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Unformatted text preview: Print Name: ____________________ Student No._________ MC P1 P2 P3 P4 Total PHYSICS 024 1st MIDTERM EXAM Saturday, 19 November 2005 Time: 10:00 AM - 12:30 PM 1. This is a closed book test. You may use only a calculator, and the list of formulas provided on the last page. If you tear off the last page, please do it carefully so the remaining pages remain stapled. 2. Except for multiple-choice questions, for maximum credit you should supply complete solutions, not just the answers. Don’t forget units! Present all work that you wish to be marked on the page where the problem is stated. You may use the reverse side for rough work. 3. Feel free to use sketches or diagrams in solving the problems. 4. There are 24 multiple-choice questions and 4 problems. For a complete exam, do all the multiple choice questions (make your choice clear!) and any 3 problems. If you do all 4 problems, the best 3 will be counted. Marks: 24(multiple choice) + 3(problems) 12 = 60 Page 1 Take g = 9.8 m/s2 unless stated otherwise. 1. The Newton has units of A. kg m/s B. kg m/s2 C. kg s/m2 D. m2 s/kg E. kg m2/s 2. The coordinate of an object is given as a function of time by x = 7t – 3t2, where x is in metres and t is in seconds. Its average velocity over the interval from t = 0.0 s to t = 4.0 s is: A. –5.0 m/s B. +5.0 m/s C. –11 m/s D. –14 m/s E. +11 m/s 3. The diagram shows a velocity-time graph for a car moving in a straight line. At point Q the car must be: A. moving with zero acceleration B. traveling downhill C. traveling below ground-level D. reducing speed E. traveling in the reverse direction to that at point P 4. The pilot of an airplane notes that its velocity relative to the air is 130 km/h due west. The air is moving in a wind at 60 km/h toward the north. The velocity of the plane relative to the ground is A. 190 km/h at 45o north of west B. 70 km/h at 45o south of west C. 143 km/h due west D. 143 km/h 25o north of west E. 143 km/h 25o south of west 5. An object is not subject to any forces. Which of the following statements is correct? A. It can only be at rest. B. It can move with constant speed in a circular path. C. It can be in motion with a constant speed and direction. D. If it is in motion, it will gradually come to rest. E. It can move in a parabolic path. 6. A particle moves at constant speed in a circular path. The instantaneous velocity and instantaneous acceleration vectors are: A. both tangent to the circular path B. both perpendicular to the circular path C. opposite to each other D. perpendicular to each other E. none of the above 7. A 1500-kg car is being pulled by a tow truck along a horizontal road with an acceleration of 2.0 m/s2. What horizontal force is being exerted by the tow truck on the car if a frictional force of 500 N opposes the motion of the car? A. 500 N B. 1500 N C. 2500 N D. 3000 N E. 3500 N Page 2 8. A 700-kg elevator accelerates downward at 3.0 m/s2. The tension force of the cable on the elevator is: A. 2.1 kN, up B. 2.1 kN, down C. 4.8 kN, up D. 4.8 kN, down E. 9.0 kN, up 9. A 25-kg chair is pushed across a frictionless horizontal floor with a force of 200 N, directed 19° below the horizontal. The magnitude of the normal force of the floor on the chair is: A. 25 N B. 68 N C. 180 N D. 250 N E. 310 N 10. A sofa weighing 1000 N is initially at rest and a horizontal force F is applied to it. The coefficients of static and kinetic friction are μs = 0.30 and μk = 0.10 . Which statement is correct? A. If F = 200 N, the frictional force will be 200 N. B. If F = 200 N, the sofa will start to move. C. If F = 100 N, the sofa will start to move with constant velocity. D. If the sofa moves, a 300-N force will keep it moving with constant velocity. E. None of the above. 11. A book rests on a table, exerting a downward force on the table. The reaction to this force is: A. the force of the Earth on the book B. the force of the table on the book C. the force of the Earth on the table D. the force of the book on the Earth E. the inertia of the book 12. The velocity of a 4.0-N hockey puck, sliding across a level ice surface, decreases at the rate of 0.61 m/s2. The coefficient of kinetic friction between the puck and ice is: A. 0.062 B. 0.41 C. 0.62 D. 1.2 E. 9.8 13. An astronaut who weighs 800 N at the surface of the Earth is in a spacecraft one Earth radius from the surface of the Earth. The gravitational force exerted by the Earth on the astronaut is A. 0 N B. 10 N C. 200 N D. 400 N E. 800 N 14. A 40-kg girl is on a Ferris wheel, which moves in a vertical circle of radius 16 m at 12 m/s. At the bottom of the circle, the seat exerts a force on her of A. 32 N upward B. 32 N downward C. 392 N upward D. 752 N upward E. 752 N downward 15. The work done by a given force is A. negative when it is opposite to the displacement B. greatest when it is perpendicular to the displacement C. the same no matter what the direction of the displacement is D. always positive E. negative when it is perpendicular to the displacement Page 3 16. The three forces acting on a simple pendulum (gravity, tension, air resistance) are to be listed in the order of: 1. the force that always does negative work 2. the force that does no work 3. the force that alternates between doing positive and negative work Which order below is correct? A. B. C. D. E. Gravity, tension, air resistance Tension, air resistance, gravity Air resistance, tension, gravity Air resistance, gravity, tension Tension, gravity, air resistance 17. A 0.40-kg ball is dropped from a height of 50 m and reaches a speed of 20 m/s just before it hits the ground. How much mechanical energy was lost due to air resistance? (g=10 m/s2) A. 40 J B. 80 J C. 120 J D. 160 J E. 200 J 18. A passenger elevator lifts a given load from the first floor to the tenth in less time than it takes for a freight elevator to do the same lift. A. The freight elevator does less work. B. The passenger elevator does less work. C. The freight elevator operates at a lower power level. D. The passenger elevator operates at a lower power level. E. Both elevators did the same amount of work and operate at the same power level. 19. A 100-W motor is used to pump water from a depth of 20 m. In one minute the mass of water it can raise is (g=10 m/s2) A. 5.0 kg B. 10 kg C. 30 kg D. 100 kg E. 300 kg 20. The woundup spring of a clock possesses: A. kinetic but no potential energy B. potential but no kinetic energy C. both potential and kinetic energy D. neither potential nor kinetic energy E. depends on the system of units 21. The x,y coordinates in metres of the centre of mass of the threeparticle system shown are: A. 0, 0 B. 1.3 m, 1.7 m C. 1.4 m, 1.9 m D. 1.9 m, 2.5 m E. 1.4 m, 2.5 m 22. The mass of an object: A. is slightly different at different locations on the Earth B. is a vector C. is independent of the gravitational force on the object D. is the same for all objects of the same size and shape E. is zero in deep space far from any stars Page 4 23. A 5-kg object can move along the x axis. It is subjected to a force F in the positive x direction; a graph of F as a function of time t is shown. Over the time the force is applied the change in the velocity of the object is: A) 0.8 m/s B) 1.1 m/s C) 1.6 m/s D) 2.3 m/s E) 4.0 m/s 24. A fast car hits the back of a truck moving in the same direction and they become locked together. If frictional forces with the road surface are negligible, A) kinetic energy will be conserved B) they will continue to move at the original speed of the truck C) the centre of mass will come to rest D) the centre of mass will continue to move with the same velocity E) none of the above Page 5 P1. A placekicker must kick a football from a point 36.0 m from the goal, which has a cross bar 3.05 m high. When kicked the ball leaves the ground with a speed of 20.0 m/s at an angle of 57.0o to the horizontal. Neglect air resistance. 2 a. How long does it take for the ball to reach the goal? 2 b. By how much does the ball clear or fall short of clearing the crossbar? 2 c. Does the ball approach the crossbar while still rising or while falling? Show a specific calculation to support your answer. 2 d. Using an energy method, calculate the speed of the ball just as it passes over or under the crossbar. 4 d. State whether each of the following quantities is conserved in the flight of the ball and give a reason for your answer: 1. horizontal component of linear momentum of the ball 2. vertical component of linear momentum of the ball 3. gravitational potential energy of the ball 4. kinetic energy of the ball Page 6 P2. An airplane of mass m is flying in a horizontal circle of radius (dashed line) 3.00 103 m at a constant speed of 100 m/s. The forces acting on it are its weight Fg, and a lift force L, which is always normal to the wings. 2 a. Explain in words why the airplane must bank (tilt) towards the centre of the circle at some angle in order to execute this circular motion. 2 Lift L Weight Fg b. Write Newton’s 2nd Law for the airplane in 2 separate equations, one for the vertical direction and one for the radial direction. 2 c. Use the equations of part b to find tan , and hence the numerical value of in degrees. 2 d. If the airplane’s mass m = 1.20 104 kg , calculate the magnitude of the lift force L. 2 e. During the period that the plane flies along a 1.00-km arc of its circular path, how much work is done on it by each of the forces shown in the figure? Explain. 2 f. Is the linear momentum of the airplane conserved as it flies along its circular path? Explain. Page 7 P3. Students are doing collision experiments with carts on a level air track (negligible friction). In one experiment, a cart of mass 2m is given a velocity vˆ towards a stationary cart of i mass m. 2m vˆ i m 3 a. One student claims that the outcome of the collision is that the cart of mass 2m has final velocity 1 vˆ , while the cart of mass m has velocity vˆ . i 3i Show a specific calculation that tests whether this is a possible outcome, state your conclusion, and explain why your test is valid. 3 b. Another student puts some chewing gum on the back of the stationary cart so that the two carts stick together after the collision. Find the final velocity of the two carts, expressed in i terms of v and ˆ . Explain your method. (Neglect the small mass of the gum.) 2 c. For the chewing-gum collision, calculate the impulse (magnitude and direction) on each i cart. Your results should be expressed in terms of the symbols m, v, and ˆ . 4 d. A third student attaches a small light spring to the back of the stationary cart to create an elastic collision. She claims that the final velocities are 1 vˆ for the cart of mass 2m, and 4 vˆ 3i 3i for the cart of mass m. Apply two tests to decide whether i. the results are possible ii. the collision is really elastic as claimed. Page 8 P4. A 10.0-kg block is released from point A in the adjacent figure. It is eventually brought to rest (momentarily) by a spring with spring constant k = 2.50 103 N/m . 3 A 2.50 m a. Assuming there is no friction anywhere on its path, calculate how fast the block will be moving just before it hits the spring. 3 b. Still assuming no friction anywhere, calculate how much the spring will be compressed at the instant the block comes to rest. 3 3 c. Now instead, assume that there is a rough part of the path between B and C where the coefficient of kinetic friction is 0.15, and zero everywhere else. Calculate how much the spring will be compressed at the instant the block comes to rest. A 2.50 m 3.50 m B C d. Calculate the amount of mechanical energy lost between B and C when this path is rough as described in part c. Where does this energy go? Page 9 FORMULAS AND CONSTANTS CONSTANT ACCELERATION vxf = vxi + ax t x = vxit + 1 ax t 2 2 vxf 2 = vxi 2 + 2ax x x= 1 2 (v xi + vxf )t u r r F ext = ma NEWTON’S 2nd LAW GRAVITY Fg = Gm1m2 r 2 U g = Gm1m2 r and Near surface of Earth Fg = mg and U g = mgy atan = dv dt CIRCULAR MOTION arad = v 2 r inward FRICTION fk = μk N SPRINGS fs μs N Fs = kx Ws = 1 kxi2 2 ENERGY Emech = K + U POWER Pav = W t i mi xi M kx f2 U s = 1 kx 2 2 u r For constant force W = F fk d = K + U ur r Instantaneous P = F v MOMENTUM & CENTRE OF MASS r r r ru r p = mv I = p = F av t xCM = 1 2 yCM = i u r r r F ext = M aCM = dptot dt mi yi M ALGEBRA Solution of ax 2 + bx + c = 0 is x = b ± b2 4ac CONSTANTS g = 9.80 m/s2 G = 6.67 10-11 N m2/kg2 Masses: Mearth = 5.98 1024 kg Msun = 1.99 Radius of the Earth: RE = 6.38 103 km 2a 1030 kg Page 10 r r ...
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