Download Module 21: Magnetic Field

NOTES and Problems for ANDES
July, 2007
Kinematics graphs:
Multiple choice problems:
Matching x(t) and v(t) and a(t) graphs
Choosing all three (one at a time) graphs:
Ex. A car, traveling in the positive x direction, is approaching a stop sign. Assume that the car’s
acceleration is constant while stopping and the car comes to a complete stop. Choose the x(t) and
v(t) and a(t) graphs that best describe the motion of the car.
More problems on the graphs for free fall.
“What if?” and reflective questions
Vectors section:
For existing problems, such as VEC1B, additional questions can be added that ask, “Does the
swimmer move faster in the east direction or in the north direction?” Then next, “Now, the
swimmer swims at 2 m/s at 35 degrees north of east. How does the east component of the
swimmer’s velocity compare to its original value?” It is also possible to add qualitatively stated
questions, ex. “What happens to the north component of the swimmer’s velocity if the angle
(east of north) increases?”
A person walks out of his cabin and goes 10 mi at 30 degrees north of east. After this hike, he is
__________ miles north and __________ miles east of his cabin.
What happens if?
If he instead walks directly east, how far north does he end up from his cabin?
If he walks the same distance at 50 degrees north of east, then he ends up (further or closer?) in
the direction east from the cabin. Ask the same for north and then repeat for various angles.
The same thing for the forces, for example, how does the normal force change if a person pushes
downward at 15 degrees below horizontal instead of the upward?
A Big Bird is sitting on a wire. The wire sags so that it makes an angle  with the horizontal on
both sides of Big Bird. How does the tension in the wire change if the wire is made to sag less
(angle  is getting smaller)?
Add FBD problems for two-body problems, such as DT6C, DT10A
Gravitational field problems:
A 70 kg student orbits Earth at an elevation equal to Earth’s radius (or orbital radius equal to
twice Earth’s radius or the distance from the center of earth is equal to twice the earth’s radius)
find the student’s weight in orbit. Find the student’s apparent weight in orbit. Find the student’s
orbital period. Suppose the orbital radius doubles, how does that effect all the parameters above?
Other sections could have questions on the affect of a variable change on the other variables.
Work-energy (added planetary gravitational potential energy):
A 2700 kg space craft is in a circular orbit 1800 km above the surface of Mars. How much work
must the spacecraft engines perform to move the spacecraft to a circular orbit with radius 3000
km?
Zero, a hypothetical planet, has a mass of 4.0 1023 kg, a radius of 3.0 106 m, and no
atmosphere. A 9 kg space probe is to be launched vertically from its surface.
If the probe is launched with an initial kinetic energy of 5.0 107 J, what will be its kinetic
energy when it is 4.0 106 m from the center of Zero? If the probe is to achieve a maximum
distance of 8.0 106 m from the center of Zero, with what initial kinetic energy must it be
launched from the surface of Zero?
Suppose an asteroid of a mass m falls from a distance equal to the radius of Moon’s orbit around
Earth. How much work would be done by the gravitational force before the asteroid hits the
surface of Earth? How much kinetic energy would it gain before hitting Earth’s surface?
Determine the amount work done by the force of gravity on the Moon assuming Moon’s orbit is
circular.
Determine the work done by the tension force when a stopper is whirled in a horizontal circle.
Graph questions: Work as area under the Fx(x) graph:
A single force acts on a 5 kg object. The force is directed along the x-axis and varies in
magnitude as given by the graph below. The velocity of the object at x=0 is 2 m/s in the negative
x-direction. (a) What is the kinetic energy of the body at x = 3.0 m? (b) At what value of x will
the body have a kinetic energy of 8.0 J? (c) What is the maximum kinetic energy attained by the
body between x = 0 and x = 5.0 m?
Linear Momentum:
LMOM2A “Ignore any rotation of the ball or the pin” – normally pins topple, not just fly out into
space
LMOM4A makes me uncomfortable because the situation described in three-dimensional and
rotation plays a major part, but must be ignored to be able to answer the question.
LMOM5 and LMOM6 are too hard too quickly! May be if the problem with a rigid support is
added to the Dynamics section (above) then it would be easier for students to remember or figure
out the significance of the “rigid rod” statement.
Two ice skaters, Daniel and Rebecca, are practicing. Daniel's mass is 69.9 kg, and Rebecca's
mass is 49.3 kg. Daniel stops to tie his shoelace and, while at rest, is struck by Rebecca, who is
moving at 12.5 m/s before she collides with him. After the collision, Rebecca has a velocity of
magnitude 9.9 m/s at an angle of 37.3° from her initial direction. Both skaters move on the
frictionless horizontal surface of the rink.
(a) What are the magnitude and direction of Daniel's velocity after the collision?
(b) What is the change in total kinetic energy of the two skaters as a result of the collision?
A car with mass 800 kg traveling east collides with a 1600 kg pickup truck traveling north. The
two vehicles stick together as a result of the collision, and, after the collision, the wreckage is
sliding at 16.0 m/s in the direction 24.0° east of north. Calculate the speed of each vehicle before
the collision. Assume the collision occurs during a heavy rainstorm and ignore friction forces
between the vehicles and the wet road.
An 8.00-g bullet is fired into a ballistic pendulum and lodges inside the 2-kg pendulum bob. (a)
Find the ratio of the total kinetic energy after the collision to the kinetic energy before the
collision. What accounts for the missing energy? (b) After the collision the pendulum swings
upward. Find the maximum angle reached by the pendulum before it starts swinging back down.
An 8.00 g bullet is fired into a 250 g block that is initially at rest at the edge of a 1.00 m high
table. The bullet remains in the block, and after the impact the block lands 2.00 m horizontally
from the bottom of the table. Determine the initial speed of the bullet.
Suppose that the 200-g head of a golf club travels at 55 m/s just before it strikes a 48-g golf ball
initially at rest on a tee. If the club head slows to at 40 m/s (in the same direction) after the
collision, what is the speed of the golf ball just after impact, and what fraction of the original
kinetic energy of the club head was lost to thermal energy? Assume that the mass of the club is
concentrated mostly in the head.
A certain radioactive nucleus can transform to another nucleus by emitting an electron and a
neutrino. Suppose that in such a transformation, the initial nucleus is stationary, the electron and
neutrino are emitted along perpendicular paths, and the magnitudes of the linear momenta are
1.5x10-22 kgm/s for the electron and 6.7x10-23 kgm/s for the neutrino. As a result of the
emissions, the new nucleus moves (recoils). (a) What is the magnitude of its linear momentum?
(b) What is the angle between its path and the path of the electron? (c) What is the angle between
its path and the path of the neutrino? (d) What is its kinetic energy if its mass is 6.5x10-26 kg?
Electrostatic Field
CHARGE1A and 1B : I would prefer if the question of proton transfer wasn’t addressed, but I
can just skip this one. It is a pity though because I do assign problems on counting the number of
transferred particles. In my experience students have more trouble figuring out if the electrons
are added or taken away than understanding that the protons are locked inside nuclei. Ion versus
electron mobility does come up, but this is not the situation.
The other field problems are OK for me. Again, the addition of “what if” questions and also
changing a variable by a factor would be great.
The next two questions are the same as many that exist in Andes but use actual nuclei instead of
general “particles”. These may also require students to look up the atomic number, charge, etc.
for the particles in question. The students should not forget how to use the periodic table or other
“chem.” skills just because they are in Physics now; there is not much purpose in learning all this
without any applications.
What is the electric field of an iron (or any other) nucleus at a distance of 5.00x10-10 m from the
nucleus? The atomic number of iron is 26. Assume that the nucleus may be treated as a point
charge.
What is the electric field of a proton at a distance of 5.28x10-11 m from the proton? (This is the
radius of the electron orbit in the Bohr model for the ground state of the hydrogen atom.)
Combining weight and electrostatics:
What must be the charge (sign and magnitude) on a 2.00 g particle (on earth) to remain
stationary when placed in a downward-directed electric field of magnitude 800 N/C?
What is the magnitude of an electric field in which the electrical force on a proton (electron,
doubly ionized sodium, etc.) is equal in magnitude to its weight on earth?
Equilibrium with electrostatics:
A 2-g pith ball is suspended from a light 20-cm long string in a 200 V/m horizontal electric field.
The pith ball is in equilibrium and the string makes a 10o angle with the vertical. Determine the
charge on the pith ball.
Two identical 2-g pith balls are hanging from the same support on 20-cm long light strings. The
pith balls are equally charged and the supporting strings make a 20o angle with each other.
Determine the charge on each pith ball.
Motion with electrostatics:
Assuming that Bohr’s model of hydrogen atom is correct, determine the orbital speed of an
electron in orbit around a proton. Take the orbital radius to be Ra = 5.28x10-11 m. Students can
look up or be given the charge and mass values.
A region next to a charged metal disk has a uniform electric field E= 200 N/C directed East. An
electron enters this electric field at 5x106 m/s in the same direction as the electric field. Sketch
the force, acceleration, and velocity vectors of the electron at the initial moment. Sketch the
force, acceleration, and velocity vectors of the electron at the moment when the electron is
instantaneously at rest. How far does the electron travel before stopping (instantaneously)?
A region next to a charged metal disk has a uniform electric field E= 200 N/C directed East. An
electron enters this electric field at 5x106 m/s at 37o North of East. Sketch the force, acceleration,
and velocity vectors of the electron at the initial moment. Sketch the force, acceleration, and
velocity vectors of the electron at the moment when the electron reaches its maximum eastward
displacement. Find the velocity of the electron when it reaches its maximum eastward direction.
Find the maximum eastward displacement of the electron. How long does the electron take to
reach this position? How far in the northward direction does the electron travel at the same time?
Textbooks have versions of the above problems for electric field between two oppositely charged
parallel plates. Those may be easier to state clearly, but still require sketches.
Module 21: Magnetic Field
This section in ANDES mixes two topics I deal with separately, the sources of magnetic field,
(moving charged particles, currents, loops, solenoids) and the affect of magnetic field on the
stuff stuck into it (mostly moving charged particles, but also current carrying wires and loops).
It would help if this module were divided into two. If that’s not possible, the module can work by
assigning specific problems and warning students about the content.
The first time through I use this section to teach the Lorenz Force and the motion of charged
particles in magnetic field. The problems are mostly based on specific devices, such as a
cyclotron, a velocity selector, mass spectrometer, and Hall probes, and also Aurora lights and
Van Allen belts.
Questions asking about the radius, the frequency, and the period of motion of charged particles
in magnetic field may be added to the Lorenz force problems already there.
A proton enters Earth’s magnetic field in an equatorial region almost perpendicularly to Earth’s
magnetic field. Determine the period of the proton’s circular motion if Earth’s magnetic field is
5x10-7 T in the region.
A proton travels with a speed of 5.0 106 m/s at an angle of 36° with the direction of a magnetic
field of 0.20 T in the +y direction. What are (a) the magnitude of the magnetic force on the
proton and (b) the proton's acceleration? (c) How fast is the proton moving along the direction of
the magnetic field? (d) What is the radius of the circle the protons makes around the magnetic
field?
From Tipler:
An electron from the sun with a speed of 1.0 107 m/s enters the earth's magnetic field high
above the equator where the magnetic field is 6 10-7 T. The electron moves nearly in a circle
except for a small drift along the direction of the earth's magnetic field that will take the electron
toward the north pole. (a) What is the radius of the circular motion? (b) What is the radius of the
circular motion near the north pole where the magnetic field is 2 10-5 T?
From Young and Freedman, University Physics:
Determining the Mass of an Isotope. The electric field between the plates of the
velocity selector in a Bainbridge mass spectrometer is 1.14 105 V/m, and the
magnetic field in both regions is 0.530 T. A stream of singly charged selenium ions
moves in a circular path with a radius of 31.0 cm in the magnetic field. Determine
the mass of one selenium ion.
Determine the mass number of this selenium isotope. (The mass number is equal to the mass of
the isotope in atomic mass units, rounded to the nearest integer. One atomic mass unit = 1 u =
1.66 10-27 kg.)
Electrostatic Potential:
The topic of potential and potential energy is discussed using the examples of gravitational field
g first, then uniform electrostatic field, and then the central electrostatic and gravitational fields.
The following problems may not be possible in ANDES and are assigned following field
mapping labs (gravitational – contour map, and electrostatic).
A topographic contour map shows lines of equal gravitational
potential energy. Examine the map of an island and answer the
questions below. a. Approximately at what angle do the contour lines
intersect the rivers? b. A car drives around the island following one
of the contour lines. The amount of work done on the car by the
force of gravity
depends on the elevation of the contour line
is equal to zero
depends on the speed of the car
depends on the mass of the car
c. A 72 kg climber descends from the highest point on the island down to the camp at an
elevation of 2000 feet. How much work is done by the force of gravity on the climber? (Hint: 1'
= 0.3048 m)
Two large parallel conducting plates are 25 cm apart and have charges of equal magnitude and
opposite sign on their facing surfaces. The electrostatic field is essentially uniform between the
plates. An electrostatic force of 4.2x10-15 N acts on an electron placed anywhere between the two
plates.
(a) How much work is done by the field in moving an electron from the negative to the positive
plate?
(b) If the electron starts from rest at the negative plate, what is its speed when it reaches the
positive plate?
(c) Find the electric field anywhere between the plates.
(d) What is the potential difference between the plates?
(e) For a uniform electric field, potential difference V between two points a distance d apart
(along the field) is related to the field E as
V=E/d
V=Ed
V=d/E
An electron enters a uniform electric field with an initial velocity of 4.10x105 m/s in the same
direction as the electric field. How much work does the electric field do to stop the electron?
What is the change in the potential energy of the electron? What is the difference in electrostatic
potential between the points in the field from the point the electron enters to the point where the
electron stops (instantaneously)?
Suppose an electron is released from rest in a uniform electric field whose magnitude is 6.20x103
N/C. (a) How much work is done by the field in moving the electron through a distance of 4 cm?
(b) Through what potential difference will it have passed after moving through this distance? (c)
How fast will the electron be moving after it has traveled this distance?
From Halliday and Resnik
When an electron moves from A to B along an electric field line in Fig. 25-34,
the electric field does 5.07 10-19 J of work on it. What are the electric
potential differences(a) VB - VA, (b) VC - VA, and (c) VC - VB
(a) In the figure shown, does the electric potential increase toward the right or
toward the left? (b) If the adjacent equipotential surfaces differ by 10 V and
the right-most one is at an electric potential of -100 V, what is the electric
potential of the left-most one? (c) If we move an electron toward the right, is
the work done on the electron by our force? (d) If we move an electron
toward the right, is the work done on the electron by the electric field positive
or negative?
Note:
I have some specific needs for circuits also, but I’ll do that at a later date since there is plenty of
time and the circuits sections in ANDES are not bad.
This concludes the main conceptual sections: forces, (motion), fields, energy, and
momentum.
The topics left to do: atomic physics: atomic collisions, atomic model and radiation; special
relativity and energy-mass equivalence; nuclear physics; waves. I may just stay with my existing
assignments for that. If you’d like to see those, please let me know and I’ll e-mail you the
problem sets.