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All Textbook Solutions for Physics: Principles with Applications
14P15P16P17P18PA box weighing 77.0 N rests on a table. A rope tied to the box runs vertically upward over a pulley and a weight is hung from the other end (Fig. 4-45). Determine the force that the table exerts on the box if the weight hanging on the other side of the pulley weighs (a) 30.0 N, (b) 60.0 N, and (c) 90.0 N.Figure 4-46
Problem 21.
21. (I) Draw the free-body diagram for a basketball player (a) just before leaving the ground on a jump, and (b) while in the air. See Fig. 4-46.
21PArlene is to walk across a “high wire" strung horizontally between two buildings 10.0 m apart. The sag in the rope when she is at the midpoint is 10.0°, as shown in Fig. 4-47. If her mass is 50.0 kg, what is the tension in the rope at this point? Figure 4-47 Problem 23.A window washer pulls herself upward using the bucket-pulley apparatus shown in Fig.4-48. (a) How hard must she pull downward to raise herself slowly at constant speed? (b) if she increases this force by 15%, what will her acceleration be? The mass of the person plus the bucker is 72 kg.One 3.2-kg paint bucket is hanging by a massless cord from another 3.2-kg paint bucket, also hanging by a massless cord, as shown in Fig. 4-49 (a) If the buckets are at rest, what is the tension in each cord? (b) If the two buckets are pulled upward with an acceleration of 1.25 m/s2by the upper cord, calculate the tension in each cord. Figure 4-49 Problem 2525PA train locomotive is pulling two cars of the same mass behind it, Fig. 4-51. Determine the ratio of the tension in the coupling (think of it as a cord) between the locomotive and the first car (FT1), to that between the first car and the second car (FT2), for any nonzero acceleration of the train. Figure 4-51 Problem 27.27PA 27-kg chandelier hangs from a ceiling on a vertical 4.0-m-long wire. (a) What horizontal force would be necessary to displace its position 0.15 m to one side? (b) What will be the tension in the wire?29PFigure 4-53 [shows a block (mass mA) on a smooth horizontal surface, connected by a thin cord that passes over a pulley to a second block (mB), which hangs vertically. (a) Draw a free-body diagram for each block, showing the force of gravity on each, the force (tension) exerted by the cord, and any normal force.(b) Apply Newton's second law to find formulas for the acceleration of the system and for the tension in the cord. Ignore friction and the masses of the pulley and cord. Figure 4-53 Problems 32 and 33. Mass mArests on a smooth horizontal surface; mBhangs vertically.31P32P35. (Ill) Suppose the pulley in Fig. 4-55 is suspended by a cord C. Determine the tension in this cord after the masses are released and before one hits the ground. Ignore the mass of the pulley and cords.
Figure 4-55
Problem 35
34PA force of 35.0 N is required to start a 6.0-kg box moving across a horizontal concrete floor. (a) What is the coefficient of static friction between the box and the floor? (b) If the 35.0-N force continues, the box accelerates at 0.60 m/s2. What is the coefficient of kinetic friction?36P37P38P39PA box is given a push so that it slides across the floor. How far will it go, given that the coefficient of kinetic friction is 0.15 and the push imparts an initial speed of 3.5 m/s?41P42P43P46. (II) For the system of Fig. 4-32 (Example 4-20), how large a mass would box A have to have to prevent any motion from occurring? Assume
45P46P47PA person pushes a 14.0-kg lawn mower at constant speed with a force of F = 88.0 N directed along the handle, which is at an angle of 45.0° to the horizontal (Fig. 4-58) (a) Draw the free-body diagram showing all forces acting on the mower. Calculate (b) the horizontal friction force on the mower, then (c) the normal force exerted vertically upward on the mower by the ground (d) What force must the person exert on the lawn mower to accelerate it from rest to 1.5 m/s in 2.5 seconds, assuming the same friction force? Figure 4-58 Problem 50.49P(a) A box sits at rest on a rough 33° inclined plane. Draw the tree-body diagram, showing all the forces acting on the box. (b) How would the diagram change if the box were sliding down the plane? (c) How would it change if the box were sliding up the plane after an initial shove?51P52P53PA 25.0-kg box is released on a 27° incline and accelerates down the incline at 0.30 m/s2. Find the friction force impeding its motion. What is the coefficient of kinetic friction?55P56PThe crate shown in Fig. 4-60 lies on a plane tilted at an angle =25.0 to the horizontal, with k=0.19.(a) Determine the acceleration of the crate as it slides down the plane. (b) If the crate starts from rest 8.15 m up along the plane from its base, what will be the crate's speed when it reaches the bottom of the incline? v Figure 4-60A crate is given an initial speed of 3.0 m/s up the 25.0° plane shown in Fig. 4-60. (a) How far up the plane will it go? (b) How much time elapses before it returns to its starting point? Assume k = 0.12.59P60PThe coefficient of kinetic friction for a 22-kg bobsled on a track is 0.10. What force is required to push it down along a 6.0° incline and achieve a speed of 60 km/h at the end of 75 m?On an icy day, you worry about parking your car in your driveway, which has an incline of 12°. Your neighbor's driveway has an incline of 9.0°, and the driveway across the street is at 6.0°. The coefficient of static friction between tire rubber and ice is 0.15. Which driveway(s) will be safe to park in?Two masses mA= 2.0 kg and mB= 5.0 kg are on inclines and are connected together by a string as shown in Fig. 4-61. The coefficient of kinetic friction between each mass and its incline is k = 0.30. If mAmoves up, and mB moves down, determine their acceleration. [Ignore masses of the (frictionless) pulley and the cord.] Figure 4-61 Problem 65.64P65P66GP67GP68GP69GP70GP71GP72GP73GP74GP75GP76GP77GP78GP79GP80GP81GP82GP83GP84GP85GP86GP87GP88GP89GPHow many '‘accelerators” do you have in your car? There are at least three controls in the car which can be used to cause the car to accelerate. What are they? What accelerations do they produce?A car rounds a curve at a steady 50 km/h. If it rounds the same curve at a steady 70 km/h, will its acceleration be any different? Explain.Will the acceleration of a car be the same when a car travels around a sharp curve at a constant 60 km/h as when it travels around a gentle curve at the same speed? Explain.4Q5Q6Q7Q8Q9Q10Q10. A car maintains a constant speed v as it traverses the hill and valley shown in Fig. 5-34. Both the hill and valley have a radius of curvature R. At which point, A, B, or C, is the normal force acting on the car (a) the largest, (b) the smallest? Explain. (c) Where would the driver feel heaviest and (d) lightest? Explain. (e) How fast can the car go without losing contact with the road at A?
12Q13QDoes an apple exert a gravitational force on the Earth? If so, how large a force? Consider an apple (a) attached to a tree and (b) falling.15Q16Q17Q18Q19Q20Q21Q22Q23Q24QA child sitting 1.20 m from the center of a merry-go-round moves with a speed of 1.10 m/s. Calculate (a) the centripetal acceleration of the child and (b) the net horizontal force exerted on the child (mass = 22.5 kg)A jet plane traveling 1890 km/h (525 m/s) pulls out of a dive by moving in an arc of radius 5.20 km. What is the plane's acceleration in g's?3PWhat is the magnitude of the acceleration of a speck of clay on the edge of a potter's wheel turning at 45 rpm (revolutions per minute) if the wheel's diameter is 35 cm?5. (II) A 0.55-kg ball, attached to the end of a horizontal cord, is revolved in a circle of radius 1.3 m on a frictionless horizontal surface. If the cord will break when the tension in it exceeds 75 N, what is the maximum speed the ball can have?
How fast (in rpm) must a centrifuge rotate if a particle 7.00 cm from the axis of rotation is to experience an acceleration of 125,000 g's?7PHow large must the coefficient of static friction be between the tires and the road if a car is to round a level curve of radius 125 m at a speed of 95 km/h?9P10PHow many revolutions per minute would a 25-m-diameter Ferris wheel need to make for the passengers to feel “weightless" at the topmost point?12P13P14P15P16P17P18P19P20P21P22P23PDetermine the tangential and centripetal components of the net force exerted on the car (by the ground) in Example 5-8 when its speed is 15 m/s. The car's mass is 950 kg.25PFor each of the cases described below, sketch and label the total acceleration vector, the radial acceleration vector, and the tangential acceleration vector. (a) A car is accelerating from 55 km/h to 70 km/h as it rounds a curve of constant radius. (b) A car is going a constant 65 km/h as it rounds a curve of constant radius. (c) A car slows down while rounding a curve of constant radius.27PCalculate the force of Earth's gravity on a spacecraft 2.00 Earth radii above the Earth's surface if its mass is 1850 kg.At the surface of a certain planet, the gravitational acceleration g has a magnitude of 12.0 m/s2. A 24.0-kg brass ball is transported to this planet. What is (a) the mass of the brass ball on the Earth and on the planet, and (b) the weight of the brass ball on the Earth and on the planet?At what distance from the Earth will a spacecraft traveling directly from the Earth to the Moon experience zero net force because the Earth and Moon pull in opposite directions with equal force?31P32P33P34P35P36P37P38P39P40P41. (II) Every few hundred years most of the planets line up on the same side of the Sun. Calculate the total force on the Earth due to Venus, Jupiter, and Saturn, assuming all four planets are in a line, Fig. 5-44. The masses are mV = 0.815 mE, mJ = 318 mE, mSat = 95.1 mE, and the mean distances of the four planets from the Sun are 108,150, 778, and 1430 million km. What fraction of the Sun's force on the Earth is this?
Figure 5-44
42 (II) Four 7.5-kg spheres are located at the corners of a square of side 0.80 m. Calculate the magnitude and direction of the gravitational force exerted on one sphere by the other three.
43. (II) Determine the distance from the Earth's center to a point outside the Earth where the gravitational acceleration due to the Earth is of its value at the Earth’s surface.
44.(II) A certain neutron star has five times the mass of our Sun packed into a sphere about 10 km in radius. Estimate the surface gravity on this monster.
45. (I) A space shuttle releases a satellite into a circular orbit 780 km above the Earth. How fast must the shuttle be moving (relative to Earth's center) when the release occurs?
46P47PCalculate the period of a satellite orbiting the Moon, 95 km above the Moon’s surface. Ignore effects of the Earth. The radius of the Moon is 1740 km.49PWhat will a spring scale read for the weight of a 58.0-kg woman in an elevator that moves (a) upward with constant speed 5.0 m/s, (b) downward with constant speed 5.0 m/s, (c) with an upward acceleration 0.23 g, (d) with a downward acceleration 0.23 g,and (e) in free fall?51P52PA Ferris wheel 22.0 m in diameter rotates once every 12.5 s (see Fig. 5-9). What is the ratio of a person's apparent weight to her real weight at (a) the top, and (b) the bottom?At what rate must a cylindrical spaceship rotate if occupants are to experience simulated gravity of 0.70 g? Assume the spaceship’s diameter is 32 m, and give your answer as the time needed for one revolution. (See Question 9, Fig 5-33 )(a) Show that if a satellite orbits very near the surface of a planet with period T, the density (=mass per unit volume) of the planet is =m/V=3/GT2 . (b) Estimate the density of the Earth, given that a satellite near the surface orbits with a period of 85 min. Approximate the Earth as a uniform sphere.Neptune is an average distance of 4.5 x 109 km from the Sun. Estimate the length of the Neptunian year using the fact that the Earth is 1.50 x 108 km from the Sun on average.The asteroid Icarus, though only a few hundred meters across, orbits the Sun like the planets. Its period is 410 d. What is its mean distance from the Sun?58PDetermine the mass of the Earth from the known period and distance of the Moon.60P61P62P63P64P65P66GP67GP68GP69GP70GP71GP72GP73GP74GP75GP76GP77GP78GP79GP80GP81GP82GP83GP84GP85GP86GP87GP88GP89GP90GP91GP92GP93GP94GPIn what ways is the word “work’' as used in everyday language the same as it is defined in physics? In what ways is it different? Give examples of both.Can a centripetal force ever do work on an object? Explain.Why is it tiring to push hard against a solid wall even though you are doing no work?Can the normal force on an object ever do work? Explain.You have two springs that are identical except that spring 1 is stiffer than spring 2 (k1 > k2). On which spring is more work done: (a) if they are stretched using the same force; (b) if they are stretched the same distance?If the speed of a particle triples, by what factor does its kinetic energy increase?List some everyday forces that are not conservative, and explain why they aren't.A hand exerts a constant horizontal force on a block that is free to slide on a frictionless surface (Fig. 6-30). The block starts from rest at point A, and by the time it has traveled a distance d to point B it is traveling with speed vB. When the block has traveled another distance d to point C, will its speed be greater than, less than, or equal to 2ve? Explain your reasoning.You lift heavy book from a table to a high shelf. List the forces on the book during this process, and state whether each is conservative or nonconservative.10QA hill has a height h. A child on a sled (total mass m) slides down starting from rest at the top. Does the speed at the bottom depend on the angle of the hill if (a) it is icy and there is no friction, and (b) there is friction (deep snow)? Explain your answers.Analyze the motion of a simple swinging pendulum in terms of energy, (a) ignoring friction, and (b) taking friction into account. Explain why a grandfather clock has to be wound up.In Fig. 6-31, water balloons are tossed from the roof of a building, all with the same speed but with different launch angles. Which one has the highest speed when it hits the ground? Ignore air resistance. Explain your answer. Figure 6-31What happens to the gravitational potential energy when water at the top of a waterfall falls to the pool below?Experienced hikers prefer to step over a fallen log in their path rather than stepping on top and stepping down on the other side. Explain.16QThe energy transformations in pole vaulting and archery are discussed in this Chapter. In a similar fashion, discuss the energy transformations related to: (a) hitting a golf ball; (b) serving a tennis ball; and (c) shooting a basket in basketball.18Q17. Two identical arrows, one with twice the speed of the other, are fired into a bale of hay. Assuming the hay exerts a constant “frictional" force on the arrows, the faster arrow will penetrate how much farther than the slower arrow? Explain.
20Q21QDescribe the energy transformations that take place when a skier starts skiing down a hill, but after a time is brought to rest by striking a snowdrift.23Q24Q25QA 75.0-kg firefighter climbs a flight of stairs 28.0 m high. How much work does he do?The head of a hammer with a mass of 1.2 kg is allowed to fall onto a nail from a height of 0.50 m. What is the maximum amount of work it could do on the nail? Why do people not just “let it fall” but add their own force to the hammer as it falls?How much work did the movers do (horizontally) pushing a 46.0-kg crate 10.3 m across a rough floor without acceleration, if the effective coefficient of friction was 0.50?A 1200-N crate rests on the floor. How much work is required to move it at constant speed (a) 5.0 m along the floor against a friction force of 230 N, and (b) 5.0 m vertically?What is the minimum work needed to push a 950-kg car 710 m up along a 9.0° incline? Ignore friction.Estimate the work you do to mow a lawn 10 m by 20 m with a 50-cm-wide mower. Assume you push with a force of about 15 N.In a certain library the first shelf is 15.0 cm off the ground, and the remaining four shelves are each spaced 38.0 cm above the previous one. If the average book has a mass of 1.40 kg with a height of 22.0 cm, and an average shelf holds 28 books (standing vertically), how much work is required to fill all the shelves, assuming the books are all laying flat on the floor to start?A lever such as that shown in Fig. 6-35 can be used to lift objects we might not otherwise be able to lift. Show that the ratio of output force, Fo, to input force, F1, is related to the lengths l1and lofrom the pivot by Fo/F1, = I1/Io. Ignore friction and the mass of the lever, and assume the work output equals the work input. Figure 6-35A box of mass 4.0 kg is accelerated from rest by a force across a floor at a rate of 2.0 m/s2 for 7.0 s. Find the net work done on the box.A 380-kg piano slides 2.9 m down a 25° incline and is kept from accelerating by a man who is pushing back on it parallel to the incline (Fig. 6-36). Determine: (a) the force exerted by the man, (b) the work done on the piano by the man, (c) the work done on the piano by the force of gravity, and (d) the net work done on the piano. Ignore friction. Figure 6-36Recall from Chapter 4, Example 4-14, that you can use a pulley and ropes lo decrease the force needed to raise a heavy load (see Fig. 6- 37). But for every meter the load is raised, how much rope must be pulled up? Account for this, using energy concepts.A grocery cart with mass of 16 kg is being pushed at constant speed up a 12o ramp by a force Fpwhich acts at an angle of 17o below the horizontal. Find the work done by each of the forces mg,FN,Fp on the cart if the ramp is 7.5 m long.The force on a particle, acting along the x axis, varies as shown in Fig. 6-38. Determine the work done by this force to move the particle along the x axis: (a) from x=0.0 to x=10.0 m; (b) from x=0.0 to x=15.0 m.A 17,000-kg jet takes off from an aircraft carrier via a catapult (Fig. 6-39a). The gases thrust out from the jet's engines exert a constant force of 130 kN on the jet; the force exerted on the jet by the catapult is plotted in Fig. 6-39b. Determine the work done on the jet: (a) by the gases expelled by its engines during launch of the jet; and (b) by the catapult during launch of the jet. Figure 6-39At room temperature, an oxygen molecule, with mass of 5.31 x 10-26 kg, typically has a kinetic energy of about 6.21 x 10-21 J. How fast is it moving?(a) If the kinetic energy of a particle is tripled, by what factor has its speed increased? (b) If the speed of a particle is halved, by what factor does its kinetic energy change?How much work is required to stop an electron (m=9.111031kg) which is moving with a speed of 1.10106m/s ?How much work must be done to stop a 925-kg car travelling at 95 km/h?19PA baseball (m = 145 g) traveling 32 m/s moves a fielder’s glove backward 25 cm when the ball is caught. What was the average force exerted by the ball on the glove?21P22P23P24. (Ill) One car has twice the mass of a second car, but only half as much kinetic energy. When both cars increase their speed by 8.0 m/s, they then have the same kinetic energy. What were the original speeds of the two cars?
25. (Ill) A 265-kg load is lifted 18.0 m vertically with an acceleration a = 0.160 g by a single cable Determine (a) the tension in the cable; (b) the net work done on the load; (c) the work done by the cable on the load; (d) the work done by gravity on the load; (e) the final speed of the load assuming it started from rest.
26. (I) By how much does the gravitational potential energy of a 54-kg pole vaulter change if her center of mass rises about 4.0 m during the jump?
A spring has a spring constant k of 88.0 N/m. How much must this spring be compressed to store 45.0 J of potential energy?28P29. (II) A 66.5-kg hiker starts at an elevation of 1270 m and climbs to the top of a peak 2660 m high. (a) What is the hiker's change in potential energy? (b) What is the minimum work required of the hiker? (c) Can the actual work done be greater than this? Explain.
30PA novice skier starting from rest, slides down an icy frictionless 8.0° incline whose vertical height is 105 m How fast is she going when she reaches the bottom?32. (I) Jane, looking for Tarzan, is running at top speed (5.0 m/s) and grabs a vine hanging vertically from a tall tree in the jungle. How high can she swing upward? Does the length of the vine affect your answer?
A sled is initially given a shove up a frictionless 23.0° incline. It reaches a maximum vertical height 1.22 m higher than where it started at the bottom. What was its initial speed?34P35. (II) A spring with k=83 N/m hangs vertically next to a ruler. The end of the spring is next to the 15-cm mark on the ruler If a 2.5-kg mass is now attached to the end of the spring, and the mass is allowed to fall, where will the end of the spring line up with the ruler marks when the mass is at its lowest position?
36P37P38P39P40P41P42. (II) What should be the spring constant k of a spring designed to bring a 1200-kg car to rest from a speed of 95 km/h so that the occupants undergo a maximum acceleration of 4.0 g?
43. (Ill) An engineer is designing a spring to be placed at the bottom of an elevator shaft. If the elevator cable breaks when the elevator is at a height h above the top of the spring, calculate the value that the spring constant k should have so that passengers undergo an acceleration of no more than 5.0 g when brought to rest. Let M be the total mass of the elevator and passengers.
44P45. (III) A cyclist intends to cycle up a 7.50° hill whose vertical height is 125 m. The pedals turn in a circle of diameter 36.0 cm. Assuming the mass of bicycle plus person is 75.0 kg, (a) calculate how much work must be done against gravity. (b) If each complete revolution of the pedals moves the bike 5.10 m along its path, calculate the average force that must be exerted on the pedals tangent to their circular path. Neglect work done by friction and other losses.
46P47P48P49P50P51P52. (II) You drop a ball from a height of 2.0 m, and it bounces back to a height of 1.6 m. (a) What fraction of its initial energy is lost during the bounce? (b) What is the ball's speed just before and just after the bounce? (c) Where did the energy go?
53. (II) A 66-kg skier starts from rest at the top of a 1200-m-long trail which drops a total of 230 m from top to bottom. At the bottom, the skier is moving 11.0 m/s. How much energy was dissipated by friction?
54. (II) A projectile is fired at an upward angle of 38.0° from the top of a 135-m-high cliff with a speed of 165 m/s. What will be its speed when it strikes the ground below? (Use conservation of energy.)
55. (II) The Lunar Module could make a safe landing if its vertical velocity at impact is 3.0 m/s or less. Suppose that you want to determine the greatest height h at which the pilot could shut off the engine if the velocity of the lander relative to the surface at that moment is (a) zero; (b) 2.0 m/s downward; (c) 2.0 m/s upward. Use conservation of energy to determine h in each case. The acceleration due to gravity at the surface of the Moon is 1.62 m/s2.
56. (III) Early test flights for the space shuttle used a “glider” (mass of 980 kg including pilot). After a horizontal launch at 480 km/h at a height of 3500 m, the glider eventually landed at a speed of 210 km/h. (a) What would its landing speed have been in the absence of air resistance? (b) What was the average force of air resistance exerted on it if it came in at a constant glide angle of 12° to the Earth's surface?
How long will It take a 2750-W motor to lift a 385-kg piano to a sixth-story window 16.0 m above?58. (I) (a) Show that one British horsepower (550 ft . Ib/s) is equal to 746 W. (b) What is the horsepower rating of a 75-W lightbulb?
An 85-kg football player traveling 5.0 m/s is stopped in 1.0 s by a tackier. (a) What is the original kinetic energy of the player? (b) What average power is required to stop him?60P61PA shot-putter accelerates a 7.3-kg shot from rest to 14 m/s in 1.5 s. What average power was developed?63P64. (II) How much work can a 2.0-hp motor do in 1.0 h?
65P66P67P68P69P70. (II) What minimum horsepower must a motor have to be able to drag a 370-kg box along a level floor at a speed of 1.20 m/s if the coefficient of friction is 0.45?
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