pcs211 2019 exam

Studocu is not sponsored or endorsed by any college or university PCS211_FEX_2019 Physics: Mechanics (Toronto Metropolitan University) Studocu is not sponsored or endorsed by any college or university PCS211_FEX_2019 Physics: Mechanics (Toronto Metropolitan University) Downloaded by natalia paz (nataliapaz26@outlook.com) lOMoARcPSD|31885521

Department of Physics PCS 211 - PHYSICS I, MECHANICS Final Exam – December 9 , 2019 Put a check mark beside the name of your professor: Instructions - Read them attentively  For item 100 on your TRS form please fill the exam VERSION number (A or B)  The test consists of 25 multiple choice questions. Answer all questions.  Each question is worth 1 mark (the total mark is 25).  For each multiple choice question: o You need to show all the work you’ve done to arrive at the answ er in the space provided in this booklet. If no work is shown to justify the answer to a question, the resultant mark may be zero, even if the answer in the scantron is correct. o Transfer your choices to the bubble sheet only when you’re sure of them. o Some answers are rounded off a bit so don’t panic ! o Select the option that is numerically closest to your answer, circle it in this booklet and then copy it to the bubble sheet carefully using a pencil.  Duration of the exam: 3 hours.  Pagers and cell phones must be silenced and placed out of reach. Earphones are not allowed. If a phone rings, its owner is responsible for disrupting the exam and the phone will be confiscated or the owner will be asked to leave the room resulting in a zero on the test.  Sharing of pens, erasers and calculators is not permitted.  Talking to another student or glancing over another student’s paper is not permitted and may result in a charge of academic misconduct.  Formula sheets are not allowed. The only calculators allowed are either the Sharp EL-546 or C asio FX-991 . If you are found to have another type of calculator (even if not programmable) it will be confiscated for the duration of the test.  All Ryerson Examination rules apply.  The exam booklet has a total of ** pages. You are responsible for checking that you have all pages. Please Print Clearly: Student:_____________________________ ___________________________ Last Name First Name Student Number: _____________________ Student Section: _______________ Please put the first letter of your family name inside the circle Dr. I. Abbas Dr. J. Yuan Dr. V. Toronov Dr. J. Tanguay Dr. J. Hu Your signature here (no signature, no mark!) Downloaded by natalia paz (nataliapaz26@outlook.com) lOMoARcPSD|31885521

A) α 1 = 20 deg, β 1 = 36 deg, γ 1 = 44 deg B) α 1 = 46 deg, β 1 = 53 deg, γ 1 = 67 deg C) α 1 = 100 deg, β 1 = 30 deg, γ 1 = 4.5 deg D) α 1 = 150 deg, β 1 = 130 deg, γ 1 = 16 deg E) α 1 = 20 deg, β 1 = 130 deg, γ 1 = 110 deg Average 4. A small sphere is hung by a string from the ceiling of a van. When the van is stationary, the sphere hangs vertically. However, when the van accelerates, the sphere swings backward so that the string makes an angle of  with respect to the vertical. Find the acceleration of the van when   10.0  . (a) 5.93 m/s 2 (b) 4.82 m/s 2 (c) 3.69 m/s 2 (d) 1.73 m/s 2 (e) 6.94 m/s 2 Solve The force acting on the sphere which accelerates it is the horizontal component of the tension in the string. Newton's second law for the horizontal motion of the sphere gives T sin  = ma The vertical component of the tension in the string supports the weight of the sphere is, T cos  = mg From the above equations we get, tan a g   Downloaded by natalia paz (nataliapaz26@outlook.com) lOMoARcPSD|31885521

  2 2 tan 9.80 m/s tan10.0 1.73 m/s a g      5. Two blocks of mass 3.50 kg and 8.00 kg are connected by a massless string that passes over a frictionless pulley as shown in the figure. The inclines are frictionless. Find the tension in the string. (a) 21.8 N (b) 27.4 N (c) 34.2 N (d) 42.8 N (e) 50.5 N Downloaded by natalia paz (nataliapaz26@outlook.com) lOMoARcPSD|31885521

8. A highway curve of radius 500 m is designed for traffic moving at a speed of 90 km/h. what is the correct banking angle of the road? Ignore friction. (a) 5.6 ˚ (b) 6.4 ˚ (c) 7.3 ˚ (d) 8.2 ˚ (e) 9.4 ˚ On a banked road, the normal force on a vehicle has a horizontal component that provides the necessary centripetal acceleration. 2 sin r mv F n r     cos 0 cos z F n mg n mg         Dividing the two equations and making the conversion 90 km/h 25 m/s  yields: 2 2 2 (25 m/s) tan 0 128 7 3 (9 8 m/s )500 m v rg            9. It is proposed that future space station create an artificial gravity by rotating. Suppose a space station is constricted as a 1000 m diameter cylinder that rotates about its axis. The inside surface is the deck of the space station. What rotation period w ill provide “normal” gravity? (a) 29 s (b) 32 s (c) 38 s (d) 45 s (e) 63 s Newton’s second law along the r -axis is: 2 r F n mr      cos n  sin n  cos n Downloaded by natalia paz (nataliapaz26@outlook.com) lOMoARcPSD|31885521

To create “normal” gravity, the normal force by the inside surface of the space station equals mg . Therefore, 2 2 2 500 m 2 2 45 s 9 8 m/s g r mg mr T T r g               10. A 2.5-kg object suspended from the ceiling by a string that has a length of 2.5 m is released from rest with the string 40 ° below the horizontal position. What is the tension in the string at the instant when the object passes through its lowest position? Hint: Use the energy considerations. a. 11 N b. 25 N c. 42 N d. 18 N e. 32 N Downloaded by natalia paz (nataliapaz26@outlook.com) lOMoARcPSD|31885521

e. − 4.1 m/s 14. Two particles A and B of equal mass are located at some distance from each other. Particle A is at rest while B moves away from A at speed v . What happens to the center of mass of the system of two particles? (a) It does not move. (b) It moves with a speed v away from A. (c) It moves with a speed v toward A. (d) It moves with a speed ½ v away from A. (e) It moves with a speed ½ v toward A. 15. Due to the gravitational interaction between the two stars in a binary system, each moves in a circular orbit around their center of mass. One star has a mass of 15 x 10 30 kg; its center is located at x = 1.0 AU and y = 5.0 AU. The other has a mass of 3.0 x 10 30 kg; its center of mass is at x = 4.0 AU and y = 2.0 AU. Find the center of mass ( x cm , y cm ) of the system composed of two stars. (1AU = distance between the Earth and the Sun = 1.5 x 10 8 km) (a) (0.94AU, 4.83 AU) (b) (4.83AU, 0.94 AU) (c) (4.5AU, 1.5 AU) (d) (1.5AU, 4.5 AU) (e) (1.5AU, 0.94 AU) EASY M = m 1 + m 2 = 15 x 10 30 kg + 3.0 x 10 30 kg = 18 x 10 30 kg x cm = ( m 1 x 1 + m 2 x 2 ) / M= (15x10 30 kg x1.0AU + 3.0x10 30 kg x 4.0AU)/18 x 10 30 kg = 1.5 AU Downloaded by natalia paz (nataliapaz26@outlook.com) lOMoARcPSD|31885521

y cm = ( m 1 y 1 + m 2 y 2 ) / M= (15x10 30 kg x5.0AU + 3.0x10 30 kg x 2.0AU)/18 x 10 30 kg = 4.5 AU 16. The rotating blade of a blender turns with constant angular acceleration 1.5 rad/s 2 . How much time does it take to reach an angular velocity of 36.0 rad/s, starting from rest? (a) 7.59 s (b) 17s (c) 12s (d) 24 s (e) 15.2 s AVERAGE ? ? 2 = ? ? 2 + 2?? ? = ( 36 ??? ? ) 2 2( 1.5??? ? 2 ) = 432??? ? = ? ? ? + 1 2 ?? 2 ? = √ 432?2 1.5 = 24? 17. A discus thrower moves the discus in a circle of radius 80.0 cm. At a certain instant, the thrower is spinning at an angular speed of 10 rad/s and the angular speed is increasing at 50 rad/s 2 . Find the magnitude of the total acceleration of the discus at this instant. (a) 40 ? ? 2 (b) 80 ? ? 2 (c) 120 ? ? 2 (d) 89.4 ? ? 2 (e) 69.3 ? ? 2 AVERAGE ? ? = ?? = (0.8?) (50 ??? ? 2 ) = 40 ? ? 2 ? ? = ? 2 ? = ( 10??? ? ) 2 (0.8?) = 80 ?/? 2 ? = √? ? 2 + ? ? 2 = √(40 ? ? 2 ) 2 + (80 ? ? 2 ) 2 = 89.4 ? ? 2 Downloaded by natalia paz (nataliapaz26@outlook.com) lOMoARcPSD|31885521

19. Determine the moment of the force F about an axis extending between A and C . (a) 8.09 lb∙ft (b) 12.1 lb∙ft (c) 14.4 lb∙ft (d) 16.6 lb∙ft (e) 19.9 lb∙ft Downloaded by natalia paz (nataliapaz26@outlook.com) lOMoARcPSD|31885521

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Find the moment of inertia about an axis that passes through mass A and is perpendicular to the page. (a) 1 2 g∙m 2 (b) 8.2 g∙m 2 (c) 7.5 g∙m 2 (d) 6 .2 g∙m 2 (e) 4.1 g∙m 2 SOLUTION: 2 2 2 2 2 A A A B B C C D D 2 2 2 2 2 (0 100 kg)(0 m) (0 200 kg)(0 08 m) (0 300 kg)(0 1281 m) (0 200 kg)(0 10 m) 0 0082 kg m i i i I m r m r m r m r m r                     22. A 10 g bullet traveling at 400 m/s strikes a 10 kg, 1.0-m-wide door at the edge opposite the hinge. The bullet embeds itself in the door, causing the door to swing open. What is the angular velocity of the door just after impact? Model: For the bullet + door system, the angular momentum is conserved in the collision. The moment of inertia of the door is m D L 2 /3 where m D is the mass of the door. (a) 9.8 rad/s (b) 6.9 rad/s (c) 4.9 rad/s (d) 3.9 rad/s (e) 1.2 rad/s Solution: As the bullet hits the door, its velocity v is perpendicular to r  Thus the initial angular momentum about the rotation axis, with , r L  is 2 i B B (0 010 kg)(400 m/s)(1 0 m) 4 0 kg m /s L m v L       After the collision, with the bullet in the door, the moment of inertia about the hinges is door bullet I I I   2 2 D B 1 3 m L m L   2 2 2 1 (10 0 kg)(1 0 m) (0 010 kg)(1 0 m) 3 343 kg m 3         Therefore, 2 f (3 343 kg m ) L I       Using the angular momentum conservation equation 2 f i (3 343 kg m ) L L     2 4 0 kg m /s  and thus 1 2 rad/s     23. A 2.0 kg object moving to the right with speed 0.50 m/s experiences the force shown. What are the object’s speed and direction after the force ends? a) 0.50 m/s left b) 0. 00 m/s At rest c) 0.50 m/s right d) 1.0 m/s right e) 2.0 m/s right Downloaded by natalia paz (nataliapaz26@outlook.com) lOMoARcPSD|31885521

24. Four students run up the stairs in the time shown. Which student has the largest power output? (b) ANSWEWR: B 25. Two blocks of masses m 1 and m 2 are connected by a light cord that passes over a pulley of mass M , as shown. Block m 2 slides on a frictionless horizontal surface. The blocks and pulley are initially at rest. When m 1 is released, the blocks accelerate and the pulley rotates. The total angular momentum of the system of the two blocks and the pulley relative to the axis of rotation of the pulley is (select one correct answer) a) the same at all times. b) proportional to ℓ 1 , the length of string from the pulley to m 1 . c) proportional to ℓ 2 , the length of string from the pulley to m 2 . d) conserved because the Earth doesn’t move. e) proportional to the velocity of the blocks. Downloaded by natalia paz (nataliapaz26@outlook.com) lOMoARcPSD|31885521