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J.D. Wilson, A.J. Buffa, B. Lou, College Physics with Mastering Physics, 7th edition, Addison-Wesley 2009.

Chapter 7

1. The Cartesian coordinates of a point on a circle are (1.5 m, 2.0 m). What are the polar coordinates (r, ϑ) of this point?

2. The polar coordinates of a point are (5.3 m, 32°). What are the point’s Cartesian coordinates?

3. Convert the following angles from degrees to radians, to two significant figures: (a) 15°, (b) 45°, (c) 95°, and (d) 120°.

4. Convert the following angles from radians to degrees: (a) π/6 rad, (b) 5π/12 rad, (c) 3π/4 rad, and (d) π rad.

5. Express the following angles in degrees, radians and/or revolutions (rev) as appropriate: (a) 105°, (b) 1.8 rad, and (c) 5/7 rev.

6. You measure the length of a distant car to be subtended by an angular distance of 1.5°. If the car is actually 5.0 m long, approximately how far away is the car?

7. How large an angle in radians and degrees does the diameter of the Moon subtend to a person on the Earth?

8. The hour, minute, and second hands on a clock are 0.25 m, 0.30 m, and 0.35 m long, respectively. What are the distances traveled by the tips of the hands in a 30-min interval?

9. A car with a 65-cm diameter wheel travels 3.0 km. How many revolutions does the wheel make in this distance?

10. Two gear wheels with radii of 25 cm and 60 cm have interlocking teeth. How many radians does the smaller wheel turn when the larger wheel turns 4.0 rev?

11. You ordered a 12-in. pizza for a party of five. For the pizza to be distributed evenly, how should it be cut in triangular pieces?

12. To attend the 2000 Summer Olympics, a fan flew from Mosselbaai, South Africa (34° S, 22°E) to Sydney, Australia (34° S, 151° E). (a) What is the smallest angular distance the fan has to travel: (1) 34°, (2) 12°, (3) 117°, or (4) 129°? (b) Determine the appropriate shortest flight distance, in kilometers.

13. A bicycle wheel has a small pebble embedded in its tread. The rider sets the bike upside down, and accidentally bumps the wheel, causing the pebble to move through an arc length of 25.0 cm before coming to rest. In that time, the wheel spins 35°. (a) The radius of the wheel is therefore (1) more than 25.0 cm, (2) less than 25.0 cm, (3) equal to 25.0 cm. (b) Determine the radius of the wheel.

14. At the end of her routine, an ice skater spins through 7.50 revolutions with her arms always fully outstretched at right angles to her body. If her arms are 60.0 cm long, through what arc length distance do the tips of her fingers move during her finish?

15. (a) Could a circular pie be cut such that all of the wedge-shaped pieces have an arc length along the outer crust equal to the pie’s radius? (b) If not, how many such pieces could you cut, and what would be the angular dimension of the final piece?

16. Electrical wire with a diameter of 0.50 cm is wound on a spool with a radius of 30 cm and a height of 24 cm. (a) Through how many radians must the spool be turned to wrap one even layer of wire? (b) What is the length of this wound wire?

17. A yo-yo with an axle diameter of 1.00 cm has a 90.0 cm length of string wrapped around it many times in such a way that the string completely covers the surface of its axle, but there are no double layers of string. The outermost portion of the yo-yo is 5.00 cm from the center of the axle. (a) If the yo-yo is dropped with the string fully wound, through what angle does it rotate by the time it reaches the bottom of its fall? (b) How much arc length has a piece of the yo-yo on its outer edge traveled by the time it bottoms out?

18. A computer DVD-ROM has a variable angular speed from 200 rpm to 450 rpm. Express this range of angular speed in radians per second.

19. A race car makes two and half laps around a circular track in 3.0 min. What is the car’s average angular speed?

20. What are the angular speeds of the (a) second hand, (b) minute hand, and (c) hour hand of a clock? Are the speeds constant?

21. What is the period of revolution for (a) a 9500-rpm centrifuge and (b) a 9500-rpm computer hard disk drive?

22. Determine which has the greater angular speed: particle A, which travels 160° in 2.00 s, or particle B, which travels 4π rad in 8.00 s?

23. The tangential speed of a particle on a rotating wheel is 3.0 m/s. If the particle is 0.20 m from the axis of rotation, how long will the particle take to make one revolution?

24. A merry-go-round makes 24 revolutions in a 3.0-min ride. (a) What is its average angular speed in rad/s? (b) What are the tangential speeds of two people 4.0 m and 5.0 m from the center, or axis of rotation?

25. In Exercise 13, suppose the wheel took 1.20 s to stop after it was bumped. Assume as you face the plane of the wheel, it was rotating counterclockwise. During this time, determine (a) the average angular speed and tangential speed of the pebble, (b) the average angular speed and tangential speed of a piece of grease on the wheel’s axle (radius 1.50 cm), and (c) the direction of their respective angular velocities.

26. The Earth rotates on its axis once a day and revolves around the Sun once a year. Which is greater the rotating angular speed or the revolving angular speed? Why? (b) Calculate both angular speeds in rad/s.

27. A little boy jumps onto a small merry-go-round (radius of 2.00 m) in a park and rotates for 2.30 s through an arc length of 2.55 m before coming to rest. If he landed (and stayed) at a distance of 1.75 m from the central axis of rotation of the merry-go-round, what was his average angular speed and average tangential speed?

28. The driver of a car sets the cruise control and ties the steering wheel so that the car travels at a uniform speed of 15 m/s in a circle with a diameter of 120 m. (a) Through what angular distance does the car move in 4.00 min? (b) What arc length does it travel in this time?

29.  In a noninjury, noncontact skid on icy pavement on an empty road, a car spins 1.75 revolutions while it skids to a halt. It was initially moving at 15.0 m/s, and because of the ice it was able to decelerate at a rate of only 1.50 m/s2. Viewed from above, the car spun clockwise. Determine its average angular velocity as it spun and slid to a halt.

30. An Indy car with a speed of 120 km/h goes around a level, circular track with a radius of 1.00 km. What is the centripetal acceleration of the car?

31. A wheel of radius 1.5 m rotates at a uniform speed. If a point on the rim of the wheel has a centripetal acceleration of 1.2 m/s2, what is the point's tangential speed?

32. A rotating cylinder about 16 km long and 7.0 km in diameter is designed to be used as a space colony. With what angular speed must it rotate so that the residents on it will experience the same acceleration due to gravity on Earth?

33. An airplane pilot is going to demonstrate flying in a tight vertical circle. To ensure that she doesn't black out at the bottom of the circle, the acceleration must not exceed 4.0g. If the speed of the plane is 50 m/s at the bottom of the circle, what is the minimum radius of the circle so that the 4.0g limit is not exceeded?

34. Imagine that you swing about your head a ball attached to the end of a string. The ball moves at a constant speed in a horizontal circle. (a) Can the string be exactly horizontal? Why or why not? (b) If the mass of the ball is 0.250 kg, the radius is 1.5 m, and it takes 1.2 s for the ball to make one revolution, what is the ball's tangential speed? (c) What centripetal force are you imparting to the ball via the string?

35. In Exercise 34, if you supplied a tension force of 12.5 N to the string, what angle would the string make relative to the horizontal?

36. A car with a constant speed of 83.0 km/h enters a circular flat curve with a radius of curvature of 0.400 km. If the friction between the road and the car's tires can supply a centripetal acceleration of 1.25 m/s2, does the car negotiate the curve safely? Justify the answer.

37. A student is to swing a bucket of water in a vertical circle without spilling any. (a) Explain how this task is possible. (b) If the distance from him shoulder to the centre of mass of the bucket of water is 1.0 m, what is the minimum speed required to keep the water from coming out of the bucket at the top of the swing?

38. In performing a “figure 8” maneuver, a figure skater wants to make the top part of the 8 approximately a circle of radius 2.20 m. He needs to glide through this part of the figure at approximately a constant speed, taking 4.50 s. His skates digging into the ice are capable of providing a maximum centripetal acceleration of 3.25 m/s2. Will he be able to do this as planned? If not, what adjustment can he make if he wants this part of the figure to remain the same size?

39. A light string of length of 56.0 cm connects two small square blocks, each with a mass of 1.50 kg. The system is placed on a slippery (frictionless) sheet of horizontal ice and spun so that the two blocks rotate uniformly about their common center of mass, which itself does not move. They are supposed to rotate with a period of 0.750 s. If the string can exert a force of only 100 N before it breaks, determine whether this string will work.

40. A jet pilot puts an aircraft with a constant speed into a vertical circular loop. (a) Which is greater, the normal force exerted on the seat by the pilot at the bottom of the loop or that at the top of the loop? Why? (b) If the speed of the aircraft is 700 km/h and the radius of the circle is 2.0 km, calculate the normal forces exerted on the seat by the pilot at the bottom and top of the loop. Express your answer in terms of the pilot's weight.

41. A block of mass m slides down an inclined plane into a loop-the-loop of radius r. (a) Neglecting friction, what is the minimum speed the block must have at the highest point of the loop in order to stay in the loop? (b) At what vertical height on the inclined plane (in terms of the radius of the loop) must the block be released if it is to have the required minimum speed at the top of the hoop?

42. For a scene in a movie, a stunt driver drives a 1.50 × 103 kg SUV with a length of 4.25 m around a circular curve with a radius of curvature of 0.333 km. The vehicle is to be driven off the edge of a gully 10.0 m wide, and land on the other side 2.96 m below the initial side. What is the minimum centripetal acceleration the SUV must have in going around the circular curve to clear the gully and land on the other side?

43. Consider a simple pendulum of length L that has a small mass (the bob) of mass m attached to the end of its string. If the pendulum starts out horizontally and is released from rest, show that (a) the speed at the bottom of the swing is vmax = √(2gL) and (b) the tension in the string at that point is three times the weight of the bob, or Tmax = 3mg.

44. A CD originally at rest reaches an angular speed of 40 rad/s in 5.0 s.(a) What is the magnitude of its angular acceleration? (b) How many revolutions does the CD make in the 5.0 s?

45. A merry-go-round accelerating uniformly from rest achieves its operating speed of 2.5 rpm in 5 revolutions. What is the magnitude of its angular acceleration?

46. A flywheel rotates with an angular speed of 25 rev/s. As it is brought to rest with a constant acceleration, it turns 50 rev. (a) What is the magnitude of the angular acceleration? (b) How much time does it take to stop?

47. A car on a circular track accelerates from rest. (a) The car experiences (1) only angular acceleration, (2) only centripetal acceleration, (3) both angular and centripetal accelerations? Why? (b) If the radius of the track is 0.30 km and the magnitude of the constant angular acceleration is 4.5 × 10-3 rad/s2, how long does the car take to make one lap around the track? © What is the total (vector) acceleration of the car when it has completed half of a lap?

48. Show that for a constant acceleration ϑ = ϑ0 + (ω2 – ω02)/2α

49. The blades of a fan running at low speed turn at 250 rpm. When the fan is switched to high speed, the rotation rate increases uniformly to 350 rpm in 5.75 s. (a) What is the magnitude of the angular acceleration of the blades? (b) How many revolutions do the blades go through while it is accelerating?

50. In the spin-dry cycle of a modern washing machine, a wet towel with mass of 1.50 kg is "stuck to" the inside surface of the perforated (to allow the water out) washing cylinder. To have decent removal of water, damp/ wet clothes need to experience a centripetal acceleration of at least 10g. Assuming this value, and that the cylinder has a radius of 35.0 cm, determine the constant angular acceleration of the towel required if the washing machine takes 2.50 s to achieve its final angular speed.

51. A pendulum swinging in a circular arc under the influence of gravity, as shown in Fig. 7.35, has both centripetal and tangential components of acceleration.. (a) If the pendulum bob has a speed of 2.7 m/s when the cord makes an angle of ϑ = 15° with the vertical, what are the magnitudes of the components at this time? (b) Where is the centripetal acceleration a maximum? What is the value of the tangential acceleration at that location?

52. A simple pendulum of length 2.00 m is released from a horizontal position. When it makes an angle of 30° from the vertical, determine (a) its angular acceleration, (b) its centripetal acceleration, and (c) the tension in the string. Assume the bob's mass is 1.50 kg.

53. From the known mass and radius of the Moon, compute the value of the acceleration due to gravity, gM, at the surface of the Moon.

54. The gravitational forces of the Earth and the Moon are attractive, so there must be a point on a line joining their centers where the gravitational forces on an object cancel. How far is this distance from the Earth’s center?

55. Four identical masses of 2.5 kg each are located at the corners of a square with 1.0-m sides. What is the net force on any one of the masses?

56. The average density of the Earth is 5.52 g/cm3. Assuming this is a uniform density, compute the value of G.

57. A 100-kg object is taken to a height of 300 km above the Earth’s surface. (a) What’s the object’s mass at this height? (b) What’s the object’s weight at this height?

58. A man has a mass of 75 kg on the Earth’s surface. How far above the surface of the Earth would he have to go to “lose” 10% of his body weight?

59. It takes 27 days for the Moon to orbit the Earth in a nearly circular orbit of radius 3.80 × 105 km. (a) Show in symbol notation that the mass of the Earth can be found using these data. (b) Compute the Earth's mass and compare with the value given inside the back cover of the book

60. Two objects are attracting each other with a certain gravitational force. (a) If the distance between the objects is halved, the new gravitational force will (1) increase by a factor of 2, (2) increase by a factor of 4, (3) decrease by a factor of 2, (4) decrease by a factor of 4. Why? (b) If the original force between the two objects is 0.90 N, and the distance is tripled, what is the new gravitational force between the objects?

61.  During the Apollo lunar explorations of the late 1960s and early 1970s, the main section of the spaceship remained in orbit about the Moon with one astronaut in it while the other two astronauts descended to the surface in the landing module. If the main section orbited about 50 mi above the lunar surface, determine that section’s centripetal acceleration.

62. Referring to Exercise 61, determine (a) the gravitational potential energy, (b) the total energy, (c) the energy needed to "escape" the Moon for the main section of the lunar exploration mission in orbit. Assume the mass of this section is 5000 kg.

63. The diameter of the Moon’s (nearly circular) orbit about the Earth is 3.6 × 105 km and it takes 27 days for one orbit. What is (a) the Moon’s tangential speed, (b) its kinetic energy, (c) the system potential energy and system total energy?

64. (a) What is the mutual gravitational potential energy of the configuration shown in Fig. 7.36 if all the masses are 1.0 kg? (b) What is gravitational force per unit mass at the center of the configuration?

66. An instrument package is projected vertically upward to collect data near the top of the Earth’s atmosphere (at an altitude of about 900 km). (a)  What initial speed is required at the Earth’s surface for the package to reach this height?  (b)  What percentage of the escape speed is this initial speed?

67. What is the orbital speed of a geosynchronous satellite?

68. In the year 2056, Martian Colony I wants to put a Mars-synchronous communication satellite in orbit about Mars to facilitate communications with the new bases being planned on the Red Planet. At what distance above the Martian equator would this satellite be placed?

69. The asteroid belt that lies between Mars and Jupiter may be the debris of a planet that broke apart or that was not able to form as a result of Jupiter’s strong gravitation. An average asteroid has a period of about 5.0 y. Approximately how far from the Sun would this "fifth" planet have been?

70. Using a development similar to Kepler’s law periods for planets orbiting the Sun, find the required altitude of geosynchronous satellites above the Earth.

71. Venus has a rotational period of 243 days. What would be the altitude of a synchronous satellite for this planet?

72. A small space probe is put into circular orbit about a newly discovered moon of Saturn. The moon's radius is known to be 550 km. If the probe orbits at a height of 1500 km above the moon's surface and takes 2.00 Earth days to make one orbit, determine the moon's mass.


Chapter 8


1. A wheel rolls uniformly on level ground without slipping. A piece of mud on the wheel flies off when it is at 9 o’clock position (near of wheel). Describe the subsequent motion of the mud.

2. A rope goes over a circular pulley with a radius of 6.5 cm. If the pulley makes 4 revolutions without the rope slipping, what length of rope passes over the pulley?

3. A wheel rolls 5 revolutions on a horizontal surface without slipping. If  the center of the wheel moves 3.2 m, what is the radius of the wheel?

4. A bawling ball with a radius of 15.0 cm travels down the lane so that its center is moving at 3.60 m/s. The bowler estimates that it makes about 7.50 complete revolutions in 2.00 s. Is it rolling without slipping? Prove your answer, assuming that the bowler’s quick observation limits answers to two significant figures.

5. A ball with a radius of 15 cm rolls on a level surface, and the translational speed of the center of mass is 0.25 m/s. What is the angular speed about the center of mass if the ball rolls without slipping?

6. (a) When a disk rolls without slipping, should the product rω be (1) greater than, (2) equal to, or (3) less than vCM? (B) A disk with a radius of 0.15 m rotates through 270° as it travels 0.71 m. Does the disk rolls without slipping? Prove your answer.

7. A bocce ball with a diameter of 6.00 cm rolls without slipping on a level lawn.  It has an initial angular speed of 2.35 rad/s and comes to rest after 2.50 m. Assuming constant deceleration, determine (a) the magnitude of its angular deceleration and (b) the magnitude of the maximum tangential acceleration of the ball’s surface.

8. A cylinder with a diameter of 20 cm rolls with an angular speed of 0.050 rad/s on a level surface.  If the cylinder experiences a uniform tangential acceleration of 0.018 m/s2 without slipping until its angular speed is 1.2 rad/s, through how many complete revolutions does the cylinder rotate during the time it accelerates?

9. In Fig. 8.4a, if the arm makes a 37° angle with the horizontal and a torque of 18 m N to be produced, what force must the biceps muscle supply?

10. The drain plug on a car’s engine has been tightened to a torque of 25 m N. If a 0.15 –m-long wrench is used to change the oil, what is the minimum force needed to loosen the plug?

11. In Exercise 10, due to limited work space, you must crawl under the car. The force thus cannot be applied perpendicularly to the length of the wrench.  If the applied force makes a 30° angle with the length of the wrench, what is the force required to loosen the drain plug?

12. How many different positions of stable equilibrium and unstable equilibrium are there for a cube? Consider each surface, edge, and corner to be a different position.

13. Two children are sitting on opposite ends of a uniform seesaw of negligible mass. (a) Can the seesaw be balanced if the masses of the children are different? How? (b) If a 35-kg child is 2.0 m from the pivot point (or fulcrum), how far from the pivot point will her 30 kg playmate have to sit on the other side for the seesaw to be in equilibrium?

14. A uniform meterstick pivoted at its center, as in Example 8.5, has a 100-g mass suspended at the 25.0-cm position.  (a) At what position should a 75.0 g mass be suspended to put the system in equilibrium? (b) What mass would have to be suspended at the 90.0-cm position for the system to be in equilibrium?

15. A worker applies a horizontal force to the top edge of a crate to get it to tip forward (Fig. 8.36). If the create has a mass of 100 kg and is 1.6 m tall and 0.80 m in depth and width, what is the minimum force needed to make the crate start tipping? (Assume the center of mass of the crate is at its center and static friction great enough to prevent slipping).

16. Show that the balanced meterstick in Example 8.5 is in static rotational equilibrium about a horizontal axis through the 100-cm end of the stick.

17. Telephone and electrical lines are allowed to sag between poles so that the tension will not be too great when something hits or sits on the line. (a) Is it possible to have the lines perfectly horizontal? Why or why not? (b) Suppose that a line were stretched almost perfectly horizontally between two poles that are 30 m apart. If a 0.25-kg bird perches on the wire midway between the poles and the wire sags 1.0 cm, what would be the tension in the wire?

18. In Fig. 8.37, what is the force Fm supplied by the deltoid muscle so as to hold up the outstretched arm if the mass of the arm is 3.0 kg?

19. In Figure 8.4b, determine the force exerted by the bicep muscle, assuming that the hand is holding a ball with a mass of 5.00 kg. Assume that the mass of the forearm is 8.50 kg with its center of mass located 20.0 cm away from the elbow joint. (the black dot in the figure). Assume also that the center of mass of the ball in the hand is 30.0 cm away from the elbow joint.

20. A bowling ball (mass 7.00 kg and radius 17.0 cm) is released so fast that it skids without rotating down the lane (at least for a while). Assume the ball skids to the right and the coefficient of sliding friction between the ball and the lane surface is 0.400. (a) What is the direction of the torque exerted by the friction on the ball about the center of mass of the ball? (b) Determine the magnitude of this torque (again about the ball's center of mass).

21. A variation of Russell traction (Fig. 8.38) supports the lower leg in a cast. Suppose that the patient’s leg and cast have a combined mass of 15.0 kg and m1 is 4.50 kg. (a) What is the reaction force of the leg muscles to the traction? (b) What must m2 be to keep the leg horizontal?

22. In doing physical therapy for an injured knee joint, a person raises a 5.0-kg weighted boot as shown in Fig. 8.39. Compute the torque due to the boot for each position shown.

23. An artist wishes to construct a birds and bees mobile, as shown in Fig. 8.40. If the mass of the bee on the lower left is 0.10 kg and each vertical support string has a length of 30 cm, what are the masses of the other birds and bees?

24. The location of a person’s center of gravity relative to his or her height can be found using the arrangement shown in Fig. 8.41.  The scales are initially adjusted to zero with the board alone.  (a) Would you expect the location of the center of gravity to be (1) midway between the scales, (2) toward the scale at the person’s head, or (3) toward the scale at the person’s feet? Why? (b)  Locate the center of gravity of the person relative to the horizontal dimension.

25. (a) How many uniform, identical textbooks of width 25.0 cm can be stacked on top of each other on a level surface without the stack falling over if each successive book is displaced 3.00 cm in width relative to the book below it? (b) (b) If the books are 5.00 cm thick, what will be the height of the center of mass of the stack above the level surface?

26. If four metersticks were stacked on a table with 10 cm, 15 cm, 30 cm, and 50 cm, respectively, hanging over the edge, as shown in Fig. 8.42, would the top meterstick remain on the table?

27. A 10.0 kg solid uniform cube with 0.500-m sides rests on a level surface. What is the minimum amount of work necessary to put the cube into an unstable equilibrium position?

28. While standing on a long board resting on a scaffold, a 70-kg painter paints the side of a house, as shown in Fig. 8.43. If the mass of the board is 15 kg, how close to the end can the painter stand without tipping the board over?

29. A mass is suspended by two cords as shown in Fig. 8.44. What are tensions in the cords?

30. If the cord attached to the vertical wall in Fig. 8.44 were horizontal (instead of at a 30° angle), what would the tensions in the cords be?

31. A force is applied to a cord wrapped around a solid 2.0-kg cylinder as shown in Fig. 8.45. Assuming the cylinder rolls without slipping, what is the force of friction acting on the cylinder?

32. In circus act, a uniform board (length 3.00 m, mass 35.0 kg) is suspended from a bungie-type rope at one end, and the other end rests on a concrete pillar. When a clown (mass 75.0 kg) steps out halfway onto the board, the board tilts so the rope end is 30° from the horizontal and the rope stays vertical. (a) In which situation will the rope tension be larger: (1) the board without the clown on it, (2) the board with the clown on it, or (3) you can’t tell from the data given? (b) Calculate the force exerted by the rope in both situations.

33. The forces acting on Einstein and the bicycle (fig. 2 of the Insight 8.1, Stability in Action) are the total weight of Einstein and the bicycle (mg) at the center of gravity of the system, the normal force (N) exerted by the road, and the force of static friction (fs) acting on the tires due to the road. (a) If Einstein is to maintain balance, should the tangent of the lean angle q (tan q) be (1) greater than, (2) equal to, or (3) less than fs/N? (b) The angle q in the picture is about 11°. What is the minimum coefficient of static friction ms between the road and the tires? (c) If the radius of the circle is 6.5 m, what is the maximum sped of Einstein’s bicycle?

34. A fixed 0.15-kg solid disk pulley with a radius 0.075 m is acted on by a net torque of 6.4 m N. What is the angular acceleration of the pulley?

35. What net torque is required to give a uniform 20-kg solid ball with a radius of 0.20 m an angular acceleration of 20 rad/s2?

36. For the system of masses shown in Fig. 8.46, find the moment of inertia about (a) the x-axis, (b) the y-axis, and (c) an axis through the origin and perpendicular to the page (z-axis). Neglect the masses of the connecting rods.

37. A 2000-kg Ferris wheel accelerates from rest to an angular speed of 20 rad/s in 12 s. Approximate the Ferris wheel as a circular disk with a radius of 30 m. What is the net torque on the wheel?

38. Two objects of different masses are joined by a light rod. (a) Is the moment of inertia about the center of mass the minimum or the maximum? Why? (b) If the two masses are 3.0 kg and 5.0 kg and the length of the rod is 2.0 m, find the moments of inertia of the system about an axis perpendicular to the rod, through the center of the rod and center of mass.

39. Two masses are suspended from a pulley as shown in Fig. 8.47. The pulley itself has a mass of 0.20 kg, a radius of 0.15 m, and a constant torque of 0.35 m N due to the friction between the rotating pulley and its axle. What is the magnitude of the acceleration of the suspended masses if m1 = 0.40 kg and m2 = 0.80 kg?

40. To start her lawn mower, Julie pulls on a cord that is wrapped around a pulley. The pulley has a moment of inertia about its central axis of I = 0.550 kg m2 and a radius of 5.00 cm. There is an equivalent frictional torque impeding her pull of τf = 0.430 m N. To accelerate the pulley at α = 4.55 rad/s2, (a) how much torque does Julie need to apply to the pulley? (b) How much tension must the rope exert?

41. For the system shown in Fig. 8.48, m1 = 8.0 kg, m2 = 3.0 kg, q = 30°, and the radius and mass of the pulley are 0.10 m and 0.10 kg, respectively. (a) What is the acceleration of the masses? (b) If the pulley has a constant frictional torque of 0.050 m N when the system is in motion, what is the acceleration of the masses?

 42. A meterstick pivoted about a horizontal axis through the 0-cm end is held in a horizontal position and let go. (a) What is the initial tangential acceleration of the 100-cm position? Are you surprised by this result? (b) Which position has a tangential acceleration equal to the acceleration due to gravity?

43. Pennies are placed every 10 cm on a meterstick. One end of the stick is put on a table and the other end is held horizontally with a finger, as shown in Fig. 8.49. If the finger is pulled away, what happens to the pennies?

44. A uniform 2.0-kg cylinder of radius 0.15 m is suspended by two strings wrapped around it (Fig. 8.50). As the cylinder descends, the strings unwind from it. What is the acceleration of the center of mass of the cylinder?

45. A planetary space probe is in the shape of a cylinder. To protect it from heat on one side (from the Sun's rays), operators on the Earth put it into a "barbecue mode," that is, they set it rotating about its long axis. To do this, they fire four small rockets mounted tangentially as shown in Fig. 8.51 (the probe is shown coming toward you). The object is to get the probe to rotate completely once every 30 s, starting from no rotation at all. They wish to do this by firing all four rockets for a certain length of time. Each rocket can exert a thrust of 50.0 N. Assume the probe is a uniform solid cylinder with a radius of 2.50 m and a mass of 1000 kg and neglect the mass of each rocket engine. Determine the amount of time the rockets need to be fired.

46. A ball of radius R and mass M rolls down an incline of angle θ. (a) For the ball to roll without slipping, should be the tangent of the maximum angle of incline (tan θ) be equal to (1) 3μs/2, (2) 5μs/2, (3) 7μs/2, or (4) 9μs/2? Here, μs is the coefficient of static friction. (b) If the ball is made of wood and the surface is also wood, what is the maximum angle of incline?

47. A constant retarding torque of 12 m N stops a rolling wheel of diameter 0.80 m in a distance of 15 m. How much work is done by the torque?

48. A person opens a door by applying a 15-N force perpendicular to it at a distance 0.90 m from the hinges. The door is pushed wide open (to 120°) in 2.0 s. (a) How much work was done? (b) What was the average power delivered?

49. In Fig. 8.23, a mass m descends a vertical distance from rest. (Neglect friction and the mass of the string) (a) From the conservation of mechanical energy, will the linear speed of the descending mass be (1) greater than, (2) equal to, or (3) less than √(2gh)? Why? (b) If m = 1.0 kg, M = 0.30 kg, and R = 0.15 kg, what is the linear speed of the mass after it has descended a vertical distance of 2.0 from rest?

50. A constant torque of 10 m N is applied to the rim of a 10-kg uniform disk of radius 0.20 m. What is the angular speed of the disk about an axis through its center after it rotates 2.0 revolutions from rest?

51. A 2.5-kg pulley of radius 0.15 m is pivoted about an axis through its center. What constant torque is required for the pulley to reach an angular speed of 25 rad/s after rotating 3.0 revolutions, starting from rest?

52. A solid ball of mass m rolls along a horizontal surface with a translational speed of v. What percent of its total kinetic energy is translational?

53. Estimate the ratio of the translational kinetic energy of the Earth as it orbits the Sun to the rotational kinetic energy it has about it N-S axis.

54. You wish to accelerate a small merry-go-round from rest to a rotational speed of one-third of a revolution per second by pushing tangentially on it. Assume the merry-go-round is a disk with a mass of 250 kg and a radius of 1.50 m. Ignoring friction, how hard do you have to push tangentially to accomplish this in 5.00 s?

55. A pencil 18 cm long stands vertically on its point end on a horizontal table. If it falls over without slipping, with what tangential speed does the eraser end strike the table?

56. A uniform sphere and a uniform cylinder with the same mass and radius roll at the same velocity side by side on a level surface without slipping. If the sphere and the cylinder approach an inclined plane and roll up it without slipping, will they be at the same height on the plane when they come to a stop? If not, what will be the percentage difference of the heights?

57. A hoop starts from rest at a height 1.2 m above  the base of an inclined plane and rolls down under the influence of gravity. What is the linear speed of the hoop’s center of mass just as the hoop leaves the incline and rolls onto a horizontal surface?

58. A cylindrical hoop, a cylinder, and a sphere of equal radius and mass are released at the same time from the top of an inclined plane. Using the conservation of mechanical energy, show that the sphere always gets to the bottom of the incline first with the fastest speed and that the hoop always arrives last with the slowest speed.

59. For the following objects, which all roll without slipping, determine the rotational kinetic energy about the center of mass as a percentage of the total kinetic energy: (a) a solid sphere, (b) a thin spherical shell, and (c) a thin cylindrical shell.

60. An industrial flywheel with a moment of inertia of 4.25 × 102 kg m2 rotates with a speed of 7500 rpm. (a) How much work is required to bring the flywheel to rest? (b) If this work is done uniformly in 1.5 min, how much power is required?

61. A hollow, thin-shelled ball and a solid ball of equal mass are rolled up an inclined plane (without slipping) with both balls having the same initial velocity at the bottom of the plane. (a) Which ball rolls higher on the incline before coming to rest? (b) Do the radii of the balls make a difference? (c) After stopping, the balls roll back down the incline. By the conservation of energy, both balls should have the same speed when reaching the bottom of the incline. Show this explicitly.

62. In a tumbling clothes dryer, the cylindrical drum (radius 50.0 cm and mass 35.0 kg) rotates once every second. (a) Determine the rotational kinetic energy about its central axis. (b) If it started from rest and reached that speed in 2.50 s, determine the average net torque on the dryer drum.

63. A steel ball rolls down an incline into a loop-the loop of radius R (Fig. 8.52a). (a) What minimum speed must the ball have at the top of the loop in order to stay on the track? (b) At what vertical height (h) on the incline, in terms of the radius of the loop, must the ball be released in order for it to have the required speed at the top of the loop? (Neglect frictional losses.) (c) Figure 8.52b shows the loop-the-loop of a roller coaster. What are the sensations of the riders if the roller coaster has the minimum speed or a greater speed at the top of the loop?

64. What is the angular momentum of a 2.0-g particle moving counterclockwise (as viewed from above) with an angular speed of 5π rad/s in a horizontal circle of radius 15 cm? (Give the magnitude and direction.)

65. A 10-kg rotating disk of radius 0.25 m has an angular momentum of 0.45 kg m2/s. What is the angular speed of the disk?

66. Compute the ratio of the magnitudes of the Earth’s orbital angular momentum and its rotational angular momentum. Are these moments in the same direction?

67. The Earth revolves about the Sun and spins on its axis, which is tilted 23½º to its orbital plane. (a) Assuming a circular orbit, what is the magnitude of the angular momentum associated with the Earth’s orbital motion about the Sun? (b) What is the magnitude of the angular momentum associated with the Earth’s rotation on its axis?

68. The period of the Moon’s rotation is the same as the period of its revolution: 27.3 days (sidereal). What is the angular momentum for each rotation and revolution?

69. Circular disks are used in automobile clutches and transmissions. When a rotating disk couples to a stationary one through frictional force, the energy from the rotating disk can transfer to the stationary one. (a) Is the angular-speed of the coupled disks (1) greater than, (2) less than, or (3) the same as the angular speed of the original rotating disk? Why? (b) If a disk rotating at 800 rpm couples to a stationary disk with three times the moment of inertia, what is the angular speed of the combination?

70. An ice skater has a moment of inertia of 100 kg m2 when his arms are outstretched and a moment of inertia of 75 kg m2 when his arms are tucked in close to his chest. If he starts to spin at an angular speed of 2.0 rps (revolutions per second) with his arms outstretched, what will his angular speed be when they are tucked in?
71. An ice skater spinning with outstretched arms has an angular speed of 4.0 rad/s. She tucks in her arms, decreasing her moment of inertia by 7.5%. (a) What is the resulting angular speed? (b) By what factor does the skater’s kinetic energy change? (c) Where does the extra kinetic energy come from?

72. A billiard ball at rest is struck (bold arrow in Fig. 8.53) by a cue with an average force of 5.50 N lasting for 0.050 s. The cue contacts the ball’s surface so that the lever arm is half the radius of the ball, as shown. If the cue ball has a mass of 200 g and a radius of 2.50 cm, determine the angular speed of the ball immediately after the blow.

73. A comet approaches the Sun as illustrated in Fig. 8.54 and is deflected by the Sun’s gravitational attraction. This event is considered a collision, and b is called the impact parameter. Find the distance of closest approach (d) in terms of the impact parameter and the velocities (v0 at large distances and v at closest approach). Assume that the radius of the Sun is negligible compared to d. (As the figure shows, the tail of a comet always “points” away from the Sun.)

74. While repairing his bicycle, a student turns it upside down and sets the front wheel spinning at 2.00 rev/s. Assume the wheel has a mass of 3.25 kg and all of the mass is located on the rim, which has a radius of 41.0 cm. To slow the wheel, he places his hand on the tire, thereby exerting a tangential force of friction on the wheel. It takes 3.50s to come to rest. Use the change in angular momentum to determine the force he exerts on the wheel. Assume the frictional force of the axle is negligible.

75. A kitten stands on the edge of a lazy Susan (a turntable). Assume that the lazy Susan has frictionless bearings and is initially at rest. (a) If the kitten starts to walk around the edge of the lazy Susan, the lazy Susan will (1) remain lazy and stationary, (2) rotate in the direction opposite that in which the kitten is walking, or (3) rotate in the direction the kitten is walking. Explain. (b) The mass of the kitten is 0.50 kg, and the lazy Susan has a mass of 1.5 kg and a radius of 0.30 m. If the kitten walks at a speed of 0.25 m/s, relative to the ground, what will be the angular speed of the lazy Susan? (s) When the kitten has walked completely around the edge and is back at its starting point, will that point be above the same point on the ground as it was at the start?

Chapter 9

1. A tennis racket has nylon strings. If one of the strings with a diameter of 1.0 mm is under a tension of 15 N, how much is it lengthened from its original length of 40 cm?

2. Suppose you use the tip of one finger to support a 1.0-kg object. If your finger has a diameter of 2.0 cm, what is the stress on your finger?

3. A 2.5-m nylon fishing line used to hold up a 8.0-kg fish has a diameter of 1.6 mm. How much is the line elongated?

4. A 5.0-m-long rod is stretched 0.10 m by a force. What is the strain in the rod?

5. A 250-N force is applied at a 37° angle to the surface of the end of a square bar. The surface is 4.00 cm on a side. What are (a) the compressional stress and (b) the shear stress on the bar?

6. A 4.0-kg object is supported by an aluminum wire of length 2.0 m and diameter 2.0 mm. How much will the wire stretch?

7. A copper wire has a length of 5.0 m and a diameter of 3.0 mm. Under what load will its length increase by 0.30 mm?

8. A metal wire 1.0 mm in diameter and 2.0 m long hangs vertically with a 6.0-kg object suspended from it. If the wire stretches 1.4 mm under the tension, what is the value of Young’s modulus for the metal?

9. When railroad tracks are installed, gaps are left between the rails. (a) Should a greater gap be used if rails are installed on (1) a cold day or (2) a hot day? Or (3) does the temperature not make any difference? Why? (b) Each steel rail is 8.0 m long and has a cross-sectional area of 0.0025 m2. On a hot day, each rail thermally expands as much as 3.0 × 10-3 m. If there were no gaps between the rails, what would be the force on the ends of each rail?

10. A rectangular steel column (20.0 cm × 15.0 cm) supports a load of 12.0 metric tons. If the column is 2.00 m in length before being stressed, what is the decrease in length?

11. A bimetallic rod as illustrated in Fig. 9.34 is composed of brass and copper. (a) If the rod is subjected to a compressive force, will the rod bend toward the brass or the copper? Why? (b) Justify your answer mathematically if the compressive force is 5.00 × 104 N.

12. Two same-size metal posts, one aluminum and one copper, are subjected to equal shear stresses. (a) Which post will show the larger deformation angle, (1) the copper post or (2) the aluminum post? Or (3) Is the angle the same for both? Why? (b) By what factor is the deformation angle of one post greater than the other?

13. A 85.0-kg person stands on one leg and 90% of the weight is supported by the upper leg connecting the knee and hip joint – the femur. Assuming the femur is 0.650 m long and has a radius of 2.00 cm, by how much is the bone compressed?

14. Two metal plates are held together by two steel rivets, each of diameter 0.20 cm and length 1.0 cm. How much force must be applied parallel to the plates to shear off both rivets?

15. (a) Which of the liquids in Table 9.1 has the greatest compressibility? Why? (b) For equal volumes of ethyl alcohol and water, which would require more pressure to be compressed by 0.10%, and how many times more?

16. How much pressure would be required to compress a quantity of mercury by 0.010%?

17. A brass cube 6.0 cm on each side is placed in a pressure chamber and subjected to a pressure of 1.2 × 107 N/m2 on all of its surfaces. By how much will each side be compressed under this pressure?

8. A cylindrical eraser of negligible mass is dragged across a paper at a constant velocity to the right by its pencil. The coefficient of kinetic friction between eraser and paper is 0.650. The pencil pushes down with 4.20 N. The height of the eraser is 1.10 cm and its diameter is 0.760 cm. Its top surface is displaced horizontally 0.910 mm relative to the bottom. Determine the shear modulus of the eraser material.

19. A 45-kg traffic light is suspended from two steel cables of equal length and radii 0.50 cm. If each cable makes a 15° angle with the horizontal, what is the fractional increase in their length due to the weight of the light?

20. In his original barometer, Pascal used water instead of mercury. (a) Water is less dense than mercury, so the water barometer would have (1) a higher height than, (2) a lower height than, or (3) the same height as the mercury barometer. Why? (b) How high would the water column have been?  

21. If you dive to a depth of 10 m below the surface of a lake, (a) what is the pressure due to the water alone? (b) What is the absolute pressure at that depth?

22. In an open U-tube, the pressure of a water column on one side is balanced by the pressure of a column of gasoline on the other side. (a) Compared to the height of the water column, the gasoline column will have (1) a higher height, (2) a lower height, or (3) the same height. Why? (b) If the height of the water column is 15 cm, what is the height of the gasoline column?

23. A 75.0-kg athlete performs a single-hand handstand. If the area of the hand in contact with the floor is 125 cm2, what pressure is exerted on the floor?

24. A rectangular fish tank measuring 0.75 m × 0.50 m is filled with water to a height of 65 cm. What is the gauge pressure on the bottom of the tank?

25. (a) What is the absolute pressure at a depth of 10 m in a lake? (b) What is the gauge pressure?

26. The gauge pressure in both tires of a bicycle is 690 kPa. If the bicycle and the rider have a combined mass of 90.0 kg, what is the area of contact of each tire with the ground? (Assume that each tire supports half the total weight of the bicycle.)

27. In a sample of seawater taken from an oil spill, an oil layer 4.0 cm thick floats on 55 cm of water. If the density of the oil is 0.75 × 103 kg/m3, what is the absolute pressure on the bottom of the container?

28. In a lecture demonstration, an empty can is used to demonstrate the force exerted by air pressure (Fig. 9.35). A small quantity of water is poured into the can, and the water is brought to a boil. Then the can is sealed with a rubber stopper. As you watch, the can is slowly crushed with sounds of metal bending. (Why is a rubber stopper used as a safety precaution?) (a) This is because of (1) thermal expansion and contraction, (2) a higher steam pressure inside the can, or (3) a lower pressure inside the can as steam condenses. Why? (b) Assuming the dimensions of the can are 0.24 m × 0.16 m × 0.10 m and the inside of the can is in a perfect vacuum, what is the total force exerted on the can by the air pressure? 

29. What is the fractional decrease in pressure when a barometer is raised 40.0 m to the top of a building?

30. To drink a soda (assume same density as water) through a straw requires that your lower the pressure at the top of the straw. What does the pressure need to be at the top of a straw that is 15.0 cm above the surface of the soda in order for the soda to reach your lips?

31. During a plane flight, a passenger experiences ear pain due to a head cold that has clogged his Eustachian tubes.  Assuming the pressure in his tubes remained at 1.00 atm (from sea level) and the cabin pressure is maintained at 0.900 atm, determine the air pressure force (including its direction) on one eardrum, assuming it has a diameter of 0.800 cm.

32. Here is a demonstration Pascal used to show the importance of a fluid’s pressure on the fluid’s depth (Fig. 9.36): An oak barrel with a lid of area 0.20 m2 is filled with water. A long, thin tube of cross-sectional area 5.0 × 10-5 m2 is inserted into a hole at the center of the lid, and water is poured into the tube. When the water reaches 12 m high, the barrel bursts. (a) What was the weight of the water in the tube? (b) What was the pressure of the water on the lid of the barrel? (c) What was the net force on the lid due to the water pressure?

33. The door and the seals on an aircraft are subject to a tremendous amount of force during flight. At an altitude of 10000 m (about 33000 ft), the air pressure outside the airplane is only 2.7 × 104 N/m2, while the inside is still at normal atmospheric pressure, due to pressurization of the cabin. Calculate the force due to the air pressure on a door of area 3.0 m2.

34. The pressure exerted by a person’s lungs can be measured by having the person blow as hard as possible into one side of a manometer. If a person blowing into one side of an open-tube manometer produces an 80-cm difference between the heights of the columns of water in the manometer arms, what is the gauge pressure of the lungs?

35. In a head-on auto collision, the driver, who had his air bags disconnected, hits his head on the windshield, fracturing his skull. Assuming the driver’s head has a mass of 4.0 kg, the area of the head to hit the windshield to be 25 cm2, and an impact time of 3.0 ms, with what speed does his head hit the windshield?

36.  A cylinder has a diameter of 15 cm (Fig. 9.37). The water level in the cylinder is maintained at a constant height of 0.45 m. If the diameter of the spout pipe is 0.50 cm, how high is h, the vertical stream of water?

37.  In 1960, the U.S. Navy’s bathyscaphe Trieste (a submersible) descended to a depth of 10912 m (about 35000 ft) into the Mariana Trench in the Pacific Ocean. (a) What was the pressure at that depth? (Assume that seawater is incompressible.) (b) What was the force on a circular observation window with a diameter of 15 cm?

38. The output piston of a hydraulic press has a cross-sectional area of 0.25 m2. (a) How much pressure on the input piston is required for the press to generate a force of 1.5 × 106 N? (b) What force is applied to the input piston if it has a diameter of 5.0 cm?

39. A hydraulic lift in a garage has two pistons: a small one of cross-sectional area 4.00 cm2 and a large one of cross-sectional area 250 cm2 (a) If this lift is designed to raise a 3500-kg car, what minimum force must be applied to the small piston? (b) If the force is applied through compressed air, what must be the minimum air pressure applied to the small piston? 

40. The Magdeburg water bridge is a channel bridge over the River Elbe in Germany (Fig. 9.38). Its dimension are length 918 m, width 43.0 m, and depth 4.25 m. (a) When filled with water, what is the weight of the water? (b) What is the pressure on the bridge floor?

41. A hypodermic syringe has a plunger of area 2.5 cm2 and a 5.0 ×10-3-cm2 needle. (a) If a 1.0-N force is applied to the plunger, what is the gauge pressure in the syringe’s chamber? (b) If a small obstruction is at the end of the needle, what force does the fluid exert on it? (c) If the blood pressure in a vein is 50 mm Hg, what force must be applied on the plunger so that fluid can be injected into the vein?  

42. A funnel has a cork blocking its drain tube. The cork has a diameter of 1.50 cm and is held in place by static friction with the sides of the drain tube. When water is added to a height of 10.0 cm above the cork, it comes flying out of the tube. Determine the maximum force of static friction between the cork and drain tube. Neglect the weight of the cork. 

43. (a) If the density of an object is exactly equal to the density of a fluid, the object will (1) float, (2) sink, (3) stay at any height in the fluid, as long as it is totally immersed. (b) A cube 8.5 cm on each side has a mass of 0.65 kg. Will the cube float or sink in water? Prove your answer.

44. A rectangular boat, as illustrated in Fig. 9.39, is overloaded such that the water level is just 1.0 cm below the top of the boat. What is the combined mass of the people and the boat?  

45. An object has a weight of 8.0 N in air. However, it apparently weighs only 4.0 N when it is completely submerged in water. What is the density of the object? 

46. When a 0.80-kg crown is submerged in water, its apparent weight is measured to be 7.3 N. Is the crown pure gold?

47. A steel cube 0.30 m on each side is suspended from a scale and immersed in water. What will the scale read?

48. A solid ball has a weight of 3.0 N. When it is submerged in water, it has an apparent weight of 2.7 N. What is the density of the ball?

49. A wood cube 0.30 m on each side has a density of 700 kg/m3 and floats levelly in water. (a) What is the distance from the top of the wood to the water surface? (b) What mass has to be placed on top of the wood so that its top is just at the water level? 

50. (a) Given a piece of metal with a light string attached, a scale, and a container of water in which the piece of metal can be submersed, how could you find the volume of the piece without using the variation in the water level? (b) An object has a weight of 0.882 N. It is suspended from a scale, which reads 0.735 N when the piece is submerged in water. What are the volume and density of the piece of metal? 

51. An aquarium is filled with a liquid. A cork cube, 10.0 cm on a side, is pushed and held at rest completely submerged in the liquid. It takes a force of 7.84 N to hold it under the liquid. If the density of cork is 200 kg/m3, find the density of the liquid.

52. A block of iron quickly sinks in water, but ships constructed of iron float. A solid cube of iron 1.0 m on each side is made into sheets. To make these sheets into a hollow cube that will not sink, what should be the minimum length of the sides of the sheets?  

53. Plans are being made to bring back the zeppelin, a lighter-than-air airship like the Goodyear blimp that carries passengers and cargo, but is filled with helium, not flammable hydrogen as was used in the ill-fated Hindenburg. (See opening Physics Facts.) One design calls for the ship to be 110 m long and to have a total mass (without helium) of 30.0 metric tons. Assuming the ship’s “envelope” to be cylindrical, what would its diameter have to be so as to lift the total weight of the ship and the helium? 

54. A girl floats in a lake with 97% of her body beneath the water. What are (a) her mass density and (b) her weight density? 

55. A spherical navigation buoy is tethered to the lake floor by a vertical cable (Fig. 9.41). The outside diameter of the buoy is 1.00 m. The interior of the buoy consists of an aluminum shell 1.0 cm thick, and the rest is solid plastic. The density of aluminum is 2700 kg/m3 and the density of the plastic is 200 kg/m3 The buoy is set to float exactly halfway out of the water. Determine the tension in the cable. 

56. Figure 9.41 shows a simple laboratory experiment. Calculate (a) the volume and (b) the density of the suspended sphere. (Assume that the density of the sphere is uniform and that the liquid in the beaker is water.) (c) Would you be able to make the same determinations if the liquid in the beaker were mercury? (See Table 9.2.) Explain. 

57. An ideal fluid is moving at 3.0 m/s in a section of a pipe of radius 0.20 m. If the radius in another section is 0.35 m, what is the flow speed there? 

58. (a) If the radius of a pipe narrows to half of its original size, will the flow speed in the narrow section (1) increase by a factor of 2, (2) increase by a factor of 4, (3) decrease by a factor of 2, or (4) decrease by a factor of 4? Why? (b) If the radius widens to three times its original size, what is the ratio of the flow speed in the wider section to that in the narrow section? 

59. Water flows through a horizontal tube similar to that in Fig. 9.20. However in this case, the constricted part of the tube is half the diameter of the larger part. If the water speed is 1.5 m/s in the larger parts of the tube, by how much does the pressure drop in the constricted part? Express the final answer in atmospheres.

60. The speed of blood in a major artery of diameter 1.0 cm is 4.5 cm/s (a) What is the flow rate in the artery? (b) If the capillary system has a total cross-sectional area of 2500 cm2, the average speed of blood through the capillaries is what percentage of that through the major artery? (c) Why must blood flow at low speed through the capillaries? 

61. The blood flow speed through an aorta with a radius of 1.00 cm is 0.265 m/s. If hardening of the arteries causes the aorta to be constricted to a radius of 0.800 cm, by how much would the blood flow speed increase? 

62. Using the data and result of Exercise 61, calculate the pressure difference between the two areas of the aorta. (Blood density: ρ = 1.06 × 103kg/m3).

63. In a dramatic lecture demonstration, a physics professor blows hard across the top of a copper penny that is at rest on a level desk. By doing this at the right speed, he can get the penny to accelerate vertically, into the airstream, and then deflect it into a tray, as shown in Fig. 9.42. Assuming the diameter of a penny is 1.90 cm and it has a mass of 2.50 g, what is the minimum airspeed needed to lift the penny off the tabletop? Assume the air under the penny remains at rest.

64. The spout heights in the container in Fig. 9.43 are 10 cm, 20 cm, 30 cm, and 40 cm. The water level is maintained at a 45-cm height by an outside supply. (a) What is the speed of the water out of each hole? (b) Which water stream has the greatest range relative to the base of the container? Justify your answer.

65. In Conceptual Example 9.14, it was explained why a stream of water from a faucet necks down into a smaller cross-sectional area as it descends. Suppose at the top of the stream it has a cross-sectional area of 2.0 cm2, and a vertical distance 5.0 cm below the cross-sectional area of the stream is 0.80 cm2. What is (a) the speed of the water and (b) the flow rate?

66. Water flows at a rate of 25 L/min through a horizontal 7.0-cm-diameter pipe under a pressure a pressure of 6.0 Pa. At one point, calcium deposits reduce the cross-sectional area of the pipe to 30 cm2. What is the pressure at this point? (Consider the water to be an ideal fluid.)

67. As a fire-fighting method, a homeowner in the deep woods rigs up a water pump to bring water from a lake that is 10.0 below the level of the house. If the pump is capable of producing a gauge pressure of 140 kPa, at what rate (in L/s) can water be pumped to the house assuming the hose has a radius of 5.00 cm?

68. A Venturi meter can be used to measure the flow speed of a liquid. A simple such device is shown in Fig. 9.44. Show that the flow speed of an ideal fluid is given by v1 = √(2gΔh/((A1/A2)2 – 1)).

69. The pulmonary artery, which connects the heart to the lungs, is about 8.0 cm long and has an inside diameter of 5.0 mm. If the flow rate in it is to be 25 mL/s, what is the required pressure difference over its length?

70. A hospital patient receives a quick 500-cc blood transfusion through a needle with a length of 5.0 cm and an inner diameter of 1.0 mm.  If the blood bag is suspended 0.85 m above the height where the blood where the blood first starts to flow into the vein, how long does the transfusion take?

71. A nurse needs to draw 20.0 cc of blood from a patient and deposit it into a small plastic container whose interior is at atmospheric pressure. He inserts the needle end of a long tube into a vein where the average gauge pressure is 30.0 mm Hg. This allows the internal pressure in the vein to push blood into the collection container. The needle is 0.900 mm in diameter and 2.54 cm long. The long tube is wide and smooth enough that we can assume its resistance is negligible, and that all the resistance to blood flow occurs in the narrow needle. How long does it take him to collect the sample?

72. What is the difference in volume (due only to pressure changes, and not temperature or other factors) between 1000 kg of water at the surface (assume 4 ºC) of the ocean and the same mass at the deepest known depth, 8.00 km? (Mariana Trench, assume 4ºC also.)


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