Problems
Here are the assigned problems.
The problem solving handout gives
specific instructions on how to solve these problems (as well
as others you may encounter in other coruses or later in life).
Dr. Jeff's solutions can be found by clicking on the document
icons. (Remember, these are not necessarily the only solutions;
other assumptions and model may produce in different results.
Of course, not all models and assumptions are equally valid. Your
solution must match the given information and general physical
behavior of the world.)
Due September 11 (Solution  )
After seeing how
pieces of tape with like charges repel each other, you get an
idea to use the same physical effect to levitate a small sphere.
Maybe magic is not only done with smoke & mirrors, maybe electric
charges are also used! You wonder if you can use four spheres,
each with a mass of 10g and a radius of 0.5cm to levitate an identical
fifth sphere. Your intention is to use the four as a “base”
with the levitating sphere playing the role of the pyramid’s
peak. After all five are charged, the four “base” spheres are attached to a support board at the corners of a 10cm
square. To maintain the proportions of the Great Pyramid, the
levitating sphere should be about 6cm above the base. Is this
trick feasible?
Due October 6 (Solution )
You’re interested in figuring out more about the internal
structure of the sun. (Something you were contemplating while
hanging out at the beach recently.) In particular, you’d
like to figure out what is the sun’s temperature. You’ve
heard that in the sun the main reaction is where two deuteron
particles collide to produce an isotope of helium. A deuteron
particle is a proton and a neutron (which has nearly the same
mass as a proton, but zero charge). Clearly, two like charged
deuteron particles will be repelled by each other, making it difficult
for them to fuse; fortunately, they only need to approach each
other within 5 x 10-15m to actually fuse together.
You flip back through your text to learn more about temperature
and how it relates to a particle’s energy. You find that
for an ideal gas, the particle’s kinetic energy is equal
to 3/2 kBT, where kB is the Boltzman constant
(1.38 x 10-23 J/ K) and T is the temperature in Kelvin
(K). With a little bit more browsing in your text you find that
the sun’s radius is approximately 7 x 108m and
the mass is 2 x 1030kg.
You have a great summer
job in a research laboratory with a group investigating the possibility
of producing power from fusion. The device being designed confines
a hot gas of positively charged ions, called plasma, in a very
long cylinder with a radius of 2.0 cm. The charge density of the
plasma in the cylinder is 6.0 x 10-5 C/m3.
Positively charged tritium ions are to be injected into the plasma
perpendicular to the axis of the cylinder in a direction toward
the center of the cylinder. Your job is to determine the speed
that a tritium ion should have when it enters the plasma cylinder
so that its velocity is zero when it reaches the axis of the cylinder.
Tritium is an isotope of hydrogen with one proton and two neutrons.
Due October
25
(Solution )
1. You and your lab
partner were having so much fun in lab this week, you decided
to keep collecting data on the light bulb. On
the next page, you see all of your glorious data. Now that
you’ve got it, what can you do with it? After glancing at
section 27.4 of our text, you realize that you can use the data
to calculate the temperature of the tungsten filament when the
bulb is fully lit.
2. You and a friend are studying for a midterm and the session goes until the early morning. At about 4 am you decide to cook some breakfast. Despite being sleepy, things are going well— the waffles are cooking and the coffee is perking. Should you make some toast now? The 1000watt waffle iron and the 600watt coffee maker are plugged into kitchen wall electrical outlets. You will also use a kitchen wall outlet for the toaster. The kitchen wall outlets are all part of the same 110V circuit which has a 20A circuit breaker (with negligible resistance) to protect the wire carrying the largest current from getting too hot. You know that if you plug in too many appliances you will overload the circuit breaker. The toaster label says that its power output is 700 watts.
Due November 15
(Solution )
For a summer internship, you are finishing up your design of a
desk-top sized magnetic spectrometer for the purpose of measuring
the ratio of C12 to C14 atoms in a sample
in order to determine its age.* The idea is to develop
an apparatus that is sufficiently portable that it could be taken
into the field for measurements. Your initial design is
much like the spectrometer shown in figure 29-24; although, yours
does not have the velocity selector. The plan is that by
burning (vaporizing) a sample you will create a gas of carbon
atoms. These atoms will then pass through an “ionizer”
that, on average, strips one electron from each atom. By
putting the ions through an electrostatic accelerator- two capacitor
plates with small holes that permit the ions to enter and leave,
these ions are accelerated. The two plates are charged so
that they are at a voltage difference of 1000 volts. From
here, the ions enter a nearly constant, vertical magnetic field.
Your magnetic field needs to be adjusted to have the C12
and C14 ions separated by at least 2mm when they strike
the detector array.
* C14 is a radioactive isotope of carbon that behaves chemically almost identically to its more common but slightly lighter sibling, C12 . The amount of C14 in the atmosphere stays about constant since it is being produced continually by cosmic rays. Once carbon from the air is bound into an organic substance, the C14 will decay with half of them vanishing every 5730 years. The ratio of C14 to C12 in an organic substance therefore tells how long ago it died.
Given the interactions you've seen between moving charges and
magnetic fields, you decide to build a device that would allow
you to measure magnetic fields. Your device uses a long
straight wire that has a mass density of 0.025 kg/m. This
wire is suspended by two thinner wires, which are connected to
a 20A power supply such that a complete circuit is formed.
The two small wires have their opposite ends fixed, allowing the
larger one to swing like a pendulum. When the wire is placed
in a uniform magnetic field, it is deflected such that the two
smaller wires make a 10° angle with respect to the vertical.
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