Name _______________________________________________________________________ Exam #2 Physics I Fall 2007 Print your name on every page and circle section number below. 1 2 3 5 9 6 7 10 8 M/R 8-10 (Washington, DCC308) M/R 10-12 (Yamaguchi, DCC308) M/R 12-2 (Yamaguchi, DCC308) M/R 2-4 (Eah, DCC318) M/R 4-6 (Eah, DCC318) T/F 10-12 (Malak, DCC324) T/F 12-2 (Wetzel, DCC324) T/F 12-2 (Adams, DCC308) T/F 2-4 (Adams, DCC308) Questions Part A Value 60 Part B 15 Part C 25 Total 100 Score You may detach the formula sheet, but leave exam pages attached. Cheating on this exam will result in an F in the course. 1 Name _______________________________________________________________________ Part A – Multiple Choice (6 points each) Circle the letter of the best answer. 1. A car weighing 8000 N is traveling at 12 ms along a horizontal road when the brakes are applied. The car skids to a stop in 40 s. How much kinetic energy does the car lose in this time? A. 48 £ 104 J B. 59 £ 104 J C. 12 £ 105 J D. 58 £ 105J E. 48 £ 106 J 2. Suppose want to express units in terms of force (F), velocity (V) and time (T) whenever possible. The dimensions of potential energy are then: A. F/T B. FVT C. FV/T D. F/T2 E. FV2/T2 3. A 020 kg particle moves object. The potential energy where is the coordinate of it is at = 10 m, what is A. 0 along the axis due to its interaction with a stationary is given by () = (80 Jm2)2 + (20 Jm4)4, the particle. If the particle has a speed of 50ms when its speed when it is at the origin? B. 25ms C. 57ms D. 79ms E. 11ms 4. A wedge with a mass of 10 kg is at rest on a horizontal frictionless surface. A block with a mass of 50 kg is placed on top and slides down the incline, also starting from rest. The surface of the wedge is rough. At one instant the vertical component of the block's velocity is 30 ms and the horizontal component is 60 ms. At that instant the velocity of the wedge is: A. 30ms to the left 2 Name _______________________________________________________________________ B. 30ms to the right C. 60ms to the right D. 60ms to the left E. 17ms to the right 3 Name _______________________________________________________________________ 5. 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. perpendicular to each other D. opposite to each other E. none of the above 6. A block is suspended by a rope from the ceiling of a car. When the car rounds a horizontal curve with a radius of 45 m radius at 22 ms, what angle does the rope make with the vertical? A. 0± B. 25± C. 48± D. 65± E. 90± 7. A wheel with a diameter of 12 m has a constant angular acceleration of 50 rads2. The tangential acceleration of a point on its rim is: A. 50 rads2 B. 30ms2 C. 50ms2 D. 60ms2 E. 12ms2 8. The value of this product of unit vectors, k (k i ) , is: A. zero B. +1 C. -1 D. 3 E. 1.73 9. A playground merry-go-round has a radius of 30 m and a rotational inertia of 4 Name _______________________________________________________________________ 600 kg m2. It is initially spinning at 080 rads when a 20 kg child crawls from its center to the rim. When the child reaches the rim the angular velocity of the merrygo-round has magnitude: A. 062 rads B. 073 rads C. 080 rads D. 089 rads E. 11 rads 10. The unit kg¢m2/s can be used for: A. angular momentum B. rotational kinetic energy C. rotational inertia D. torque E. power Part B – (3 points each) Circle the letter of the best answer. The space shuttle launches a rigid satellite upward as shown. During the launch it spins the satellite on an axis through its center of mass then pushes it out. As it sets the satellite spinning it fires small rockets that keep the shuttle stationary, reducing the mass of the shuttle. Neglect the orbital motion of the system around the earth. 1. The rotational inertia of the satellite during the launch, A. increases B. decreases C. stays positive D. stays negative 2. The rotational kinetic energy of the satellite during the launch, 5 E. none of these Name _______________________________________________________________________ A. increases B. decreases C. is negative D. is upward E. none of these 3. The angular velocity of the satellite after launch is, A. upward B. downward C. increasing D. decreasing E. none of these 4. The angular velocity of the shuttle after launch is, A. upward B. downward C. increasing D. decreasing E. none of these 5. The magnitude of the angular momentum for shuttle plus satellite during launch, A. increases B. decreases C. stays constant E. none of these 6 Name _______________________________________________________________________ Part C – Numerical Problem (25 points) A conservative force F ((7.0 N / m) x 8.0 N )iˆ acts on a particle that moves on an x axis. The potential energy associated with this force is assigned a value of 26 J at x = 0. Show your work. (a) What is the maximum potential energy for motion on the axis? Answer: _______________J (b) Where on the axis is the potential energy equal to zero? Answer:_______________m 7 Name _______________________________________________________________________ Formula Sheet for Homework and Exams – Page 1 of 2 U Fcons dx 1. v f v 0 a t f t 0 23. 2. x f x 0 v 0 ( t f t 0 ) 12 a ( t f t 0 ) 2 24. U g m g (y y 0 ) 3. x f x 0 12 ( v 0 v f )( t f t 0 ) 25. U s 12 k ( x x 0 ) 2 4. x f x0 v f (t f t0 ) 12 a(t f t0 )2 26. 27. 28. K U Wnoncons s r v tangential r 29. a tangential r 6. v f v 02 2ax f x 0 F Fnet m a 7. T 8. a centripetal 5. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 2 2r v v2 2 r r a radial a centripetal p mv dp F Fnet d t J Fnet dt p P pi dP Fext dt 30. 0 t t 0 31. 0 0 ( t t 0 ) 12 ( t t 0 ) 2 32. 0 12 (0 )( t t 0 ) 33. 0 ( t t 0 ) 12 ( t t 0 ) 2 2 02 2 0 35a. a b a b sin( ) a b a y b z a z b y î 35b. a z b x a x b z ĵ a x b y a y b x k̂ 34. 36. 37. M mi 38. 1 1 x cm m i x i y cm m i y i M M P M v cm a b a b cos() a x b x a y b y a z b z W Fd W F dx 21. K 12 m v 2 12 m (v x v y ) 22. K f K i Wnet 2 39. 40. 41. 42. 43. 2 I m i ri 2 K rot 12 I 2 W d r F dL I d t l r p L l i L I 44x. m1 v1, x ,before m 2 v 2, x ,before m1 v1, x ,after m 2 v 2, x ,after 44y. m1 v1, y ,before m 2 v 2, y ,before m1 v1, y ,after m 2 v 2, y,after 44z. m1 v1,z ,before m 2 v 2,z ,before m1 v1,z ,after m 2 v 2,z ,after 45a. v1,f m1 m 2 2 m2 v1,i v 2 ,i m1 m 2 m1 m 2 45b. 8 v 2,f 2 m1 m m1 v1,i 2 v 2 ,i m1 m 2 m1 m 2 Formula Sheet for Homework and Exams – Page 2 of 2 46a. 46b. 47a. 47b. 48a. 48b. 49. m m | F | G 1 2 2 r m m F G 1 2 2 r̂ r 1 | q1 || q 2 | | F | 4 0 r2 1 q1 q 2 F (r̂ ) 4 0 r 2 1 | qi | | Ei | 4 0 ri 2 1 qi E (r̂i ) 4 0 ri 2 F qE 50. 51. 52. 1 qi 4 0 ri U qV V E dx V V x V 53y. E y y V 53z. E z z 54. F q v B mv 55. r qB 53x. E x Useful Constants (You can use the approximate values on exams.) Universal Gravitation Constant G 6.67310 11 N m 2 kg 2 6.67 10 11 Electrostatic Force Constant 1 8.987551788 10 9 N m 2 C 2 9.0 10 9 4 0 Magnetic Constant 0 4 10 7 H m 1 1.26 10 6 Speed of Light in Vacuum c 2.99792458 10 8 m s 1 3.0 10 8 Charge of a Proton e 1.602176462 10 19 C 1.6 10 19 Electron-Volt Conversion Constant 1eV 1.602176462 10 19 J 1.6 10 19 Mass of a Proton m p 1.6726215810 27 kg 1.67 10 27 Mass of an Electron m e 9.10938188 10 31 kg 9.110 31 9