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Exam #1 Review What we’ve learned: Uniform, constant acceleration and circular motion. Acceleration is caused by forces. Newton’s 3 laws and the Law of Gravity. Where We are Headed: • Lecture: We’ll spend the day reviewing for Friday’s test. • Homework: I’ll post solutions for HW #5 by the end of the day. • Exam: Exam #1 is on Friday, Oct. 4: • 9:00 Folks: Come in, get seated. • 10:00 Folks: Wait until you are invited in, then get seated ASAP. • Everyone: Enter through the upper doors, leave through the lower doors. • You can use a one-page study sheet (both sides) and a calculator. Warming Up: Questions a . en in. If to its wy ou if 14.b.Raindrops canoffall different speeds; fall quite quickly, The weight anatobject depends on some its location. slowly. describe Why might bething true? in different units. c.others Massquite and weight thethis same 15. An airplane moves through the air at speed. 5. An astronaut takes his bathroom scale atoconstant the moon and The then engines’ thrust applies a force in the direction of motion, and stands on it. Is the reading of the scale his true weight? Explain. this force is equal in magnitude and opposite in direction to 6. A light block of mass m and a heavy block the drag force. Reducing thrust will cause the plane to fly at a of mass M are attached to the ends of a rope. stillthe constant—speed. Explain Aslower—but student holds heavier block and lets why the this is so. M 16.lighter Is it possible for an object to travel in air faster block hang below it, as shown in Figurethan its terminal speed? If not, why not? If so, explain how this might happen. Q5.6 . Then she lets go. Air resistance can be Forneglected. Questions 17 through 20, determine the tension in the rope at the a. indicated What is with the atension point dot. in the rope while the blocks are falling, before either hits the r ground? "MMPCKFDUTBSFBUSFTU m b.r Would yourand answer be are different if she The strings pulleys massless, andhad the pulleys are FIGURE Q5.6 been holding the lighter block initially? frictionless. 7. 17.a. Can the normal force 18. on an object be directed 19. horizontally? If not, why not? If so, provide an example. b. Can the normal force on an object be directed downward? If not, why not? If so, provide an example. 8. A ball is thrown straight up. Taking the drag force of air into account, does it take longer for the ball to travel to the top of its kg motion or for it to fall back 5down again? 5 kg 9. You are going sledding with your friends, sliding down a snowy hill. Friction can’t be ignored. Riding solo on your sled, you FIGURE Q5.17 5 kg 5 kgchange if have a certain acceleration. Would the acceleration you let a friend ride with you, increasing the mass? Explain. FIGURE Q5.18 5 kg 10. Suppose you are holding a box in front of you and away from your body by squeezFIGURE Q5.19 ing the sides, as shown in Figure Q5.10. 20.Draw a free-body diagram showing all of the forces on the box. What is the force that is holding the box up, the force that is opposite the weight force? 5 kg n v t 0 A. For Questions 17 through 20, determine the tension in the rope at th point indicated with a dot. r "MMPCKFDUTBSFBUSFTU r The strings and pulleys are massless, and the pulleys are frictionless. 17. 18. 19. v t 0 B. v t 0 C. t 0 D. FIGURE Q5.26 27. | Eric has a mass of 60 kg. He is standing on a scale in an elevator that is accelerating downward at 1.7 m/s2. What is the approximate reading on the scale? A. 0 N B. 400 N C. 500 N D. 600 N 28. | The two blocks in Figure Q5.28 are at rest on frictionless surfaces. What must be the mass of the right block in order that the 5 kg 5 kg FIGURE Q5.17 5 kg 5 kg FIGURE Q5.18 5 kg FIGURE Q5.19 20. 5 kg 5 kg Q5.10 FIGURE 25. | A 3.0 kg puck slides due east on a horizontal frictionless surface at a constant speed of 4.5 m/s. Then a force of magnitude FIGURE Q5.20 6.0 N, directed due north, is applied for 1.5 s. Afterward, a. What is the northward component of the puck’s velocity? A. 0.50 m/s B. 2.0 m/s C. 3.0 m/s 4.0 m/s 4.5 m/s D. E. ap_05.indd 153 b. What is the speed of the puck? A. 4.9 m/s B. 5.4 m/s C. 6.2 m/s 25/06/13 D. 7.5 m/s E. 11 m/s 26. | A rocket in space, initially at rest, fires its main engines at a constant thrust. As it burns fuel, the mass of the rocket decreases. Which of the graphs in Figure Q5.26 best represents the velocity of the rocket as a function of time? v 15. An airplane moves through the air at a constant speed. Th engines’ thrust applies a force in the direction of motion, an this force is equal in magnitude and opposite in direction t the drag force. Reducing thrust will cause the plane to fly at slower—but still constant—speed. Explain why this is so. 16. Is it possible for an object to travel in air faster than its termina speed? If not, why not? If so, explain how this might happen. 5 kg FIGURE Q5.20 25/06 10:44 AM C. The friction force is zero. D. There’s not enough information to tell. 23. || A 2.0 kg ball is suspended by two light strings as shown 50° in Figure FIGURE Q6.15Q5.23. What is T the tension T in the angled y 16. A small projectile is launched parallel to the ground at height string? m = 2.0 kg h = 1 m with sufficient speed to orbit a completely smooth, airFIGURE Q5.23 A. N AB.bug 15rides N in a small less9.5 planet. hole inside the projectile. Is e the bugNweightless? Explain. C. 20 D. 26 N E. 30 N 17. is itstanding impossible astronaut inside anarms orbiting space 24. Why | While in a for lowan tunnel, you raise your and push l station from one to the byYour walking against to thegoceiling withend a force of other 100 N. massnormally? is 70 kg. d 18. If in the feelson anyou? attractive gravitational a. every What object force does theuniverse ceiling exert e force due to every other object, why don’t you feelC.a 690 pull N from A. 10 N B. 100 N someone seated next to you? D. 790 N E. 980 N 19. A mountain climber’s weight is slightly less on the top of a tall b. What force floor exert his on you? t mountain than does at thethe base, though mass is the same. Why? A. 10 N B. 100 N 690smaller N d 20. Is the earth’s gravitational force on the sun larger C. than, D.or790 N to the sun’s gravitational E. 980 N force on the earth? Explain. than, equal f 25. | A 5.0 kg dog sits on the floor of an elevator that is accelerating downward at 1.20 m/s2. Multiple-Choice Questions a. What is the magnitude of the normal force of the elevator floor on the dog? 21. | A ball on a string moves around a complete circle, once a A. 34 N B. 43 N C. 49 N D. 55 N E. 74 N second, on a frictionless, horizontal table. The tension in the 26. ||string cylindrical space stations, the second four times the b.Two What is the magnitude of the force of the dog on the elevator is measured to be 6.0 N. What would the tension be if the diameter the first, rotate as to provide the same amount ballfloor? went of around in only halfso a second? of artificial gravity. If the first station A. 4.2 N B. 49 N C. 55 N N D.makes 43 N 74 N A. 1.5 N B. 3.0 N C. 12 D. 24 N oneE.rotation in the time T, then the second station makes one rotation in time A. T/4 B. 2T C. 4T D. 16T 27. || The radius of Jupiter is 11 times that of earth, and the freefall acceleration near its surface is 2.5 times that on earth. If we someday put a spacecraft in low Jupiter orbit, its orbital speed 18/07/13 Section will 5.1 be Equilibrium Greater thatinfor an earth 1. A. | The threethan ropes Figure P5.1 satellite. are tied to a small, very light B. The same as that for an earth satellite. ring. Two of the ropes are anchored to walls at right angles, and C. an earthWhat satellite. theLess thirdthan rope that pullsfor as shown. are T1 and T2 , the magnitudes 28. | ofAthenewly discovered planet tension forces in the firsthas twotwice ropes?the mass and three times the radius of the earth. What is the at its 2. ||| The three ropes in Figure P5.2 are free-fall tied to a acceleration small, very light surface, inofterms the are free-fall acceleration at the surface ring. Two theseof ropes anchored to walls atgright angles withof the the earth? tensions shown in the figure. What are the magnitude and 3 2 2 u 4 A. B. 3 gT3 in the third C.rope? D. 3 g direction of the tension 9g 4g 29. || Suppose one night the radius of the earth doubled but its mass stayed the same. What would be an approximate new value for the free-fall acceleration at the surface of the earth? A. 2.5 m/s2 B. 5.0 m/s2 C. 10 m/s2 D. 20 m/s2 30. | Currently, the moon goes around the earth once every 27.3 days. If the moon could be brought into a new circular orbit with a smaller radius, its orbital period would be G9721_03_chap_05.indd 154 A. More than 27.3 days. B. 27.3 days. C. Less than 27.3 days. 31. || Two planets orbit a star. You can ignore the gravitational interactions between the planets. Planet 1 has orbital radius r1 and planet 2 has r2 = 4r1 . Planet 1 orbits with period T1 . Planet 2 orbits with period A. T2 = 12 T1 B. T2 = 2T1 C. T2 = 4T1 D. T2 = 8T1 the two blocks remain stationary? A. 4.9 kg B. 6.1 kg C. 7.9 kg D. 9.8 kg E. 12 kg 10 kg 40° 23° FIGURE Q5.28 29. | A football player at practice pushes a 60 kg blocking sled across the field at a constant speed. The coefficient of kinetic friction between the grass and the sled is 0.30. How much force must he apply to the sled? A. 18 N B. 60 N C. 180 N D. 600 N 30. | Two football players are pushing a 60 kg blocking sled across the field at a constant speed of 2.0 m/s. The coefficient of kinetic friction between the grass and the sled is 0.30. Once they stop pushing, how far will the sled slide before coming to rest? A. 0.20 m B. 0.68 m C. 1.0 m D. 6.6 m 31. || Land Rover ads used to claim that their vehicles could climb a slope of 45°. For this to be possible, what must be the minimum coefficient of static friction between the vehicle’s tires and the road? A. 0.5 B. 0.7 C. 0.9 D. 1.0 32. || A truck is traveling at 30 m/s on a slippery road. The driver slams on the brakes and the truck starts to skid. If the coefficient of kinetic friction between the tires and the road is 0.20, how far will the truck skid before stopping? A. 230 m B. 300 m C. 450 m D. 680 m PROBLEMS 10:51 AM 0.60 m Rope 2 T2 = 80 N 0.80 m Rope 1 30° T1 = 50 N u 100 N FIGURE P5.1 T3 FIGURE P5.2 the free-fall acceleration at the surface of the earth? A. 2.5 m/s2 B. 5.0 m/s2 C. 10 m/s2 D. 20 m/s2 30. | Currently, the moon goes around the earth once every 27.3 days. If the moon could be brought into a new circular orbit with a smaller radius, its orbital period would be A. More than 27.3 days. B. 27.3 days. C. Less than 27.3 days. 31. || Two planets orbit a star. You can ignore the gravitational interactions between the planets. Planet 1 has orbital radius r1 and planet 2 has r2 = 4r1 . Planet 1 orbits with period T1 . Planet 2 orbits with period A. T2 = 12 T1 B. T2 = 2T1 C. T2 = 4T1 D. T2 = 8T1 6. || The horse on a carousel is 4.0 m from the central axis. a. If the carousel rotates at 0.10 rev/s, how long does it take the horse to go around twice? b. How fast is a child on the horse going (in m/s)? 7. ||| The radius of the earth’s very nearly circular orbit around the sun is 1.50 * 1011 m. Find the magnitude of the earth’s (a) velocity and (b) centripetal acceleration as it travels around the sun. Assume a year of 365 days. 8. | Modern wind turbines are larger than they appear, and despite their apparently lazy motion, the speed of the blades tips can be quite high—many times higher than the wind speed. A typical modern turbine has blades 56 m long that spin at 13 rpm. At the tip of a blade, what are (a) the speed and (b) the centripetal acceleration? 18/07/13 10:51 AM Dark Matter Surrounds Our Galaxy. One Step Beyond. Optional Evening Session Details TBA Exam #1 4 scenarios, 3 questions on each Steps ! Prepare • Translate • Draw pictures • Have you seen this before? ! Solve • Set up equations • Solve ! Assess • Does your answer make sense? Look at the big picture. Practicing: Spot the Physics Why does the exhaust go back and up? The plane can’t stay upside down for very long. Why? What are the forces during the giant swing? Data v = 5.0 m/s r = 1.0 m m = 41 kg w = 400 N Questions Acceleration = ? Apparent weight = ? Compare with w. Practicing: Scenarios Scenario #3: Cavorting Crustaceans Copepods are small, abundant crustaceans that form a significant percentage of the ocean’s biomass. One species forms much of the diet of herring. To escape capture, these copepods have evolved a very rapid escape response; typical speed vs. time data is shown in the graph at right. From 0.10 to 0.20 s, rapid swimming motion results in a thrust force that gives a large acceleration; from 0.20 to 0.40 s, the large drag force on this small animal (assume a mass of 1.8 mg) slows it to rest. In what follows, we’ll make the approximation that the drag force works like a kinetic friction force—it opposes the motion and has a constant magnitude as long as the creature is in motion. Speed (m/s) 0.80 0.60 0.40 0.20 0.10 0.20 0.30 0.40 Time (s) Multiple Choice Questions (3 points): 5) When the copepod is speeding up, what is the approximate magnitude of the acceleration? A. 7 m/s2 B. 14 m/s2 C. 20 m/s2 D. 30 m/s2 6) What is the approximate distance the copepod travels during the entire escape response, including both phases, the speeding up and the slowing down? A. 10 cm B. 20 cm C. 30 cm D. 40 cm Speed (m/s) 0.80 0.60 0.40 0.20 0.10 0.20 0.30 0.40 Time (s) Short Answer Question (6 points): Given that the copepod is floating in water, the upward buoyant force offsets the downward weight force. There are only two forces you need consider, thrust and drag. Draw force and motion diagrams for both phases of the motion: the speeding up and the slowing down. Now, compute: • What is the magnitude of the drag force while the copepod is slowing down? • What is the magnitude of the thrust force while the copepod is speeding up? How do these forces compare to the creature’s weight? Scenario #2: Lifting a Load Jordan is using a rope and pulley to raise a 20 kg crate, as in the diagram at right. The crate is being held at a constant height of 2.5 m above the floor. Multiple Choice Questions (3 points): 3) With the crate held at a constant height, what is the approximate tension in the rope? A. 50 N B. 100 N C. 150 N D. 200 N 4) Suddenly the rope breaks, and the crate falls to the floor. After the break, how much time does it take for the crate to reach the floor, to the nearest 0.1 s? A. 0.4 s B. 0.5 s C. 0.6 s D. 0.7 s Short Answer Question (6 points): Jordan now attaches a rope to the crate that can support a tension of up to 250 N—but no more. What is the minimum time required to raise the crate from the floor back to its original height? Scenario #4: Marsupial Motion A gray kangaroo bounding across a flat stretch of ground will execute a series of jumps, moving in a series of parabolic arcs. The following problem uses typical data for a kangaroo moving at a good clip. With each jump, the kangaroo leaves the ground at a speed of 12 m/s, at an angle of 20° with respect to the horizontal. The kangaroo then moves through the air. When the kangaroo lands, the vertical component of the velocity points downward. A short time later, the stout legs of the kangaroo have reversed this vertical motion. The kangaroo’s vertical motion is now upward, and the kangaroo leaves the ground again. The horizontal component of the velocity stays the same while the kangaroo is on the ground and in the air, so the kangaroo is bouncing up and down, but is moving forward at a steady speed. This particular kangaroo is female, and has a 0.51 kg baby—called a joey—supported in her pouch. Multiple Choice Questions (3 points): 7) At the highest point of her motion, what are the kangaroo’s vertical velocity and vertical acceleration? A. vy = +4.1 m/s; ay = 0 m/s2 B. vy = 0 m/s; ay = 0 m/s2 C. vy = 0 m/s; ay = -9.8 m/s2 D. vy = -4.1 m/s; ay = -9.8 m/s2 8) The kangaroo has landed, and her vertical speed is changing. At some instant, her vertical speed is zero, but her acceleration is upward at 30 m/s2—as is that of the joey. What is the joey’s approximate apparent weight at this instant? A. 5 N B. 10 N C. 15 N D. 20 N Short Answer Question (6 points) After the kangaroo leaves the ground, how far does she travel before reaching the ground again? Human vs. Horse How do humans stack up vs. horses in track events? Horses are faster, but humans are capable of greater acceleration. A typical running speed for a fast horse is 20 m/s, much faster than a human, but the horse can only accelerate at 6.0 m/s2, about half what a good human runner can achieve. Humans are also better jumpers; the world record broad jump for a human is about 9.0 m, while that for a horse is only 7.5 m. Multiple Choice Questions (3 points): If a horse starts from rest and accelerates at the maximum value until reaching its top speed: 1) How much time does this acceleration take, to the nearest second? A. 1 s B. 2 s C. 3 s D. 4 s 2) How much distance does the horse cover during this time, to the nearest 10 m? A. 10 m B. 20 m C. 30 m D. 40 m Short Answer Question (6 points) When humans do a long jump, they get up to top speed and then redirect their motion so that it has a vertical as well as a horizontal component. Horses can’t do this nearly as well as humans. Suppose a horse, running a top speed, could redirect its motion so that it took off at a 30° angle with respect to the horizontal, moving in a parabolic trajectory until landing. The horse could then do a jump that is much longer than 7.5 m! For this theoretical jump, • For how much time would the horse be in the air? • At the high point of its motion, how high would the horse be? • How much horizontal distance would the horse cover? Next Time: Exam #1