26. For the circuit shown below, when a shorting wire (no resistance) connects the points labeled A and B, which of the numbered light bulbs become brighter?

 

 

Assume that all four bulbs are identical and have resistance R.

31. A car moves to the right along a one-dimensional track for total time T in two parts.

 

 

What is the ratio of the distance traveled during Part One of the trip to the distance traveled during Part Two of the trip?

34. The diagram below shows the path taken by a monochromatic light ray traveling through three media.

 

 

The symbols v₁, λ₁, and f₁ represent the speed, wavelength, and frequency of the light in Medium 1, respectively. Which of the following relationships for the light in the three media is true?

35. A piece of an ideal fluid is marked as it moves along a horizontal streamline through a pipe, as shown in the figure.  In Region I, the speed of the fluid on the streamline is V. The cylindrical, horizontal pipe narrows so that the radius of the pipe in Region II is half of what it was in Region I.  

 

 

What is the speed of the marked fluid when it is in Region II?

36. For the RC circuit shown, the resistance is R = 10.0 Ω, the capacitance is C = 5.0 F and the battery has voltage  = 12 volts . The capacitor is initially uncharged when the switch S is closed at time t = 0 . At some time later, the current in the circuit is 0.50 A.

 

 

What is the magnitude of the voltage across the capacitor at that moment?

37. For the figure shown, the variable resistance in the circuit on the left is increased at a constant rate. What is the direction of the magnetic field at the point P at the center of the left-hand circuit and in what direction is the conventional current through the resistor in the right-hand circuit?

 

38. A small object of mass M and charge Q is connected to an insulating massless string in a vacuum on Earth. A uniform electric field exists throughout the region of the vacuum as indicated. The mass remains in static equilibrium at an angle of θ with the vertical as shown in the figure.

 

 

When the string is cut, which of the illustrated paths best indicates the trajectory of the mass?

39. For the compound machine comprised of the inclined plane and pulley shown, a 75.0 N force is required to slide a box with mass M = 10.0 kg up the incline at a constant speed.

 

What is the efficiency of this compound machine?

40. A uniform solid cylinder of mass M = 2.00 kg and radius R = 10.0 cm is connected about an axis through the center of the cylinder to a horizontal spring with spring constant 4.00 N/m.

 

 

The cylinder is pulled back, stretching the spring 1.00 m from equilibrium. When released, the cylinder rolls without slipping. What is the speed of the center of the cylinder when it returns to equilibrium?

 

 

IMPORTANT: All Division 01 students STOP HERE. Your last answer should be number 40. Numbers 41-50 should remain blank for Division 01 students.

All Division 02 students continue to Questions 41 – 50.

 

 

41. For the circuits shown below, which will take the least time to charge the capacitor(s) to 90% of the full charge? All batteries are ideal and identical with emf ξ, all resistors are identical with resistance R, and all capacitors are identical with capacitance C and are initially uncharged.

42. A uniform, solid disk with mass M and radius R is rotating on a fixed, frictionless platform with constant angular speed ω_o about a fixed axis through its center. A second uniform solid disk of mass 2M and radius 2R is placed from rest directly on top of the first disk so that the centers of the disks line up. When equilibrium is established, the disks are spinning at the same rate. What is the angular speed of the disks at equilibrium?

43. A real object is located in front of a convex lens at a distance greater than the focal length of the lens. What type of image is formed and what is true of the image’s size compared to that of the object?

 

47. A spatially uniform electric field is constrained within the circular region of radius R as shown. The field is directed out of the plane of the page and its strength is increasing uniformly in time.

 

 

What is the direction of the force on the proton in the figure if the proton is moving to the right at the instant shown? Ignore gravity.

Questions 48 – 49 deal with the following information:

 

An electromagnetic wave has an electric field given by the expression (in Cartesian coordinates):

 

48. What is the direction of the energy flow for the wave?

50. What is the magnitude of the linear momentum (in units of kg ⋅m/sec) of an electron moving in a straight line if it has 3.2×10⁻¹³ J of kinetic energy?