Newton’s Laws Rotation Electrostatics Potpourri Magnetism 200 200 200 200 200 400 400 400 400 400 600 600 600 600 600 800 800 800 800 800 1000 1000 1000 1000 1000

(A) mgHT (B) mgH/T (C) mg/HT An object of mass m is lifted at constant velocity a vertical distance H in time T. The power supplied by the lifting force is (A) mgHT (B) mgH/T (C) mg/HT (D) mgT/H (E) zero

(B) mgH/T

(A) 2 F (B) F (C) (2/3)F (D) 0.5F (E) (1/3)F When the frictionless system shown above is accelerated by an applied force of magnitude F, the tension in the string between the blocks is (A) 2 F (B) F (C) (2/3)F (D) 0.5F (E) (1/3)F

(E) (1/3)F

(C) ½(ml+m2)v (D) ½(m2 - m1)v (E) m2v A system consists of two objects having masses ml and m2 (ml < m2). The objects are connected by a massless string, hung over a pulley as shown above, and then released. When the speed of each object is v, the magnitude of the total linear momentum of the system is (A) (m1 + m2) v (B) (m2 - m1) v (C) ½(ml+m2)v (D) ½(m2 - m1)v (E) m2v

(B) (m2 - m1) v

The following graphs, all drawn to the same scale, represent the net force F as a function of displacement x for an object that moves along a straight line. Which graph represents the force that will cause the greatest change in the kinetic energy of the object from x = 0 to x = x1?

(E)

A racing car is moving around the circular track of radius 300 meters shown above. At the instant when the car's velocity is directed due east, its acceleration is directed due south and has a magnitude of 3 meters per second squared. When viewed from above, the car is moving (A) clockwise at 30 m/s (B) clockwise at 10 m/ s (C) counterclockwise at 30 m/s (D) counterclockwise at 10 m/s (E) with constant velocity

(A) clockwise at 30 m/s

Torque is the rotational analogue of (A) kinetic energy (B) linear momentum (C) acceleration (D) force (E) mass

(D) force

Daily Double

A particle of mass m moves with a constant speed v along the dashed line y = a. When the x‑coordinate of the particle is xo, the magnitude of the angular momentum of the particle with respect to the origin of the system is (A) zero (B) mva (C) mvxo (D) (E)

(B) mva

A uniform stick has length L A uniform stick has length L. The moment of inertia about the center of the stick is Io. A particle of mass M is attached to one end of the stick. The moment of inertia of the combined system about the center of the stick is (A) (D) (B) (E) (C)

(A)

A cylinder rotates with constant angular acceleration about a fixed axis. The cylinder’s moment of inertia about the axis is 4 kg m². At time t = 0 the cylinder is at rest. At time t = 2 seconds its angular velocity is 1 radian per second. What is the angular momentum of the cylinder at time t = 2 seconds? (A) 1 kgm m²/s (B) 2 kgm m²/s (C) 3 kgm m²/s (D) 4 kgm m²/s (E) It cannot be determined without knowing the radius of the cylinder

(D) 4 kgm m²/s

An ant of mass m clings to the rim of a flywheel of radius r, as shown above. The flywheel rotates clockwise on a horizontal shaft S with constant angular velocity . What is the magnitude of the minimum adhesion force necessary for the ant to stay on the flywheel at point III? (A) mg (B) m²r (C) m²r² + mg (D) m²r - mg (E) m²r + mg

(E) m²r + mg

The electric field E just outside the surface of a charged conductor is directed perpendicular to the surface (B) directed parallel to the surface (C) independent of the surface charge density (D) zero (E) infinite

(A) directed perpendicular to the surface

A closed surface, in the shape of a cube of side a, is oriented as shown above in a region where there is a constant electric field of magnitude E parallel to the x‑axis. The total electric flux through the cubical surface is (A) ‑Ea2 (B) zero (C) Ea2 (D) 2Ea2 (E) 6Ea2

(B) zero

The figure above shows a spherical distribution of charge of radius R and constant charge density . Which of the following graphs best represents the electric field strength E as a function of the distance r from the center of the sphere?

C

Daily Double

Points R and S are each the same distance d from two unequal charges, +Q and +2Q, as shown above. The work required to move a charge ‑Q from point R to point S is (A) dependent on the path taken from R to S (B) directly proportional to the distance between R and S (C) positive ( D) zero (E) negative

( D) zero

A rigid insulated rod, with two unequal charges attached to its ends, is placed in a uniform electric field E as shown above. The rod experiences a (A) net force to the left and a clockwise rotation (B) net force to the left and a counterclockwise rotation (C) net force to the right and a clockwise rotation (D) net force to the right and a counterclockwise rotation (E) rotation, but no net force

(B) net force to the left and a counterclockwise rotation

An isolated capacitor with air between its plates has a potential difference Vo and a charge Qo. After the space between the plates is filled with oil, the difference in potential is V and the charge is Q. Which of the following pairs of relationships is correct? (A) Q= Qo and V>Vo (B) Q= Qo and V<Vo (C) Q> Qo and V=Vo (D) Q< Qo and V<Vo (E) Q> Qo and V>Vo

(B) Q=Qo and V<Vo

(A) 0.25 T (B) 0.5 T (C) T (D) 2T (E)4T A simple pendulum of length l. whose bob has mass m, oscillates with a period T. If the bob is replaced by one of mass 4m, the period of oscillation is (A) 0.25 T (B) 0.5 T (C) T (D) 2T (E)4T

(C) T

Assume the capacitor C is initially uncharged Assume the capacitor C is initially uncharged. The following graphs may represent different quantities related to the circuit as functions of time t after the switch S is closed Which graph best represents the voltage versus time across the resistor R ? (A) (B) (C) (D) (E)

(A) 2m/s2 (B) 4m/s2 (C) 5m/s2 (D) 7 m/s2 The mass of Planet X is one‑tenth that of the Earth, and its diameter is one‑half that of the Earth. The acceleration due to gravity at the surface of Planet X is most nearly (A) 2m/s2 (B) 4m/s2 (C) 5m/s2 (D) 7 m/s2 (E) 10 m/s2

(B) 4m/s2

If i is current, t is time, E is electric field intensity, and x is distance, the ratio of to may be expressed in coulombs (B) joules (C) newtons (D) farads (E) henrys

(D) farads

Two long, parallel wires, fixed in space, carry currents I1 and I2 Two long, parallel wires, fixed in space, carry currents I1 and I2. The force of attraction has magnitude F. What currents will give an attractive force of magnitude 4F? (A) 2I1 and ½I2 (B) I1 and ¼I2 (C) ½I1 and ½I2 (D) 2I1 and 2I2 (E) 4I1 and 4I2

(D) 2I1 and 2I2

A charged particle is projected with its initial velocity parallel to a uniform magnetic field. The resulting path is a spiral (B) parabolic arc (C) circular arc (D) straight line parallel to the field (E) straight line perpendicular to the field

(D) straight line parallel to the field

A solid cylindrical conductor of radius R carries a current I uniformly distributed throughout its interior. Which of the following graphs best represents the magnetic field intensity as a function of r, the radial distance from the axis of the cylinder

(A)

Two very long parallel wires carry equal currents in the same direction into the page, as shown above. At point P, which is 10 centimeters from each wire, the magnetic field is zero (B) directed into the page (C) directed out of the page (D) directed to the left (E) directed to the right

(E) directed to the right

A proton traveling with speed v enters a uniform electric field of magnitude E, directed parallel to the plane of the page, as shown in the figure above. There is also a magnetic force on the proton that is in the direction opposite to that of the electric force. Which of the following is a possible direction for the magnetic field?

(D)

Which of the following statements about conductors under electrostatic conditions is true? (A) Positive work is required to move a positive charge over the surface of a conductor. (B) Charge that is placed on the surface of a conductor always spreads evenly over the surface. (C) The electric potential inside a conductor is always zero. (D) The electric field at the surface of a conductor is tangent to the surface. (E) The surface of a conductor is always an equipotential surface.