1d3exam2003-solutions - PHYSICS 1D03 Day Class Name 3 Lu -...

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Unformatted text preview: PHYSICS 1D03 Day Class Name 3 Lu - Ham/7 Duration of Examination: 3 Hours Student Number Instructors: Dr. Sills (section C01) Dr. McKay (sections C02, C03) Instructor: Dr. Venus (section C04) Dr. Harris (section C05) Lecture Section: McMaster University Final Examination December 2003 THIS EXAMNATION PAPER INCLUDES 1? PAGES AND 26 QUESTIONS. YOU ARE RESPONSIBLE FOR ENSURING THAT YOUR COPY OF THE PAPER IS COMPIETE. BRING AN Y DISCREPANCY TO THE ATTENTION OF YOUR INVIGILATOR. Special Instructions: 0 Only the Casio fic-991 calculator is permitted. 0 Either pen or pencil may be used. 0 Answer all questions directly on the examination paper in the spaces provided. In Part A (multiple choice). only the answer is marked. In Part B, you must provide a solution showing clearly how the answer was obtained. Your solutions may be continued onto the blank page following the last question, if you indicate clearly where this continuation may be found. a In Part A (multiple-choice). each correct answer is worth 2 marks, and wrong or blank answers count as zero. In Part B, a complete and correct solution is worth 3 marks. O A sheet of formulae is attached as the last page of this examination. Do not write solutions on either side of this sheet; they will not be marked. I This paper must be returned with your answers. PLEASE DO NOT WRITE IN THIS AREA continued on page 2... Page 2 of 17 pages Part A (multiple choice): Print the letter corresponding to the best or most nearly correct answer in the box beside each question. Each correct answer is worth 2 marks. 1. Two rocks are dropped from a cliff. one a few tenths of a second after the first. If air resistance is ignored, as they fall LE answer - bf .___ C V, U; j M > o 2. An object rotates such that its angular position varies as a function of time as shown in the graph. The angular acceleration of the object A) is positive 9 B) is negative C) changes from positive to negative D) changes from negative to positive answer fl C0 ikwcfieefin oé>o 3. Two blocks, of masses M and 2M, are in contact on a levei frictionless surface. A force Fp can be applied either to the large block (diagram 1), or to the small block (diagram 2). If the magnitude of F}: is the same in both cases, the force exerted on the small block by the larger one _ Diagram 1 A) is the same it} both diagrams 1 and2 ) F}: M q B) is larger [11 diagram 1 F P 2M '1' C) is larger in diagram 2 D) The answer depends on the magnitude of the force FF answer r )3: W Diagmmz h Q C 3-2 )5 FF iEJ—(é’bd continued on next page... Page 3 of 1'? pages 4. A box weighing 200 N is pulled at constant speed along a level floor by a force F 9 =10() N which is at an angle of 37° to the horizontal. The coefficient of sliding friction is A) 0.4 FP B) 0.5 o C) 0.6 37 D) 0.3 10020 answer C k T, Q0 ,1) ZOOM — 00,0 —. N606 A g _ fl 1 .6. y 0 , S” 7 k x 40 5. Two rods of different lengths are held at a small angle to the vertical, with one end on the floor. The)r are released from rest and fall over. Assuming they do not slip on the floor, the angular acceleration A) is the same for both sticks B) is larger for the longer stick C) is larger for the shorter stick D) depends on whether the rods are made of the same material 1 Q 1 ‘ answer /\ g/h-x.’ Q L --r wj Z 2" c “'3 IoOmji 4: 7%"de l :__w’ __ ‘X I W “C a 6. A mass m is suspended, as illustrated. from two wires making angles of 60° and 30° with the horizontal. The tension in the shorter wire is A) mg ‘ mo V B) 0.87 mg C) 0.58 mg D) 0.50 mg answer 8 continued on next page... Page 4 0f 17 pages 7. A uniform plank of mass m is balanced on a point situated U3 of the way along the length of the plank. by placing a block at one end of the plank. The mass of the block is A) m B) m C) 2m D) 3m answer ’9 E (4 8. The torque that a particular electric motor can provide is small when the motor isn't rotating, increases to a maximum at 2400 revolutions per minute (rpm), then decreases to zero as motor speed increases to 3600 rpm. The rotation rate at which the motor can provide maximum power is U T a: me A) 3600 rpm. B) 2400 rpm. 00 (4) C) greater than zero but less then 2400 rpm. torque a PC 3 D) greater than 2400 rpm but less than 3600 rpm. 5'19le r B) zero rpm, as long as the torque is not zero at this speed. answer . ? ‘: 7: 9 C4) mm D 2400 3600 9. A man walks once amund a square path in an open field, starting and finishing at the same corner. There is a strong wind blowing from the North. which exerts a force of 100 N on him in the direction it is blowing. The square is 100 m on each side, and oriented so that the sides are exactly east-west and north-south. How much work does the wind do on the man over the whole path? A)OJ B) 10000] .s 0200001 (OOUVYIOUM-t (*kaleCIW-x) ‘0 D)40000] answer Pr continued on next page... Page 5 of 1? pages 10. A block slides along a surface with a measured velocity v = (1.8 i 0.1) nuts and has a mass measured at m = (1.85 i 0.09) kg. The absolute uncertainty in its kinetic energy is 3332?} 9y: a 93‘ E .37 33:2: v '8 ’ w ’68 E) 0.5] Id“: 1 W I ‘- 3 00 3, answer 2’ 0/ fl ' l; {{le ékfilflw: 0/0 bk“? 0.493 11. Two solid spheres with different masses and different radii roll down the same ramp. starting at rest from the same height. When they reach the bottom, they have l ‘\ A) equal velocities / L 1 _ B )L — “\(f B) equal momenta 7L K '1; MM -}— ,Jz'. IL) " I C) equal kinetic energies¢ fl) D) none of the above. 7/, C, 5 5 answer fl 1M} )4: Melt) U": lf~éW¢jAk 12. A puck and stick are both sliding on a frictionless surface when they have an elastic collision. The collision conserves A) energy and momentum only B) momentum and angular momentum only C) energy and angular momentum only D) energy, momentum. and angular momentum. K Answer D continued on next page... Page 6 of 17 pages I3. A string is wrapped around a cylinder and pulled with a horizontal force T, so that the cylinder rolls on level ground. The horizontal force T acts parallel to the top surface of the cylinder as shown in the diagram. The force of friction on the cylinder points: _A) Tothelcfi. flag“ p as Sivan T a" o ierlg t. I C) IsZero. D) Notenoughinformation. CM ‘fi" #674“ at“ C answer m a _: Tff (D (3)" C9: LIMP-L) 1‘ “2‘0 ) 14. An open-topped railroad car is coasting along a horizontal track with initial velocity v0. Rain falls vertically into the car at a constant rate. Ignoring air resistance and friction at the wheels. the acceleration a of the car A) is zero. 5 non-zero and 3 increases with time. M inciting-g) P 4015M I IS non-zero, an constant in time. “55 her” Contain/ti, C7 "(QCMQVDC answer 1M 0‘ 0 tr: _——-—" ° -~ Lt} i : 4—6ch 5.9;) m U' 1c k IS. A particle of mass 1 kg moves in the xy plane. lf‘its position at a certain time is given by r = (5 i — 5 j) mm and its veloci b v = (6 i) mfs, then its angular momentum, relative to the origin, at that time is A) 30 k kg‘mzls : 'I 3 gm 5 i- -mzs :3 A a an ass ’ n x» a v— ..tp m «a m 2 I l 1.. J TC") \F‘ r m\" continued on next page... Page 7 of 17 pages 16. A verticai axle holds a bicycle wheel which is rotating quickly in the clockwise direction. in the horizontal plane. ‘5 applied so that the top of the axle tips to the right. The torque vector must point A) to the left ' - e ng t C) into the page D) out of the page. answer ‘1) fl 7:: egg, A: 1?. A simple pendulum swings back and forth with an amplitude of 10° degrees and a period of 2.0 seconds. The time it takes to swing from B = 10° to B = 5° is g? ‘ second D) U8 second fl 18. If displacement is zero at the equilibrium position. which statement best describes the kinematics of a simple harmonic oscillator? A) Displacement and velocity are always in the same direction. 3L B) Displacement and velocity are never in the same direction. fi- ! 'splacement and acceleration are always in the same direction. < m n lacement and acceleration are never in the same direction. L—r answer T) continued on next page... /'?w~)s4 Page 8 of 17 pages Part B (Problems): Write a clear solution showing how the answer is obtained. Each problem is worth 3 marks. 19. A ball thrown straight up from the ground reaches a height of 10.0 m at a time 0.80 s after it is thrown. Find the next time it is 10.0 m above the ground. gfiumrm .HQ 7; €a/Lné’i {:0‘85 “‘4 M ma?!) , ma. .2 a 1-. /ér42 % :5) “of J. ijf 8'9 {(0.83 Pk | Rs is ix m E ‘K’ N N. 5 f l ‘10 \ m w continued on next page... Page 9 of 17 pages 20. A racing car drives in a horizontal circle at constant speed on a road banked at angle 6' to the horizontal. When the speed is chosen so that there is no sideways frictional force on the car. the normal force on the car is equal to 1.5 times its weight. Calculate the radial acceleration of the car at this speed. Citra— 4L. answer // “:42 continued on next page... Page 10 of 17 pages 21. A cylinder of radius R = 5.0 cm rotates, with friction, about an axle through its center. A mass m = 0.60 kg is suspended from a string wrapped around the cylinder as shown. When the system is released. the cylinder rotates with constant angular acceleration 36 radiansisecond. If the moment of inertia of the cylinder, about the axle. is I = 0.0050 kglm , calculate the frictional torque the axle exerts on the cylinder. answer 0. 060 /U'~x ?_-_==.. continued on next page... '20'V0 Page 11 of 17' pages 22. The truss ABCD is made of members with negligible mass forming equilateral triangles. and supports a weight of 600 N at pin C. The truss is fixed at pin A. and supported at pin D. Find the internal force in member BD. and state whether this is a compressive or tensile force. P“ C v 8341' continued on next page... . J I, ,1 5 ll W Page 12 of 17 pages 23. The pulley shown rotates about a frictiouless axle. If the pulley and two blocks are released from rest, find the speed of the block M after it has fallen 25 cm, given moment of inertia I = 0.040 kg-mz and radius R = 5.0 cm for the pulley; m = 2.5 kg; and M = 5.0 kg. continued on next page... 40' Page 13 of 1? pages 24. A ISO-gram ball dropped from rest from a height of 10.0 m bounces off the floor and rebounds to a height of 7.0m. Find the impulse imparted to the ball by the floor. jiwbj: :Zx U]: U: W " Milk/‘5 MM /. M 1 View /7 4&7” I! continued on next page... 49 : (,1 Page 14 of 17 pages 25. A pendulum is comprised of a mass of 100 g at the end of a 50 cm string. If the pendulum has its maximum positive angular velocity of 1.5 radiaan at the time t = 0.80 s. write the angle the string makes with the vertical as a function of time in the form 6 P [Mm __ O 6(r)=6locos (wt+¢). I \ r21 éflbbT and evaluate the constants €90. a). and $3. fl: Jr try/W] ($670))“ Ms. J answer _} 90 r or Foe/j L1) :— 6/ (v2??°) fl: .— 3’. //rr~/ ___#___,_._ _ ! _____.___._————__.___ / continued on next page... Page 15 of l? pages 26. Draw graphs. including as much useful information as possible, of: a) vertical acceleration as a function of time for an elastic bouncing ball. a ( 77% ~16 b) tangential acceleration as a function of time for a swinging pendulum. c) angular acceleration as a function of time for a rotating disc with a constant, negative torque due to frictiOn. Oz 6W6? END OF EXAMINATION continued on next page... (7'09 ...
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This note was uploaded on 02/05/2010 for the course PHYSICS 1D03 taught by Professor N. mckay during the Spring '08 term at McMaster University.

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1d3exam2003-solutions - PHYSICS 1D03 Day Class Name 3 Lu -...

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