1 of 14 Exam 2 – Version A Physics 2010 Name Student ID # Circle your TA Circle the Day and Start Time of your recitation/lab Section Tues Wed 8am 10am Thu 12pm 2pm Please do not open the exam until you are told to do so. Thanks! This exam consists of 25 multiple choice questions, each worth the same amount. Your exam should have 14 pages (7 pieces of paper). The last 3 sides are blank, which you may use for scratch work. There is also room for work after each question. Please read and follow the Instructions at the top of the bubble sheet. Check each box as you complete the instructions below: Print and bubble in your name and student ID number on the bubble sheet. (Carefully, please!) VERY IMPORTANT: Bubble in your Exam version, (this one is version “A”), in the LOWER LEFT of your bubble sheet in the area marked “TEST VERSION” As you take the exam, mark the correct answer on the bubble sheet. You can circle your answers on the paper copy of the exam for your future reference. But, the bubble sheet always takes precedence over anything written on your exam Relax! A TA will announce when you can start. “On my honor, as a University of Colorado at Boulder student, I have neither given nor received unauthorized assistance on this work” Signature ____________________________________________ Version A 2 of 14 Average velocity: v = x t Average acceleration: a= v t Equations for motion with constant acceleration: v = v0 + aDt 1 x = x0 + v0 Dt + aDt 2 2 v 2 = v0 2 + 2a(x - x0 ) v + v0 v= 2 x = x0 + vDt Magnitude of acceleration from gravity at the Earth’s surface: g = +9.81 m/s2 (by convention, the symbol g is ALWAYS positive!) π ~ 3.14 sin() = opposite/hypotenuse cos() = adjacent/hypotenuse tan() = opposite/adjacent √2 ~ 1.41, √3 ~ 1.73 Newton’s 1st law: An object travels with constant velocity unless acted on by a net force. Newton’s 2nd law: 𝐅𝑛𝑒𝑡 = ∑ 𝐅𝑖 = 𝑚𝐚 Newton’s 3rd law: 𝐅𝐴 𝑜𝑛 𝐵 = −𝐅𝐵 𝑜𝑛 𝐴 2 Uniform circular motion, with radius 𝑟 and speed 𝑣, has acceleration 𝐚 = 𝑣 ⁄𝑟 pointing towards the center of the circle (centripetal). Newton’s universal law of gravity between masses 𝑚1 and 𝑚2 , separated by 𝑟12 : 𝐺𝑚1 𝑚2 𝐹𝑔𝑟𝑎𝑣𝑖𝑡𝑦 = ⁄𝑟 2 with 𝐺 = 6.67 x 10-11 N m2/kg2 12 Kinetic friction is given by 𝐹𝑓𝑟𝑖𝑐𝑡𝑖𝑜𝑛 = 𝜇𝐾 𝑁, where 𝑁 is the normal force magnitude The maximum static friction is given by 𝐹𝑓𝑟𝑖𝑐𝑡𝑖𝑜𝑛 = 𝜇𝑆 𝑁 Work 𝑊 by constant force 𝐅 over displacement ∆𝐫 = (𝐹)(∆𝑟) cos 𝜃, where 𝜃 is the angle between the force and displacement vectors. Kinetic Energy 𝐾𝐸 of mass 𝑚 with speed 𝑣 equals 12𝑚𝑣 2 Work-kinetic energy theorem: 𝑊𝑛𝑒𝑡 = ∆𝐾𝐸 Version A 3 of 14 1. A heavy truck of mass M collides with a small sports car of mass m on an icy (frictionless) flat road. What is the ratio of the acceleration of the heavy truck to that of the sports car during the collision? A) B) C) D) E) M/m m/M 1 M2/m2 m2/M2 2. A student slides her 50.0-kg desk across the level floor of her dormitory room a distance 5.00 m at constant speed. If the coefficient of kinetic friction between the desk and the floor is 0.408. How much work did the student do? A) B) C) D) E) 1J 1 kJ 10 J 10 kJ 100 J 3. Two equal mass asteroids, labeled 1 and 2, are traveling through outer space. The kinetic energy of asteroid 1 is 9 times the kinetic energy of asteroid 2. What is the ratio of the speed of 𝑣 asteroid 1 to asteroid 2, 1⁄𝑣2 ? A) B) C) D) E) 0.111 0.333 1.000 3.000 9.000 4. Which of the following statements are always true? 1) A truck initially moving at a constant velocity will slow down unless a small net force is applied. 2) If a net force acts on an object, the object's velocity will change. 3) If a net force acts on an object, the object's speed will change. 4) If two objects have the same acceleration, they are under the influence of equal forces. A) B) C) D) E) 1) and 2) are always true 1), 2) and 3) are always true 1), 2) and 4) are always true only 2) is always true only 4) is always true Version A 4 of 14 5. A 35.0 kg block located on a horizontal floor with friction is pulled by a cord that exerts a force F=24.0 N at an angle q =30◦ above the horizontal, as shown. What is the work done by the cord on the block as it accelerates over a displacement of 2.00 m to the right? A) B) C) D) E) 24.0 J 37.2 J 41.6 J 48.0 J Not enough information given Displacement 6. Which one of the following free-body diagrams best represents the free-body diagram, with approximately correct relative force magnitudes, of a person in an elevator that is traveling upward but is gradually slowing down at a rate of 3 m/s2? ⃗⃗⃗ 𝐹𝑓 is the normal force of the floor on the person and ⃗⃗⃗ 𝐹𝑔 is the force of gravity on the person. If two forces appear equal length in the diagram, assume they are equal. 7. A ball of mass M = 1.0 kg is pulled upwards by a rope. If the acceleration of the ball is a = 1.0 m/s2 upward, the tension in the rope must be closest to A) B) C) D) E) Version A 1N 2N 5N 10 N 11 N 5 of 14 8. If an object travels at a constant speed in a circular path, the acceleration of the object is A) B) C) D) E) larger in magnitude the smaller the radius of the circle. in the same direction as the velocity of the object. smaller in magnitude the smaller the radius of the circle. in the opposite direction of the velocity of the object. zero. The following three questions refer to this situation: Two blocks are in contact on a table. A horizontal force F =5 N is applied to M2, as shown. The masses are M1=1 kg, M2=2 kg. 9. What is the magnitude of the acceleration of the blocks if the friction between the blocks and table can be neglected? A) B) C) D) E) 0.83 m/s2 1.0 m/s2 1.67 m/s2 2.5 m/s2 5.0 m/s2 10. What is the magnitude of the contact force between the two blocks if the friction between the blocks and table can be neglected? A) B) C) D) E) Version A 0N 1.0 N 1.67 N 3.34 N 5.0 N 6 of 14 11. Which diagram below best represents the free-body diagram of the left block M2 when the blocks accelerate across the table to the right with friction between the block M2 and the table surface? 𝐅𝐟𝐫 denotes the force of friction, 𝐅𝟐𝟏 the force block M1 exerts on M2, N is the normal force and W is the weight due to gravity. The force vectors are approximately to scale. 12. A 4.5 kg block located on a horizontal frictionless floor is pulled by a cord that exerts a tension force F = 12.60 N at an angle q =30◦ above the horizontal, as shown. What is the speed of the block 4.0 seconds after it starts moving? A) B) C) D) E) Version A 2.8 m/s 4.35 m/s 5.6 m/s 9.7 m/s 11.2 m/s 7 of 14 13. A frictionless pulley with zero mass is attached to the ceiling. The mass M2 = 0.250 kg is observed to accelerate downward with a = 5.00 m/s2 . To two significant digits, what is the mass m1? A) B) C) D) E) 0.012 kg 0.041 kg 0.05 kg 0. 081 kg E) 0.16 kg 14. A baseball of mass m is hit by a bat and travels upwards. Its initial speed is 𝑣0 and it leaves the bat at an angle of 60 above the horizontal direction. It reaches height h above its starting position before starting to come back down. Which formula below gives the work done by gravity on the baseball between the time it leaves the bat and the top of the motion at the height h? A) B) C) D) E) +𝑚𝑣02 /2 −𝑚𝑣02 /2 −𝑚𝑔ℎ +𝑚𝑔ℎ Depends on whether we can ignore air resistance. 15. A person is standing in an elevator that is moving upward with an increasing speed. How does the magnitude of the normal force N on the person's feet compare to the magnitude of the person's weight mg? A) N > mg B) N < mg D) impossible to tell Version A C) N = mg moving up |v| increasing 8 of 14 16. A ball of mass M = 0.30 kg on the end of a string revolves at a uniform rate in a vertical circle of radius 75.4 cm as shown in the figure. If the speed of the ball is 5.0 m/s, what is the tension in the string when the ball is at the top of its path? A) B) C) D) E) 7N 10 N 13 N 23.3 N 43. N 17. An object moves in a circle of radius R at constant speed; the period of the motion with this speed is T. If you want to change only the period but not the radius, in order to reduce the object's acceleration a by 2 (change to a/2), the new period should be A) T/4. B) T/2 C) T / 2 D) 2T E) 4T. 18. An astronaut weighs 800 N on Earth. What is her weight on planet X, a planet which has radius RX =REarth/2 and mass MX= MEarth/8? A) B) C) D) E) Version A 50 N 100 N 200 N 300 N 400 N 9 of 14 19. A 6.5 kg crate slides down a frictionless ramp with a 60 incline (relative to horizontal). What is the magnitude of the acceleration of the crate while it is sliding down the ramp? A) B) C) D) E) 1.3 m/s2 4.9 m/s2 5.6 m/s2 7.2 m/s2 8.5 m/s2 20. A box of weight 20 N is resting on a board which is initially horizontal; the surface of the board is rough, so there is friction. The coefficient of kinetic friction k = 0.1 and the coefficient of static friction s = 0.4. One end of the board is slowly raised upward; let describe the angle between the board and the horizontal. Pick the answer below which is closest to the angle at which the box just begins to slide down the ramp. A) 5.7 B) 11 C) 22 D) 68 E) 83 21. The moon (mass 7.3 x 1022 kg) orbits the earth (mass 6.0 x 1024 kg) every 27.3 days in a circular orbit of radius 3.84 x105 km. NASA launches a small satellite that has an orbit around the earth of the same radius as the moon. The mass of the satellite is 3.2 x 103 kg. How does the acceleration of the satellite compare to the acceleration of the moon? (You can ignore the gravitational attraction between the satellite and the moon.) A) The satellite’s acceleration is less than the moon’s acceleration. B) The satellite’s acceleration is equal to the moon’s acceleration. C) The satellite’s acceleration is greater that the moon’s acceleration. D) Not enough information given. Version A 10 of 14 22. A heavy mass of 100 kg is attached by an ideal string to a hanging 0.001 kg mass using a frictionless pulley. The heavy mass is resting on a frictionless horizontal table. Which of the following will occur? A) The masses will remain at rest. B) The heavy mass will move towards the pulley with constant velocity C) The heavy mass will accelerate towards the pulley. 23. A 0.1 kg box on a rotating flat turntable moves around the center of the turntable with a speed v = 0.05 m/s at a radius of 10 cm without sliding on the turntable surface. The coefficient of static friction is 0.5 and the coefficient of kinetic friction is 0.25. What is the magnitude of the friction force on the box? A) B) C) D) E) Version A 0 1.25 x 10-3 N 2.50 x 10-3 N 0.245 N 0.491 N 11 of 14 24. Two blocks connected by an ideal rope are located on a frictionless surface. They are accelerating to the right with a pull from force F (by a second ideal rope). How does the magnitude of the tension T in the rope between the blocks compare to the magnitude of the pulling force F? T A) B) C) D) F T=F T<F T>F Which is greater depends on the actual masses of the two blocks. 25. A planet in elliptical orbit around a star moves from the point in its orbit furthest from the star (A) to the closest point (P) and then back to A. Where on the orbit is the speed of the planet decreasing? P A) B) C) D) From A to P From P to A Nowhere on the orbit (speed is constant). Everywhere on the orbit Version A A 12 of 14 Version A 13 of 14 Scratch Page Version A 14 of 14 Version A