carts are identical.
3. Cart B is hollow.
4. Need more information.
Problem 4 (2.5 points)
Two people on roller blades throw a ball back and forth. After a couple of throws they are
1. standing where they were initially.
2. standing further away from each other.
3. moving away from each other.
4. moving towards each other.
Problem 5 (2.5 points)
In the Rutherford experiment, what was surprising to the experimenters?
1. Sometimes the alpha particles passed right through the gold foil without being deflected.
2. Sometimes the alpha particles were deflected slightly when they passed through the gold foil.
3. Sometimes the alpha particles bounced back from the gold foil.
Problem
6 (2.5 points)
Consider the following level scheme of an atom
used in a laser. Which of the
three transitions shown in the level scheme defines the wavelength of the laser
light?
1. Transition 1.
2. Transition 2.
3. Transition 3.
Problem 7 (2.5 points)
A string is wrapped around a disk of mass M and radius R. Starting from rest, you pull the string with a constant force F along a nearly frictionless surface. At the instant when the center of the disk has moved a distance d, a length L has unwound of the disk. At this instant what is the speed of the center of mass of the disk?
1. 
2. 
3. 
4. 
5. 
Problem 8 (2.5 points)
The graph below shows a portion of a graph of various energies as function of time for a mass on a spring, subject to air resistance. Which curves in the graph represents which types of energy?
1. A = total energy, B = kinetic energy, C = potential energy.
2. A = total energy, C = kinetic energy, B = potential energy.
3. B = total energy, C = kinetic energy, A = potential energy.
4. B = total energy, A = kinetic energy, C = potential energy.
5. C = total energy, A = kinetic energy, B = potential energy.
6. C = total energy, B = kinetic energy, A = potential energy.
Problem 9 (2.5 points)
In positron-emission tomography (PET), used in medical research and diagnosis, compounds containing unstable nuclei that emit positrons are introduced into the brain, destined for a site of interest in the brain. When a positron is emitted, it travels only a short distance before nearly coming to rest. The positron forms a bound state with an electron, called positronium, which is rather similar to a hydrogen atom. The binding energy of positronium is very small compared to the rest energy of an electron. After a short time the positron and the electron annihilate. In the annihilation, the positron and the electron disappear, and all their rest energy goes into two massless photons. What is the energy of the photons that are emitted when positronium decays? The mass of the electron or the positron is 511.0 keV/c2.
1. 1022.0 keV.
2. 766.5 keV.
3. 511.0 keV.
4. 255.5 keV.
Problem
10 (2.5
points)
How many times did the Yankees win the world series?
1. 4
2. 25
3. 27
4. 45
Problem 11 (25 points) Answer in Exam Booklet 1
A massless box,
containing two blocks of mass M
connected with a spring with spring constant k, is pulled upward by a constant force F (see Figure). When
the force F is first applied, the
blocks are at rest. As a result of
the applied force, the top of the box moves a distance d during a time interval dt. Using your X-ray vision you determine
that while the top block moves up by a distance d, the bottom block only moves a distance b (b < d). Assume the spring has zero rest length.
a. What is the work done by the applied force
during this time interval?
b. What is the work done by the gravitational
force during this time interval?
c. What is the work done by the spring force
during this time interval?
d. What is the change in the kinetic energy of
the center mass of the system after the box has moved up by a distance d?
e. What is the vibrational kinetic energy of the
two blocks after the box has moved up by a distance d?
Express your answers in terms of the variables provided.
Problem 12 (25 points) Answer in Exam Booklet 1
Consider the collision of a truck of mass M and a car of mass m at an icy intersection, as shown in the Figure below.
The initial velocity of the truck and the care are v1 and v2, respectively. After the collision, the truck and the car stick together.
a. What is the angle q that specifies the direction in which the truck-car system moves after the collision?
b. What is the velocity v3 of the truck-car system after the collision?
c. How much kinetic energy is lost in the collision?
Express all your answers in terms of the variables provided.
Problem
13 (25 points) Answer in Exam Booklet 2
A material consisting of a collection of microscopic systems is kept at a high temperature. A photon detector, capable of detecting photon energies from infrared through ultraviolet, observes photons emitted with energies of 0.3 eV, 0.5 eV, 0.8 eV, 2.0 eV, 2.5 eV, and 2.8 eV. These are the only photon energies observed.
a. Draw and label a possible energy-level
diagram of a microscopic system that is consistent with the observed emission
pattern. On the diagram, indicate
the transitions corresponding to the emitted photons.
b. Would a spring-mass model be a good model for
these microscopic systems? Why or
why not?
c. The material is now cooled down to a very low
temperature, and the photon detector stops detecting photon emission. Next, a beam of light with a continuous
range of energies from infrared through ultraviolet shines on the material, and
the photon detector observes the beam of light after it passes through the
material. What photon energies in
this beam are significantly reduced in intensity? Explain.
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