General Physics Contest 2010 May 22, 2010 (9:10-10:50), Total 6 pages Part I : Choice Questions (20 single-choice questions of 3% each. Use 2B pencil to mark the answer.) 1. A particle moving along the x-axis has a position function given by x(t) = (4.00 m/s 3 ) t 3 -(5.00 m/s) t + (6.00 m). What is the average acceleration of the particle between t = 1.00 s and t = 2.00 s. (A) 24 m/s 2 (B )12 m/s 2 (C) 36 m/s 2 (D)18 m/s 2 (E)30 m/s 2. 2. Two planets have masses M and m, and the ratio M/m = 25. The distance between the planets is R. The point P is between the planets as shown, and the distance between M and P is x. At P, the gravitational force on an object due to M and m are equal in magnitude. The value of x is (A) 5R/6 (B) 25R/36 (C) R/25 (D) 6R/5 (E) none of these. 3. Two masses are connected by a heavy (1.00 kg) cable. The two masses are pulled along a smooth horizontal surface by an external force P = 22.0 N as shown in figure. Calculate the tension in the cable at its midpoint. (A) 11.0 N (B) 10.0 N (C) 8.0 N (D) 9.0 N (E) 22.0 N. 4kg 6kg P=22N 4. A lamp with a mass m is suspended from the ceiling by two cords as shown. The ratio of the magnitude of the vertical component of the tension in T 2 to that in T 3 is T 2 T 3 T 1 (A) 1:1 (B) 1:2 (C) 3 :3 (D) 3:2 (E) 3:1. 5. A mass m 2 = 1.5 kg rests on a horizontal table. The static and kinetic coefficients of friction between m 2 and the table are µ s = 0.3 and µ k = 0.25, respectively. The mass m 2 is attached by strings to masses m 1 = 2.5 kg and m 3 = 4.5 kg as shown. Masses m 1 and m 3 hang freely. The system is initially held at rest. After it is released, the acceleration of m 2 is m 2 m 1 approximately (A) 1.9 m/s 2 (B) 2.4 m/s 2 (C) 3.0 m/s 2 (D) zero (E) 13 m/s 2. m 3 1
6. The balls shown in the figure are strung on a taut wire and slide without friction. If the balls are of equal mass, the diagram that best represents an elastic collision is: After collision (A) (B) (C) (D) After collision (E) 7. A cube of side 2a and mass M is sliding on a frictionless surface with uniform velocity v 0, as shown in the Figure. It hits a small obstacle at the end of the table, which causes the cube to tilt as in Fig. b. Find the minimum value of v 0 such that the cube will fall off the table (g is the 2a Fig. a v 0 h=a F=Mg Fig. b gravitational acceleration constant on earth). (A) 2 ag( 2 1) (B) 4 ag( 2 1) (C) 16 ( 2 1) 3 ag (D) 4 ( 2 1) 3 ag (E) 8 ( 2 1) 3 ag. 8. A wooden rod of uniform cross section and of length l is hinged at the bottom of a tank which is filled with water to a height h =l/3. If the density of wood is 0.45 g/cm 3, find the angle θ from the vertical at which the rod is in equilibrium. (A) θ = 60 (B) θ = 30 (C) θ = 45 (D) θ = 37 (E) θ = 53 h=l / 3 θ 9. One source of sound is at A and another is at B. The two sources are in phase. The distance AB =10.0 m. The frequency of the sound wave from both sources is 1000 Hz and both the same amplitude. The speed of sound in air is 330 m/s. A receiver is at point C, and AB is perpendicular to AC. The greatest distance AC for which the signal at C is a minimum is (A) 330 cm (B) 152 m (C) 330 m (D) 303 m (E) 100 m. A B C 2
10. A speedboat moving at 20.6 m/s sounds a signal on its horn, producing a tone of 320 Hz. There is no wind, and the speed of sound in air is 329 m/s. The apparent frequency of the sound heard by an observer in another boat moving in the opposite direction and approaching the first at a speed of 15.4 m/s is (A) 282 Hz (B) 287 Hz (C) 316 Hz (D) 357 Hz (E) 369 Hz. 11. The specific heat of a substance is: (A) the amount of heat energy to change the state of one gram of the substance. (B) the amount of heat energy per unit mass emitted by oxidizing the substance. (C) the amount of heat energy per unit mass to raise the substance from its freezing to its boiling point. (D) the amount of heat energy per unit mass to raise the temperature of the substance by 1 C. (E) the temperature of the object divided by its mass. 12. Two ideal gases, each consisting of N monatomic molecules, are in thermal equilibrium with each other and equilibrium is maintained as the temperature is increased. A molecule of the first gas has mass m and a molecule of the second has mass 4m. The ratio of the changes in the internal energies E 4m / E m is: (A) 1/4 (B) 1/2 (C) 1 (D) 2 (E) 4. 13. The temperatures T C of the cold reservoirs and the temperatures T H of the hot reservoirs for four Carnot heat engines are engine 1: T C = 400K and T H = 500K engine 2: T C = 500K and T H = 600K engine 3: T C = 400K and T H = 600K engine 4: T C = 600K and T H = 800K Rank these engines according to their efficiencies, least to greatest (A) 1, 2, 3, 4 (B) 1 and 2 tie, then 3 and 4 tie (C) 2, 1, 3, 4 (D) 1, 2, 4, 3 (E) 2, 1, 4, 3 14. Consider the following procedural steps: 1. ground an electroscope. 2. remove the ground from the electroscope. 3. touch a charged rod to the electroscope. 4. bring a charged rod near, but not touching, the electroscope. 5. remove the charged rod. To charge an electroscope by induction, use the sequence: (A) 1, 4, 5, 2 (B) 4, 1, 2, 5 (C) 3, 1, 2, 5 (D) 4, 1, 5, 2 (E) 3, 5 3
15. Two charged point particles are located at two vertices of an equilateral triangle and the electric field is zero at the third vertex. We conclude: (A) the two particles have charges with opposite signs and the same magnitude. (B) the two particles have charges with opposite signs and different magnitudes. (C) the two particles have identical charges. (D) the two particles have charges with the same sign but different magnitudes. (E) at least one other charged particle is present. 16. 10C (Coulomb) of charge are placed on a spherical conducting shell. A particle with a charge of 3C is placed at the center of the cavity. The net charge on the outer surface of the shell is: (A) 7C (B) 3C (C) 0C (D) +3C (E) +7C 17. Two conducting spheres are far apart. The smaller sphere carries a total charge Q. The larger sphere has a radius that is twice that of the smaller and is neutral. After the two spheres are connected by a conducting wire, the charges on the smaller and larger spheres, respectively, are: (A) Q/2 and Q/2 (B) Q/3 and 2Q/3 (C) 2Q/3 and Q/3 (D) zero and Q (E) 2Q and Q 18. Capacitors C 1 and C 2 are connected in parallel. The equivalent capacitance is given by: (A) C 1 C 2 /(C 1 + C 2 ) (B) (C 1 + C 2 )/C 1 C 2 (C)1/(C 1 + C 2 ) (D) C 1 /C 2 (E) C 1 + C 2 19. The current is from left to right in the conductor shown. The magnetic field B is into the page and point S is at a higher potential than point T. The charge carriers are: (A) positive (B) negative (C) neutral (D) absent (E) moving near the speed of light B 20. A constant current is sent through a helical coil. The coil: (A) tends to get shorter (B) tends to get longer (C) tends to rotate about its axis (D) produces zero magnetic field at its center (E) none of the above 4
Part II: Problems (4 problems of 10% each. Answer the questions as clear as possible.) 1. A person stands on a platform that can rotate Axis of rotation about a vertical axis. The person holds a heavy ω 1 ω 2 weight of mass M in each of his hands which R R R R 2 2 are stretched out as shown in Fig1-a. The M M M M platform was set in uniform circular motion with angular velocity ω 1. At same time, the F=mg(external) person brings his arms closed to his body so that the distance of each mass to the rotation axis is reduced from R to R/2, as shown in Fig1-b. The rotational inertias of the person and the platform are negligible. Find: (a) the gain of rotation energy; Fig. 1-a. Fig. 1-b. (b) the work done by hands when the weights were pulled in. 2. A cart consists of a body of mass m and two wheels, each of mass M and radius R. The cart is attached to a spring of constant k. The other end of the spring is fixed to a wall as shown in Fig. 2. Find an expression for the horizontal oscillatory motion of the cart. k m R M Fig. 2. 5
3. The cycle in Fig. 3 represents the operation of a gasoline internal combustion engine. Assume the gasoline-air intake mixture is an ideal gas with γ = 1.30. What are the ratios (a) T 2 /T 1, T 3 /T 1 and T 4 /T 1, (b) p 3 /p 1 and p 4 /p 1? (c) What is the engine efficiency? Fig. 3. 4. Figure 4 shows a parallel-plate capacitor of plate area A and plate separation d. A potential difference V 0 is applied between the plates. The battery is then disconnected, and a dielectric slab of thickness b and dielectric constant κ is placed between the plates as shown. Assume A= 115 cm 2, d = 1.24 cm, V 0 = 85.5 V, b = 0.780 cm, and κ = 2.61. (Permittivity constant ε 0 = 8.85 x 10-12 F/m) Fig. 4. (a) What is the capacitance C 0 before the dielectric slab is inserted? What free charge appears on the plates? (b) What is the electric field E 0 in the gaps between the plates and the dielectric slab? (c) What is the electric field E 1 in the dielectric slab? (d) What is the potential difference V between the plates after the slab has been introduced? (e) What is the capacitance with the slab in place between the plates of the capacitor? 6