26. A 4.00 kg mass is in uniform circular motion as shown in the figure. The string to which the mass is attached has a length of L = 3.00 m and forms an angle of θ = 50.0° with the vertical. What is the speed of the mass?
27. A 2.0 kg mass moves at 10.0 m/s when it has a collision in space. The mass’s speed was unchanged, but the direction of its velocity was altered by 80°. If the collision lasted 0.25 s, what was the magnitude of the average force exerted on the mass?
28. A shipment of parts is labeled in units of “ohm∙second.” Which one of the following choices represents an equivalent unit?
29. Two lightbulbs (X and Y) are connected in series to a battery. Bulb X is brighter than bulb Y. Assume all circuit elements are ideal. If bulbs X and Y are connected in parallel with each other to the same battery, which one of the following choices best represents what is observed?
30. Two cars, P and Q, each start from rest at the origin and will move along the x-axis. The acceleration vs. time graph for each car is shown. Which one of the following choices correctly identifies the relationship for both the speeds (vP and vQ) and the positions (xP and xQ) of the cars at time T?
31. A solid cylinder rolls without slipping on a rough inclined plane. Which one of the following choices best represents the type and direction of friction (if any) acting on the cylinder as it rolls up the incline?
32. A projectile is launched at an angle of 40° above the horizontal with a speed of 30 m/s. How much time passes before the position of the projectile makes an angle of 20° above the horizontal from the original launch point?
33. Two long wires are fixed in space so that the conventional current in the left wire (2 A) comes out of the plane of the page and the conventional current in the right wire (3 A) goes into the plane of the page. In which Region(s) is there a place on the x-axis (aside from infinity) at which the magnetic field is equal to zero from these currents?
34. A 9.20 m long uniform plank rests on a frictionless ice pond. A 52 kg box rests on the plank’s left end while a 71 kg person stands at the plank’s right end. After the person walks to the left on the plank and stands at the same location as the box, the plank has slid 3.84 m to the right relative to the pond’s shore. Which one of the following choices best represents the mass of the plank?
35. A metal bar is moving to the left across a set of frictionless conducting rails as seen in the figure. Throughout the region between the rails, there is a uniform magnetic field directed into the plane of the page. The resistors labeled 𝑋 and 𝑌 are identical. Which one of the following choices correctly indicates the direction of the conventional current in the resistors and the relation between the magnitude of the currents through each resistor at the instant shown?
36. A scientist performs an experiment in which she determines the shortest length of a gas column needed to create resonance for a vibrating tuning fork over a tube closed at one end. She plots the gas column length against the inverse of the frequency for a set of tuning forks and finds that she has a straight line fit through the data. Representing the slope of the line as m, which one of the following choices correctly identifies the speed of waves through the gas in the experiment?
37. Which one of the following choices best approximates the magnitude of the Earth’s angular momentum (expressed in base MKS units) associated with its orbit around the Sun?
38. A small 2.0 kg block rests at the bottom of a bucket. The bucket is spun in a vertical circle of radius L by a rope. When the bucket reaches the highest point in its motion, it moves just fast enough for the block to remain in place in the bucket. When the bucket is at an angle θ = 30° from the vertical, as seen in the figure, what is the magnitude of the normal force (perpendicular to the surface) provided by the bucket onto the block? Note that the direction of the gravitational field is indicated in the diagram by and that the block does not touch any sides of the bucket aside from the bottom of it.
39. A point wave source travels along the x-axis at constant speed vS. Stationary observers on the x-axis measure the wavelength of the waves that they receive. The ratio of the wavelength measured at a location behind the source to the wavelength measured at a location in front of the source is 1.50. If the wave speed is v, what is the source speed vS?
40. A small object of mass M is released from rest at the top of a frictionless incline. The incline has a mass M and makes an angle θ with the horizontal. The incline remains at rest on a table as the small object slides. During the slide, what is the magnitude of the normal force from the table on the incline?
All Division 1 students STOP HERE. Your last answer should be for #40. Numbers #41-#50 should remain blank for Division 1 students. All Division 2 students continue to Questions #41 – #50.
41. Pure red light shines through a diffraction grating of 1200 lines/cm and produces an interference pattern on a screen a distance 5.0 m away. Which one of the following choices best represents the distance between the first and third principal bright spots on the screen?
42. A long uniform rod, pivoted at one end affixed to the ground, is in static equilibrium A horizontal rope acts 75% of the way up the rod while a vertical rope acts at the far end. The magnitude of each rope’s force is the same as the gravitational force acting on the rod. What is the value of the angle θ in the figure?
43. A semi-circle has radius R, total charge Q, and a charge per unit length given asλ = λo cos θ with θdefined in the figure and 𝜆oa positive constant. Which one of the following choices gives the electric field strength at the point labeled P?
44. A ball is launched vertically upward. The vertical position of the ball 0.70 s after release is the same as its vertical position 4.10 s after its release. At what time is the object first at a vertical position that is one-half of the maximum height it obtains during its flight?
45. Which one of the following magnifications cannot be produced using a single converging lens?
46. Two copper spheres, X and Y, with different radii (RX > RY) and equal excess charge +Q, are placed apart from each other. A scientist using insulating gloves connects the spheres with a copper wire. Which one of the following choices best describes what happens after the connection is made?
47. Once the circuit shown reaches equilibrium, what is the magnitude of the potential difference across the capacitor?
48. In the binary star system shown, the two stars follow circular orbits about the system’s center of mass. The stars are separated by a distance D that is large compared to their size and are subject only to their mutual gravitational attraction. The orbital period of the star of mass M is T. Which one of the following choices represents the total mass of the binary star system?
49. Two identical particles travel to the right. The particle traveling at 2.40 × 108 m/s collides with and sticks to the other particle traveling at 1.80×108 m/s. Which one of the following choices best represents the speed of the resulting object after collision?
50. A monatomic ideal gas undergoes the reversible cyclic process (ABCA) shown in the PV diagram. Process A →B is adiabatic. What is the efficiency of this engine?
Introduction: My name is Greg O'Connell, I am a delightful, colorful, talented, kind, lively, modern, tender person who loves writing and wants to share my knowledge and understanding with you.
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and that the block does not touch any sides of the bucket aside from the bottom of it. 
