I Duluth Physics Olympiad

March 29th, 2014
University of Minnesota, Duluth

Part I: Theoretical

Problem 1:

Two cars (A and B) are moving side by side with identical velocities, v. The car A then accelerates to 2v. It is easy to see that with respect to a stationary observer on the highway the kinetic energy of the car has increased by ΔE = (3)/(2)mv2, but with respect to the car B the kinetic energy of the car A has increased by ΔE = (1)/(2)mv2. Explain the paradox: the amount of gasoline burned is the same for both observers, but the change in energy is different.

Problem 2:

Consider electric wires connected in the shape of a cube, as shown. Which edge of the cube should be cut to change the resistance between points A and B most significantly?
figure cube2.png

Problem 3:

Reconstruct the missing axes of the P (pressure) vs. V (volume) graph. The graph shows a cyclic process for an ideal gas where O is the origin (P = 0;V = 0) and A is the point corresponding to the highest temperature, T, in the cycle. The axes are perpendicular to each other but are not necessarily vertical/horizontal. Describe the steps of your geometric construction.

figure kelvin2.png

Problem 4:

What is the largest potential difference one can obtain using a battery of electromotive force E and two identical capacitors? You are allowed to connect the elements in any order any number of times.

Part II: Experimental

Problem 5:

Determine the density of a cylindrical object of an unknown mass. Equipment: the object, stopwatch, spring, stand, two known masses, paper. You may use only the provided equipment (and your pen for writing).