University of Minnesota, Duluth

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

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?

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.

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.

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).