University of the Philippines College of Science Physics 71 Set A First Long Exam First Semester, AY 2014–2015 Name: Instructor: Section/Class Schedule: Student Number: Course: College: First Long Exam First Semester, AY 2014–2015 Physics 71 Instructions: Choose the letter of the best answer to each of the following questions. To change your answer, cross-out and sign your original answer and then shade your new answer. Any form of cheating in examinations or any act of dishonesty in relation to studies, such as plagiarism, shall be subject to disciplinary action. The acceleration due to gravity is g = 9.81m/s2 . Air resistance is assumed to be negligible and the ropes are assumed to be massless and inextensible unless otherwise stated. 1. Dimensyon. In simple harmonic motion, the frequency is given by r 1 k f= 2π m where π is a dimensionless constant. If the unit for m is in kg and the unit for f is in s−1 , what should be the unit of k for the equation to be dimensionally consistent? A. B. C. D. N/m2 N/m N·m N/(m · s) 2. Component Form. The displacement of a particle from the origin is given by 50.0 m, 30.00 North of East. If ı̂ points East and ̂ points North, what is the expression for this displacement in component form? A. B. C. D. 25.0 m ı̂ + 43.3 m ̂ 43.3 m ı̂ + 25.0 m ̂ 7.71 m ı̂ − 49.4 m ̂ −49.4 m ı̂ + 7.71 m ̂ 3. Boom panes. In a foreign land, 1 boom = 23.11 meters and 1 panes = 0.4189 seconds. What is the acceleration 50.00 m/s2 in units of boom/(panes)2 A. B. C. D. 0.9063 boom/(panes)2 2758 boom/(panes)2 6585 boom/(panes)2 0.3798 boom/(panes)2 A–2 First Long Exam First Semester, AY 2014–2015 Physics 71 4. The Unknown. The driver can choose two routes to get to the same destination. In the first route, he drives 12.0 m East, then 8.00 m, 28.2◦ North of East, and then an additional unknown displacement. In the second route, he drives 49.5 m, 36.1◦ North of East. What is the unknown displacement of the driver on the first route? A. (3.35 m)ı̂ + (40.4 m)̂ B. (2.57 m)ı̂ + (2.15 m)̂ C. (40.4 m)ı̂ + (3.35 m)̂ D. (2.15 m)ı̂ + (2.57 m)̂ 5. The x-t graph. Which graph represents a particle with an initial velocity that has the same direction as its constant acceleration? 6. Plot Twist. An object moving along the x-axis slows down at a constant rate. Which of the following describes the object’s acceleration vs. time graph? A. It is concave up B. It is concave down C. It is a horizontal line D. It is a diagonal line 7. Limit! A particle’s position varies with time given by the following equation: x(t) = 35.2 m + (12.5 m/s2 )t2 What is its instantaneous velocity at t = 1.00 s? A. 25.0 m/s B. 16.2 m/s C. 56.5 m/s D. 7.48 m/s A–3 First Long Exam First Semester, AY 2014–2015 Physics 71 8. Nerdy. A physicist decided to track his motion for analysis. His motion detector showed the following positiontime graph. What is his average velocity from t = 0.0 s to t = 1.5 s? A. zero B. 1.0 m/s C. 0.50 m/s D. 0.75 m/s 9. Cars 1. A car, initially moving at 20. m/s towards an intersection, starts to slow down at a uniform rate at the instant it is 10.m from the intersection. How long will it take for the car to reach the intersection? A. 0.50 s B. 1.0 s C. 2.0 s D. 4.0 s 10. Wreckless driver. A typical person can handle up to five times the value of the acceleration due to gravity before losing consciousness. What is the minimum time for a bus to reach the speed of 250. m/s from rest without the passengers passing out? A. 2.55 s B. 5.10 s C. 10.2 s D. 25.5 s 11. Flaming arrow. An archer fires a flaming arrow upward from a cliff that is 15.0 m from the ground. The arrow manages to miss the edge of the cliff as it goes down. If the arrow took 5.00 s to strike the ground from the moment it was fired, what is the arrow’s initial speed? A. 3.00 m/s B. 6.00 m/s C. 15.5 m/s D. 21.5 m/s A–4 First Long Exam First Semester, AY 2014–2015 Physics 71 12. Toss. A ball was thrown upward with an initial velocity u and reaches a maximum height h as measured from the juggler’s hands. At what fraction of the maximum height was the speed of the ball half of its initial speed? A. 3 4 B. 1 2 C. 1 4 D. 1 16 13. Come to You! Marivec, located at the origin, sees Jordan located at (5 m)ı̂ + (10 m)̂ focused on running at a constant velocity of (1 m/s)̂. At what velocity should Marivec travel if she wants to meet Jordan in 25 s? A. (0.2 m/s)ı̂ − (0.6 m/s)̂ B. (0.2 m/s)ı̂ + (0.6 m/s)̂ C. (0.2 m/s)ı̂ − (1.4 m/s)̂ D. (0.2 m/s)ı̂ + (1.4 m/s)̂ 14. Strange wind. A ball is dropped 500. m above the Earth’s surface. A strange wind gives the ball a 9.81 m/s2 acceleration directed to the East. How far shall it travel in the east direction before reaching the ground? A. 50.0 m B. 51.0 m C. 500. m D. 510. m 15. Acceleration. Which of the following is always true about the acceleration of a body in a projectile motion? A. It is tangent to the projectile’s trajectory. B. It is directed downward. C. It is directed upward. D. It is zero. 16. Go for broke! In a desperate attempt to have a girlfriend, a guy throws three bouquets at three girls. If the bouquets follow the trajectories shown, who gets a bouquet first? A. A B. B C. C D. They get the bouquets simultaneously. A–5 First Long Exam First Semester, AY 2014–2015 Physics 71 17. Time is gold. A soccer ball is kicked from the ground with an initial velocity of 12.0 m/s at an angle 60.0◦ above horizontal. At what time will the ball reach its maximum height? A. 0.533 s B. 0.610 s C. 1.06 s D. 1.22 s 18. Rejected Projectile. A projectile is given an initial speed of 50.0 m/s directed along an angle of θ = 30.0◦ with respect to the horizontal. What is its height if it is at a horizontal distance of 10.0 m from the initial position? A. 9.80 m B. 16.5 m C. 4.64 m D. 5.51 m 19. The swimmer. A swimmer heads north across the river at a speed of 5 m/s relative to the water with current flowing in the West of North direction. An observer on land sees the swimmer with a velocity of 37.7 m/s headed 23 o West of North. What is the magnitude and direction of the current? A. 33.0 m/s, 26 o from the vertical B. 44.0 m/s, 64 o from the vertical C. 33.0 m/s, 64 o from the vertical D. 44.0 m/s, 26 o from the vertical 20. Leo the leopard. What is the magnitude of the acceleration of Leo the leopard running at 10.0 m/s when rounding a turn of radius 25.0 m? A. 0.400 m/s2 B. 4.00 m/s2 C. 50.2 m/s2 D. 62.5 m/s2 21. Circular. An object with constant speed v is moving in a circular path with radius R. If the radius of the path is doubled, what should be its speed to maintain the same acceleration? √ 1 1 B. 2v D. 2v A. √ v C. v 2 2 A–6 First Long Exam First Semester, AY 2014–2015 Physics 71 22. Timbang. What is the weight of a 1.0 kg pack of apple? A. 1.0 kg B. 1.0 N C. 9.8 kg D. 9.8 N 23. Kicked block. A block was given an initial velocity such that it slides up along a rough inclined plane. Which of the following is the correct free-body diagram that shows all the forces acting on the block? → − 24. Force on a Box. A force, F , is applied on the box resting on a rough horizontal surface as shown in the figure. Consider the → − − → following forces on the box: applied force F , weight W , friction → − − f and normal force → n . Which of the following is always true about their magnitudes? A. The net force is zero. B. F ≥ f C. n > F D. W = n 25. Life of Pie. A pie is resting on top of a table. Which of the following is an action-reaction pair? A. the weight of the pie and the normal force on the pie B. the weight of the pie and the weight of the table C. the weight of the pie and the force of the pie on the earth D. the force of the table on the pie and the normal force on the pie A–7 First Long Exam First Semester, AY 2014–2015 Physics 71 26. Lizzy the lizard. Lizzy the lizard is crawling on top of a horizontal roof of a building. Which of the following is true about the forces acting on her? I. Normal force is in the opposite direction of her weight. II. Tension supports her weight. III. Her weight is countered by friction between her and the roof. A. B. C. D. I only II only III only I and III only 27. Who would even do this to a box? In the figure shown, let m = 0.95 kg and θ = 35◦ . What is the tension in the rope assuming it is massless and inextensible? A. 5.3 N B. 7.6 N C. 16 N D. 11 N 28. Stuck. Two masses, m and M , are in contact with each other, as shown in the figure. The system is in equilibrium and all surfaces are frictionless. If I double the mass of m, what will be the relative magnitude of the tension T as compared to its original magnitude? A. T2m > Tm B. T2m = Tm C. T2m < Tm D. Cannot be determined 29. Elevator Deloading. The elevator and its load have a combined mass of 1.60 × 103 kg. Find the tension in the supporting cable when the elevator, originally moving downward at 12.0 m/s, is brought to rest with a constant acceleration in a distance of 42.0 m. A. B. C. D. 2.74 × 103 N 1.57 × 104 N 1.59 × 104 N 1.84 × 104 N A–8 First Long Exam First Semester, AY 2014–2015 Physics 71 30. Ramp. An 8.00- kg crate at the top of a 1.50- m long frictionless ramp slides down from rest, reaching a speed of 3.50 m/s at the bottom. What is the angle between the ramp and the horizontal? A. 24.6◦ B. 2.98◦ C. 65.4◦ D. 87.0◦ 31. Taas-baba. In an Atwood’s machine, a 40.- kg box hangs from one end of rope that passes over a frictionless pulley with a 30.- kg counterweight suspended on the other end of the rope as shown. What is the acceleration of the counterweight? A. 0.70 m/s2 , upward B. 1.4 m/s2 , upward C. 0.70 m/s2 , downward D. 1.4 m/s2 , downward 32. SK. The coefficients of static and kinetic friction between a box and a floor are 0.8 and 0.6, respectively. You push the box with a force just enough to set the box moving. You continue to apply the same amount of force even when the box is moving. What is the box’s magnitude of acceleration ? A. 7.8 m/s2 B. 5.9 m/s2 C. 2.0 m/s2 D. zero 33. Stop Motion! A massive block is moving horizontally on a rough horizontal surface; a force of 500 N keeps it moving at a constant velocity. If the force was removed and the block comes to a stop, what is the minimum force required to move the block again once it has rested? (coefficient of kinetic friction = 0.200, coefficient of static friction = 0.500) A. 200. N B. 500. N C. 1.00 × 103 N D. 1250 N A–9 First Long Exam First Semester, AY 2014–2015 Physics 71 34. Rainy. On a rainy weather, the coefficient of static friction between the 1500- kg crate and a slippery ramp is 0.34. Up to what angle of inclination will the crate be able to rest on the ramp without sliding? A. 7.97 ◦ B. 8.04 ◦ C. 82.3 ◦ D. 18.8 ◦ 35. Pulling the crate. A man pulls on a rope attached to a crate with a constant force F on a horizontal surface. He can choose to pull the rope at angles θA = 10◦ , θB = 40◦ , and θC = 70◦ . Once the crate starts to move, how would you compare the magnitudes fA , fB and fC of the frictional force for each angle? A. fA < fB < fC B. fC < fB < fA C. fB < fA = fC D. fA = fB = fC 36. May friction. Block A with mass mA , resting on a tabletop, is connected by a horizontal cord passing over a light, frictionless pulley to a hanging block B of mass mB . The coefficient of kinetic friction between block A and the tabletop is µk . What is the magnitude of acceleration of the blocks after they are released from rest? A. (µk mB + mA )/(mA + mB ) B. (µk mB − mA )g/(mA − mB ) C. (mB + µk mA )g/(mA + mB ) D. (mB − µk mA )g/(mA + mB ) A – 10 First Long Exam First Semester, AY 2014–2015 Physics 71 37. Rough inclined plane (RIP). A block is released from rest at the top of a rough inclined plane. The plane forms an angle of 45.0◦ with respect to the horizontal and has a coefficient of kinetic friction, µk = 0.300. What is the acceleration of the block? A. 4.86 m/s2 B. 6.94 m/s2 C. 5.33 m/s2 D. 2.08 m/s2 38. Stone. A stone with mass 0.200 kg is being whirled in a horizontal circle on the end of a string with length 0.600 m. If the string makes an angle of 30.0 ◦ from the horizontal, what is the speed of the stone? A. 2.97 m/s2 B. 294 m/s2 C. 1.70 m/s2 D. 170. m/s2 39. The bank that you can trust. Determine the minimum angle at which a roadbed should be banked so that a car traveling at 20.0 m/s can safely negotiate the curve if the radius of the curve is 2.00 × 102 m. A. 0.200◦ B. 0.581◦ C. 11.5◦ D. 19.6◦ 40. The Terminal. Under what condition does a falling object attain its terminal velocity? A. When the force of gravity is greater in magnitude than the force of air resistance. B. When the force of gravity is equal in magnitude to the force of air resistance. C. When the force of gravity is less in magnitude than the force of air resistance. D. When the force of gravity is the only force acting on the object. A – 11