2006 Academic Challenge

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1 2006 Academic Challenge PHYSICS TEST - REGIONAL This Test Consists of 35 Questions Physics Test Production Team Len Storm, Eastern Illinois University Author/Team Coordinator Doug Brandt, Eastern Illinois University Author Kevin Pitts, University of Illinois at Urbana Champaign Reviewer Don Wayman, WYSE Coordinator of Test Production GENERAL DIRECTIONS Please read the following instructions carefully. This is a timed test; any instructions from the test supervisor should be followed promptly. The test supervisor will give instructions for filling in any necessary information on the answer sheet. Most Academic Challenge sites will ask you to indicate your answer to each question by marking an oval that corresponds to the correct answer for that question. Only one oval should be marked to answer each question. Multiple ovals will automatically be graded as an incorrect answer. Be sure ovals are marked as. Not as,,, etc. If you wish to change an answer, erase your first mark completely before marking your new choice. You are advised to use your time effectively and to work as rapidly as you can without losing accuracy. Do not waste your time on questions that are too difficult for you. Go on to the other questions and come back to the difficult ones later if you can. *** TIME: 40 MINUTES *** DO NOT OPEN TEST BOOKLET UNTIL YOU ARE TOLD TO DO SO! 2006 Worldwide Youth in Science and Engineering WYSE, Worldwide Youth in Science and Engineering and the WYSE Design are service marks of and this work is Copyright 2006 Board of Trustees of the University of Illinois at Urbana - Champaign. All rights reserved.

2 Fundamental Constants Quantity Symbol Value Avogadro s number N A x / mol Boltzmann s constant Electron charge magnitude k e x J / K x C Permeability of free space 7 μ o 4π 10 T m/ A Permittivity of free space ε o C / (N m ) Planck s constant h J s Electron mass m e kg Neutron mass m n kg Proton mass m p kg Speed of light in vacuum c m / s Universal gravitational constant G N m /kg Universal gas constant R J / (mol K) 2 2 Assume that the acceleration due to gravity at the surface of the earth is 9.80 m/s 2.

3 WYSE Academic Challenge Physics Test (Regional) The momentum of an object is 18.0 kg m/s east, while its kinetic energy is 20.0 J. What is the mass of the object? a) 4.05 kg b) 16.2 kg c) 8.10 kg d) 32.4 kg e) 2.22 kg For problems 2 through 4, refer to the diagram below. Starting from rest at point A, a tiny block of mass m slides, with increasing speed, down the inside surface of a frictionless spherical shell which is sitting on a table top. The acceleration due to gravity is g in the direction shown. Ignore air friction. g R R R R m A (For problems 2 through 4) B 2. When released from rest at point A, the acceleration of the block is a) zero. b) g. c) mg. d) mgr. e) 2g. 3. When the block reaches point B, the direction of the net force acting upon it is a) up. b) down. c) right. d) left. e) undefined. 4. At the instant the block reaches point B, the magnitude of the acceleration of the block is a) zero. b) g. c) mg. d) mgr. e) 2g. Physics 2

4 5. A boy whose weight, with clothing, is 400. N sits at rest in the middle of a pond on perfectly frictionless ice. The boy then throws his shoe, which has a weight of 15.0 N, in a horizontal direction and with a speed of 30.0 m/s relative to the earth. After throwing the shoe, what is the boy s speed relative to the earth? a) 117 cm/s b) 200. m/s c) 51.2 cm/s d) 800. m/s e) 1.12 m/s 6. An object with a mass of 4.00 kg is traveling eastward at m/s at time t = 0.00 s. If it accelerates with a constant acceleration of 2.00 m/s 2 west, what will the velocity of the object be at t = 8.00 s? a) 2.00 m/s to the east b) 2.00 m/s to the west c) 30.0 m/s to the west d) 30.0 m/s to the east e) none of the above 7. In the situation in problem 6, what is the displacement of the object during the 8.00 s that it is accelerating? a) 176 m to the east b) 64.0 m to the west c) 48.0 m to the east d) 48.0 m to the west e) 16.0 m to the west 8. What is the component of vector A in the direction of unit vector û? a) -48 m b) +84 m c) 83 m d) -55 m e) 48 m 9. A Joule is a unit of a) force. b) electrical power. c) velocity. d) force divided by distance. e) none of the above. û 96 m 30 o A 10. The time rate of change of the momentum of an object is equal to a) the net force acting on the object. b) the net impulse acting on the object. c) the kinetic energy of the object. d) the angular momentum of the object. e) none of the above.

5 Physics A hockey puck attached to the end of a string is whirled on an ice rink surface in a circular path at constant speed. The string is parallel to the ice rink surface. If outward means away from the center of the circle and inward means toward the center of the circle, which of the following is true? a) The puck exerts an outward force on the string, while the string exerts an equal but inward force on the puck. b) The string exerts an outward force on the puck, while the puck exerts an equal but inward force on the string. c) The string exerts a greater force on the puck than the puck exerts on the string. d) The puck exerts a greater force on the string than the string exerts on the puck. e) The net force on the puck is zero. 12. Which of the following represents a proper set of units for electric field? a) N b) N m c) N m / C d) N / C e) C / (N m) 13. To find the direction of the magnetic force on a moving charge, one could use a) Archimedes principle. b) Ampere s circuital law. c) the right hand rule. d) Ohm s law. e) Newton s 3 rd law. 14. A 20.0 m wide by 70.0 m long, rectangular barge is heading due east on Lake Michigan at a rate of 12.0 m/s relative to Navy Pier. The barge captain runs in a straight line along the width of the barge from the north side of the barge to the south side, moving with a constant speed of 4.00 m/s relative to the barge. What is the speed of the captain relative to Navy Pier? a) 4.00 m/s b) 16.0 c) 8.00 m/s d) 12.6 m/s e) none of the above 15. For the same situation as in problem 14, what is the captain s eastward displacement relative to Navy Pier, in the time it takes the captain to move from the north rail to the south rail across the width of the barge? a) 15.0 m b) 60.0 m c) 19.0 m d) 30.0 m e) 66.7 m

6 Frictionless axle V L/2 L/2 Massless, rigid rod Physics A point object, P, of mass m, moving with speed V across the surface of a frictionless table, strikes and sticks to the center point of a massless, rigid rod, causing the rod to rotate without friction about its left end. As shown, the rod has a point object, Q, of mass m, affixed to its right end. The initial direction of motion of P is perpendicular to the rod s length. Considering the system to be P, Q, and the rod, what quantity is conserved at the times just before collision and just after collision? m a) kinetic energy b) angular momentum c) linear momentum d) both a. and b. e) angular speed P Q m 17. For the same situation as in 16, if the angular speed of the rod just after collision is ω f, what is the kinetic energy of the P, Q, and rod system at this time? a) 3mL 2 ω f 2 /8 b) 3mLω f /2 c) ml 2 ω f 2 d) ml 2 ω f 2 /2 e) 5mL 2 ω f 2 /8 18. The unknown weight is held in equilibrium by two horizontal cords and two other cords, as shown. What is the tension in cord A? rigid wall A 47.0 o 50.0 N 10.0 N a) 40.9 N b) 26.6 N c) 46.6 N d) 44.1 N e) 24.1 Unknown weight 19. For the same situation as problem 18, what is the value of the unknown weight? a) 53.6 N b) 34.1 N c) 26.6 N d) 36.6 N e) 46.6 N 20. Two forces act upon an object, a 7.00 N force pulling eastward and a 5.00 N force pulling westward. The object is observed to have an acceleration with magnitude equal to 20.0 m/s 2. What is the mass of the object? a) 40.0 kg b) 1.67 kg c) 10.0 kg d) kg e) kg

7 Physics A 250 gram projectile traveling with an initial velocity of 300. m/s east hits a 5.00 kg block which had a pre-collision velocity of 4.00 m/s east. If the projectile embeds itself in the block, what is the common speed of the projectile and block after the collision? Assume that the surface on which the block slides is horizontal and frictionless m/s 300. m/s 5.00 kg block a) 19.0 m/s b) 294 m/s c) 18.1 m/s d) 67.2 m/s e) 65.6 m/s 22. T 1 and T 2 represent the tensions in two cords that hold a rigid, weightless rod in equilibrium, as shown. What is the value of T 1 /T 2? a) 1 b) 2 c) 3.46 d) e) 1.15 Frictionless axle 30.0 o T 1 Rigid, weightless rod L/2 L/ o T The motion of an object is described by the straight line graph shown below. What is the acceleration of the object at 5.00 s? a) 0.00 m/s 2 b) 8.00 m/s 2 c) m/s 2 d) 200. m/s 2 e) 9.81 m/s 2 Velocity 40.0 m/s 3.00 s 5.00 s 9.00 s time 24. Using the same graph as in problem 23, what is the displacement of the object between 3.00 s and 9.00 s? a) m b) 96.0 m c) m d) 80.0 m e) 48.0 m

8 Physics The motion of an object along the x-axis is described by the following graph. Which one of the following is true? x a) The speed of the object at 2 seconds is greater than its speed at 1 second. b) The speed of the object at 2 seconds is zero. c) The acceleration of the object at 0 seconds is zero. d) Between 0 and 2 seconds the object is moving away from the origin. e) None of the above are true time, s 26. A 5.00 kg block slides along a horizontal, frictionless surface under the action of a force that causes the block to accelerate uniformly from 4.00 m/s to 5.00 m/s in 3.00 seconds. What average power did the force deliver to the block during the 3.00 second interval? a) W b) 20.8 W c) 6.67 W d) 7.50 W e) 67.5 W 27. Two aluminum spheres have the same size and identical polished surfaces, but one has a lead interior making it three times as heavy as the other sphere. The spheres are dropped from the same height at the same time. Ignoring air friction, the time it takes the spheres to reach a horizontal floor below will be a) one third as long for the heavier sphere. b) one ninth as long for the heavier sphere. c) the same for both balls. d) one third as long for the lighter sphere. e) one ninth as long for the lighter sphere. 28. For the same set of spheres as in problem 27, now assume that the amount of air friction acting upon a sphere varies directly with the squared speed of the sphere. The spheres are dropped from the same height at the same time. Which of the following is true? a) The accelerations of the spheres are identical throughout the fall. b) The initial acceleration of the spheres is zero. c) The velocity of the spheres remains constant throughout the fall. d) According to Newton s 2 nd Law, the lighter sphere will reach the floor first. e) According to Newton s 2 nd Law, the heavier sphere will reach the floor first.

9 Physics A mass is attached to the end of a string O and suspended from a fixed support at O, as shown. Five possible force directions are indicated in the diagram. 1 and 5 are tangent to the arc, 2 and 3 lie along the string, and 4 is straight down. The mass is released at position A. When the mass 2 Position A reaches position B on its downward swing, what are the forces acting on the mass? 1 3 Position B a) a centrifugal force acting in the direction of 3 and gravity acting in the direction of b) the string force acting in the direction of 2 and gravity acting in the direction of 4. c) the string force pulling the mass forward in the direction of 5 and gravity in the direction of 4. d) an inertial force in the direction of 1 and gravity in the direction of 4. e) a centrifugal force in the direction of 3, gravity in direction 4, and the string pulling in direction 2. gravity 30. A block of mass 3M with speed 4V and a block of mass M and speed 2V slide toward each other on a frictionless, horizontal surface, as shown. During the interval of time that the blocks make contact, a) the amount of force that A exerts on B is 6 times as great as the amount of force of B on A. b) the amount force that A exerts on B is 3 times as great as the amount force of B on A. c) the amount force that A exerts on B is 2 times as great as the amount force of B on A. d) B exerts the same amount of force on A as A exerts on B. e) B exerts a greater amount of force on A than A exerts on B. 4V 2V Block A 3M Block B M 31. When a small object is placed on the principal axis of a thin lens, 20.0 cm from the lens, a real image is formed on the opposite side of the lens, 5.00 cm from the lens. What is the focal length of the lens? a) cm b) cm c) 6.67 cm d) 4.00 cm e) 25.0 cm

10 Physics A certain point source of light emits photons per second. If a detector with surface area 2.00 cm 2 is placed 40.0 cm from the source, with detector surface perpendicular to a radial line from the source to the detector, approximately how many photons does the detector intercept each second? a) 995 b) 39 c) 75 d) 497 e) 500, At some instant in time, a charged particle is moving with a velocity of 3.00 k ˆ m/s in a region of space where the electric field is 8.00 ˆ i N/C and the magnetic field is 2.00 ˆ j T. What is the magnitude of the force per charge on the particle? Assume that the only forces acting on the particle are the given magnetic and electric forces. a) 14.0 N/C b) 10.0 N/C c) 26.0 N/C d) 22.0 N/C e) 2.00 N/C 34. A certain circuit board has 3 electrical connection points (or nodes) that have been labeled A, B, and C. The following table lists the circuit elements that are connected between the nodes on this circuit board V (ideal) voltage source, positive terminal at A, negative terminal at C 800. ohm resistor connected between A and B 200. ohm resistor connected between B and C If an ideal voltmeter is connected with positive terminal at C and negative terminal at B, what value will it display? a) V b) V c) V d) V e) 7.71 V 35. A 3.00 Ω resistor and a 6.00 Ω resistor are connected in series. If the power being dissipated in the 3.00 Ω resistor is 29.6 W, what is the potential difference across the 6.00 Ω resistor? a) 59.2 V b) 18.8 V c) 14.8 V d) 3.14 V e) 1.57 V

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