Faculty of Engineering and Department of Physics ENPH 131 Final Examination Saturday, April 20, 2013; 2:00 pm 4:30 pm Universiade Pavilion Section EB01 (BEAMISH): Rows 1, 3, 5(seats 1-45) Section EB02 (FENRICH): Rows 5(seats 46-50), 7, 9, 11(seats 1-40) Section EB03 (RUHL): Rows 11(seats 41-50), 13, 15, 17(seats 1-15) Section EB04 (RAHMAN): Rows 17(seats 16-50), 19, 21, 23(1-10) Section EB05 (NEDIE): Rows 23(seats 11-50), 25, 27, 29(seats1-5) Section EB06 (ROPCHAN): Rows 29(seats 6-50), 31, 33 1. No notes or textbooks allowed. 2. Non-programmable calculators approved by the Faculty of Engineering are permitted. 3. There are two separate parts to this exam. Part A is composed of 3 problems and follows this instruction page. Part B is composed of 20 multiple choice questions and is a separate set of pages. For the problems write your solutions directly on the pages with the questions. You may write on both sides of the pages if needed. For the multiple choice questions indicate your answers on the General Purpose Answer Sheet provided. 4. Formula sheets are included at the end of the multiple choice questions. These may be removed. 5. Write your name and student ID number below and circle your section number. 6. Enter your name, student ID number, and class section number on the General Purpose Answer Sheet. Enter your student ID number under Identification Number beginning in the first column. Enter your class section number under Special Codes. For example if your section number is EB01 then enter 1 in the first column of Special Codes. 7. Show all work for the problems in a neat and logical manner. 8. The value of each question is indicated in the table below. Budget your time accordingly. 9. When finished please hand Part A (this part) and the General Purpose Answer Sheet to the appropriate section location at the back of the Pavilion where your instructor or designate will be collecting them. If you finish during the last 10 minutes of the exam time, i.e. after 4:20 pm please remain in your seat until the end of the exam period. LAST NAME: FIRST NAME: ID#: Please circle the name of your instructor: EB01: Beamish EB02: Fenrich EB03: Ruhl EB04: Rahman EB05: Nedie EB06: Ropchan
2 Please do not write in the table below. Question Value (Points) Mark Part A: Problem 1 6 Part A: Problem 2 5 Part A: Problem 3 6 Part B: Multiple Choice Questions 1-20 20 (1 mark each) Total 37
3 Problem 1. (6 marks) A block of mass m = 0.170 kg slides down a semicircular ramp of radius r = 0.800 m. The coefficient of kinetic friction is k = 0.350. a) Draw free body and kinetic diagrams for the block when it is at an angle as shown on the diagram. Clearly indicate the directions of all forces and accelerations. b) At what speed v would the block fly off the ramp at = 35.0 o? c) Now, assume the block is moving at 2.30 m/s at this position ( = 35.0 o ). Find the magnitude and direction of the block s acceleration a at this point. Is the block s speed increasing or decreasing? Is its horizontal speed increasing or decreasing?
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5 Problem 2. (5 marks) A 1.00-lb ball A is traveling horizontally at 20.0 ft/s when it strikes the centre of a 10.0-lb block B that is at rest. If the coefficient of restitution between A and B is e = 0.6, and the coefficient of kinetic friction between the plane and the block is µ k = 0.4, determine the time for the block B to stop sliding. 20.0 ft/s at rest m A = 1.00 lb A B m B = 10.0 lb
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7 Problem 3. (6 marks) A spool consists of two uniform disks of radius R = 0.750 m joined to a smaller uniform disk (hub) of radius r = 0.250 m at their common centres. The spool has a total mass of m = 2.00 kg and moment of inertia about its centre of I o = 0.540 kg. m 2. The spool has a light rope wrapped around the hub and a force of F = 10.0 N, parallel to the incline, is applied to the free end of the rope as shown. This causes the spool to accelerate up the incline, rolling without slip as it does so. The angle of the incline is 30.0 o to the horizontal. a) Draw the Free-Body and Kinetic Diagrams (FBD/KD) of the spool. You may use any of the symbols listed above, as well as: f S (static friction), K f (kinetic friction), a (linear acceleration), (angular acceleration), N (normal force), g (gravitational acceleration). b) What is the magnitude of the acceleration of the centre of the spool? c) Determine the friction force acting on the spool, expressing your answer as a magnitude and direction with respect to the nearest horizontal. Is the friction static or kinetic? View of spool from front.
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Faculty of Engineering and Department of Physics ENPH 131 Final Examination Part B (Question pages not to be handed in) Saturday, April 20, 2013; 2:00 pm 4:30 pm Universiade Pavilion PART B: Multiple Choice Questions. Mark the correct answer on the General Purpose Answer sheet. There is only one correct answer per question. (20 Questions worth 1 mark each) Formula sheets are attached after the multiple choice questions. These may be removed. There are two corrections/additions to the formula sheets as follows: 1. The equation for static friction on the first page of the formula sheets should read: Static Friction Force s N, where s is the coefficient of static friction and N is the normal force. 2. The formula sheets should also contain the following: For a continuous function F(t), the average value of F over a given interval t is given by the following equation:
2 Questions1-3. In the figure below a block of mass m, initially at rest, slides from A to C along a frictionless ramp. It then passes through a horizontal region CD where a frictional force acts on it and it comes to rest at point D. Note that the force of gravity acts vertically downwards. Answer the following questions: A C D B 1. The work done by gravity as the block moves from point A to point C is a) positive b) negative c) zero d) There is insufficient information to determine the correct answer. 2. As the block moves from point A to B the mechanical energy, i.e. the sum of kinetic and potential energy, of the block a) increases b) decreases c) remains constant d) There is insufficient information to determine the correct answer. 3. Suppose the speed of the block at point C is v c. If a similar block of mass 2m slides from rest at point A, where will the block of mass 2m come to rest? a) to the left of point D b) at point D c) to the right of point D d) There is insufficient information to determine the correct answer. 4. At time t = 0, a particle moving along an x axis is at position xo = -20 m. The signs of the particle s initial velocity vo (at time t = 0) and constant acceleration a are, respectively, for four situations: (1) +,+ ; (2) +,- ; (3) -,+ ; (4) -,-. In which of these four situations will the particle pass through the origin just once? a) (1) and (2) b) (3) and (4) c) (1) and (3) d) (2) and (4) e) (1) only
3 Questions 5-6. A wedge of mass M rests on a frictionless surface. A block of mass m = M/2 is placed on it with an initial speed of zero as shown below. The block then begins to slide down the wedge, causing the wedge to move on the horizontal surface. There is no friction between the wedge and the block. When the block passes the midway point B on its way down the wedge, the speed of the wedge is measured to be 1 m/s. Note: the force of gravity acts vertically downward. m M B 5. Which one of the following statements is true about the system consisting of both the wedge and the block? a) During the motion, both the linear momentum and the energy of the system are conserved. b) During the motion, only the linear momentum of the system is conserved, while the energy of the system is not conserved. c) During the motion, only the energy of the system is conserved, while the linear momentum of the system is not conserved. d) During the motion, neither the linear momentum nor the energy of the system is conserved. 6. Which one of the following is true about the speed of the block v m when it passes point B on its way down the wedge? a) v m < 1 m/s b) v m = 1 m/s c) 1 m/s < v m < 2 m/s d) v m = 2 m/s e) v m > 2 m/s 7. A pulley in a vertical plane of mass m = 1kg, and radius, r = 5 cm, has a downward force F applied to its rim as shown. The pulley is a uniform solid disk and is free to rotate about a horizontal frictionless axis through its centre. The force F varies with time, t, according to the graph shown. If the pulley is initially at rest when t = 0, what is the angular momentum of the pulley when t = 8s? r F F 1 N a) 0.3 kg. m 2 /s b) 6 kg. m 2 /s c) 30 kg. m 2 /s d) 40 kg. m 2 /s e) 8 kg. m 2 /s 0 4s 8s t
4 8. Two balls collide in space where the only external force acting on the balls is the force of gravity which can be considered to be a non-impulsive force during the collision. The coefficient of restitution for the collision is 0 < e < 1. Which of the following statements is correct? (Note: In each statement momentum and kinetic energy refer to the total momentum and total kinetic energy, respectively, for the two ball system.) a) Both momentum and kinetic energy are conserved. b) Momentum is conserved, but kinetic energy is not conserved. c) Momentum is not conserved, but kinetic energy is conserved. d) Neither momentum nor kinetic energy is conserved. e) Momentum is sometimes conserved, but kinetic energy is always conserved. Questions 9-10. A 200g ball is attached to a string of negligible mass that passes through a hole in the centre of a horizontal frictionless table. 9. The ball is travelling on a circular path about the centre of the table with an initial speed of 0.2 m/s when the length of the string between the ball and centre of the table is 20cm. What is the angular momentum of the ball? a) 0.008 Js b) 0.0016 Js c) 0.04 Js d) 0.8 Js 10. Someone pulls the rope through the hole in the table. Determine the ratio between the initial and final speed, v 1 and v 2, of the ball when the initial and final distances between the ball and centre of the table are r 1 and r 2 respectively. The initial and final speed of the ball is measured before and after the string is pulled through the hole respectively. In other words, the string is not being pulled at the instant that either speed is measured. a) v 2 /v 1 = (r 1 /r 2 ) 2 b) v 2 /v 1 =m (r 1 /r 2 ) c) v 2 /v 1 = r 1 /r 2 d) v 2 /v 1 = r 2 /r 1 11. Suppose that you stand at the edge of a 200 ft cliff and throw three different rocks at the same initial speed in the three directions shown. Rank from largest to smallest, indicating any ties, the magnitude of the velocity of each rock just before it hits the ground. 1 2 3 a) v 1 > v 2 > v 3 b) v 3 > v 2 > v 1 c) v 2 > v 1 = v 3 d) v 1 = v 2 = v 3
5 12. A block of mass m sits on a horizontal turntable at a distance r from the center, about which it rotates. See the figure below which shows the block and turntable looking down from above. The coefficients of friction between the block and turntable are k = s = 0.3. The turntable slowly accelerates until the block begins to slide at the position shown below. Which of the 4 paths on the diagram best show the subsequent path of the block? a) Path 1 b) Path 2 c) Path 3 Path 1 d) Path 4 r m Path 2 Path 4 Path 3 13. A wheel (on the left in the diagram below) and a uniform solid disc (on the right), having equal radii and masses, have light strings wrapped around their circumferences. Hanging from the strings, halfway between the disc and hoop, is a block of mass m, as shown below. The wheel and disc are both free to rotate about their centers without friction and the mass of the spokes in the wheel is negligible. Complete the following sentence with the correct statement. When the block is allowed to fall, does it stay on the center line, move toward the left, or move toward the right? a) stays on the center line. b) moves toward the left. c) moves toward the right.
6 14. Cars A, B and C each have a mass of 2,000 kg and an initial velocity of 35 m/s perpendicular to a wall. Car A crashes into the wall and ends up as a crumpled heap attached to the wall. Car B crashes into the wall and rebounds with a velocity of 5 m/s. Car C bounces off the wall and rebounds with a velocity of 35 m/s. Note the wall is perfectly rigid and does not move. Which car is subjected to the greatest impulse (consider only the magnitude of the impulse)? a) Car A b) Car B c) Car C d) None of the above Questions 15-16. A 50.0 kg hockey player A is skating with a speed of 1.00 m/s and doesn t see the opposing player approaching him for a body check. The 100 kg opposing player B is moving with a speed of 2.00 m/s in the direction opposite the velocity of A. Assume that the collision between the two players is perfectly plastic (inelastic), the collision takes 0.200 s, and the ice is frictionless. 15. What is the magnitude of the average force generated on the 50.0 kg hockey player by the 100 kg hockey player? a) 100 N b) 200 N c) 500 N d) 1000 N 16. How much kinetic energy is lost in this collision? a) 225 J b) 150 J c) 75 J d) 50 J 17. The 40-N crate is released from rest on the smooth inclined surface with the spring unstretched. The spring constant is k = 8 N/m. The angle of the inclined surface is 30 o to the horizontal. How far down the inclined surface does the crate slide before it stops? a) 10 m b) 9 m c) 5 m d) 2 m
7 Questions 18-19. The bar is smooth with no friction. The 10.0 kg slider at A is given a downward velocity of 7.50 m/s. 18. Does the slider reach point D? Answer yes or no. a) Yes b) No 19. What is the magnitude of the normal force the bar exerts on the slider as it passes point B? a) 857 N b) 759 N c) 661 N d) 185 N 20. Part of the gear system of a printer is shown in the figure below. The gears are in mesh which is equivalent to two circles rotating against each other without slipping. Gear A (with radius of r A = 2 cm) is initially at rest at time t = 0 and then begins to turn with a counterclockwise angular acceleration of A = 2t (rad/s 2 ), where t is in seconds. What is the angular velocity, c, of gear C at t = 4s? (r C = 4 cm, and r B = 10 cm) a) 32 rad/s counter-clockwise b) rad/s clockwise c) 16 rad/s counter-clockwise d) 8 rad/s counter-clockwise e) 8 rad/s clockwise
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Weight = mg Static Friction Force = s N, where s is the coefficient of static friction and N is the normal force Kinetic Friction Force = k N, where k is the coefficient of kinetic friction and N is the normal force Spring Force = ks, where k is the spring constant and s is the stretch or compression of the spring from its equilibrium position Some Physical Constants: Acceleration due to gravity, g = 9.81 m/s 2 = 32.2 ft/s 2 Gravitational constant, G = 6.673x10-11 Nm 2 /kg 2 Radius of the Earth, R E = 6.37x10 6 m Mass of Earth, M E = 5.98x10 24 kg Speed of light in vacuum, c = 3.00x10 8 m/s 11
sin + sin = 2 sin[(1/2)( + )]cos[(1/2)( - )] cos + cos = 2 cos[(1/2)( + )]cos[(1/2)( - )] 12
c < 0 13