Part 1: Do three of four problems, problem 1 - 4.
Problem 1:
The volume flow rate of water through a
horizontal pipe is 2 m3/min. Determine the speed of flow at a
point where the diameter of the pipe is
(a) 10 cm,
(b) 5 cm.
Problem 2:
(a) At what distance from a single conductor carrying a
direct current of 20 A is the magnetic field produced equal to earth’s magnetic
field (Bearth ~ 5 x 10-5 T)?
(b) Suppose a two-conductor household power cord supplies
20 A current to an electric heater. How does the answer to part (a) change,
qualitatively, in terms of distance from the cable, and what fundamental
conservation law is involved in producing this change?
Problem 3:
An alpha particle containing two protons is shot directly towards a platinum nucleus containing 78 protons from a very large distance with a kinetic energy of 1.7´10-12 J. What will be the distance of closest approach?
Problem 4:
What is the charge on one square kilometer of the earth’s surface if an electric field of 300 volts per meter is directed vertically downward near the surface?
Part 2: Do three of four problems, problem 5 - 8.
Problem 5:
In his short story "A Slight Case of Sunstroke", Arthur C. Clarke writes of a
stadium full of disgruntled soccer fans barbecuing the dishonest referee by
reflecting sunlight on him with mirrors found under their seats.
(a) Imagine a stadium at the equator at noon (i.e. the sun's directly
overhead), with 50,000 fans. Assuming
that sunlight delivers about 1000 watts per square meter to the surface of the
Earth, and that each fan is holding a 0.25 m2 mirror at 45o,
how much power would be available to be projected onto a dishonest referee?
(b) To be humane, let us replace the referee with a 50 kg cylinder of 37 oC
water. Assuming this cylinder absorbs all of the reflected light from the
mirror - wielding fans, how long will it take for it to reach 100 oC? (The heat capacity of water is about 4200 J/(kgoC).)
Problem 6:
A spherical region of space of radius a contains a
charge Q which is uniformly distributed within the volume
(a) Use Gauss's law to determine the magnitude of the
electric field at any radius r from the center of the sphere.
(b) The total electrostatic energy of the sphere may be
calculated from the electric field, using
(SI units).
Evaluate this expression for the uniformly charged sphere.
(c) Calculate the work
required to bring a test charge +q from infinity to the center of the
sphere, using dW = F×
dr = +qEdr.
Problem 7:
Two ammeters, 1 and 2 have different internal resistances r1 (known) and r2 (unknown). Each ammeter has an analog scale, such that the angular deviation of the needle from zero is proportional to the current. Initially the ammeters are connected in series and then to a source of constant voltage. The deviations of the needles are q1 and q2, respectively. The ammeters are then connected in parallel and then to the same voltage source. This time the deviations of the needles are q1’ and q2’, respectively. Find r2 in terms of r1 and the angles.
Problem 8:
A particle of mass M is at rest in the laboratory. Suddenly it disintegrates into two particles, one of mass m and one of mass 2m. Let M = 4m. The final particles have momenta p and p', qnd energies E and E'.
(a) What is the relationship between p and p'?
(b) Find expressions for p, p' E, and E'.
(c) Determine the speed of each final particle in the laboratory frame.
(d) Determine the speed of m in the rest frame of 2m.