Why do airplanes normally take off into the wind?

Problem 1PE At its peak, a tornado is 60.0 m in diameter and carries 500 km/h winds. What is its angular velocity in revolutions per second?

Problem 1Q If one material has a higher density than another, must the molecules of the first be heavier than those of the second? Explain.

Problem 2PE Integrated Concepts An ultracentrifuge accelerates from rest to 100,000 rpm in 2.00 min. (a) What is its angular acceleration in rad/s2 ? (b) What is the tangential acceleration of a point 9.50 cm from the axis of rotation? (c) What is the radial acceleration in m/s2 and multiples of g of this point at full rpm?

Problem 3PE Integrated Concepts You have a grindstone (a disk) that is 90.0 kg, has a 0.340-m radius, and is turning at 90.0 rpm, and you press a steel axe against it with a radial force of 20.0 N. (a) Assuming the kinetic coefficient of friction between steel and stone is 0.20, calculate the angular acceleration of the grindstone. (b) How many turns will the stone make before coming to rest?

Problem 4Q Consider what happens when you push both a pin and the blunt end of a pen against your skin with the same force. Decide what determines whether your skin is cut—the net force applied to it or the pressure.

Problem 4PE Unreasonable Results You are told that a basketball player spins the ball with an angular acceleration of 100 rad/s2 . (a) What is the ball’s final angular velocity if the ball starts from rest and the acceleration lasts 2.00 s? (b) What is unreasonable about the result? (c) Which premises are unreasonable or inconsistent?

With the aid of a string, a gyroscope is accelerated from rest to 32 rad/s in 0.40 s. (a) What is its angular acceleration in \(\mathrm{rad/s^2}\)? (b) How many revolutions does it go through in the process?

Problem 5Q A small amount of water is boiled in a 1 -gallon metal can. The can is removed from the heat and the lid put on. As the can cools, it collapses and looks crushed. Explain.

When blood pressure is measured, why must the jacket be held at the level of the heart?

Problem 7PE A gyroscope slows from an initial rate of 32.0 rad/s at a rate of 0.700 rad/s2 . (a) How long does it take to come to rest? (b) How many revolutions does it make before stopping?

An ice cube floats in a glass of water filled to the brim. What can you say about the density of ice? As the ice melts, will the water overflow? Explain.

Problem 8Q Mill an ice cube float in a glass of alcohol? Why or why not?

Problem 8PE During a very quick stop, a car decelerates at 7.00 m/s2. (a) What is the angular acceleration of its 0.280-m-radius tires, assuming they do not slip on the pavement? (b) How many revolutions do the tires make before coming to rest, given their initial angular velocity is 95.0 rad/s ? (c) How long does the car take to stop completely? (d) What distance does the car travel in this time? (e) What was the car’s initial velocity? (f) Do the values obtained seem reasonable, considering that this stop happens very quickly?

Problem 9Q A submerged can of Coke® will sink, but a can of Diet Coke® will float. (Try it!) Explain.

Problem 9PE Everyday application: Suppose a yo-yo has a center shaft that has a 0.250 cm radius and that its string is being pulled. (a) If the string is stationary and the yo-yo accelerates away from it at a rate of 1.50 m/s2 , what is the angular acceleration of the yo-yo? (b) What is the angular velocity after 0.750 s if it starts from rest? (c) The outside radius of the yo-yo is 3.50 cm. What is the tangential acceleration of a point on its edge?

(II) In a movie, Tarzan evades his captors by hiding underwater for many minutes while breathing through a long, thin reed. Assuming the maximum pressure difference his lungs can manage and still breathe is \(-85 \mathrm{~mm}-\mathrm{Hg}\), calculate the deepest he could have been.

Problem 10PE This problem considers additional aspects of example Calculating the Effect of Mass Distribution on a MerryGo-Round. (a) How long does it take the father to give the merry-go-round an angular velocity of 1.50 rad/s? (b) How many revolutions must he go through to generate this velocity? (c) If he exerts a slowing force of 300 N at a radius of 1.35 m, how long would it take him to stop them?

Problem 10Q Why don't ships made of iron sink?

Problem 11PE Calculate the moment of inertia of a skater given the following information. (a) The 60.0-kg skater is approximated as a cylinder that has a 0.110-m radius. (b) The skater with arms extended is approximately a cylinder that is 52.5 kg, has a 0.110-m radius, and has two 0.900-m-long arms which are 3.75 kg each and extend straight out from the cylinder like rods rotated about their ends.

Explain how the tube in Fig. , known as a siphon, can transfer liquid from one container to a lower one even though the liquid must flow uphill for part of its journey. (Note that the tube must be filled with liquid to start with.) FIGURE 10-45 Question 11. A siphon.

Problem 12PE The triceps muscle in the back of the upper arm extends the forearm. This muscle in a professional boxer exerts a force of 2.00×103 N with an effective perpendicular lever arm of 3.00 cm, producing an angular acceleration of the forearm of 120 rad/s2 . What is the moment of inertia of the boxer’s forearm?

Problem 12Q A barge filled high with sand approaches a low bridge over the river and cannot quite pass under it. Should sand be added to, or removed from, the barge? [Hint: Consider Archimedes' principle.)

Problem 13PE A soccer player extends her lower leg in a kicking motion by exerting a force with the muscle above the knee in the front of her leg. She produces an angular acceleration of 30.00 rad/s2 and her lower leg has a moment of inertia of 0.750 kg ? m2 . What is the force exerted by the muscle if its effective perpendicular lever arm is 1.90 cm?

Problem 13Q Will an empty balloon have precisely the same apparent weight on a scale as a balloon filled with air? Explain.

Problem 14PE Suppose you exert a force of 180 N tangential to a 0.280-m-radius 75.0-kg grindstone (a solid disk). (a)What torque is exerted? (b) What is the angular acceleration assuming negligible opposing friction? (c) What is the angular acceleration if there is an opposing frictional force of 20.0 N exerted 1.50 cm from the axis?

Problem 14Q Explain why helium weather balloons, which are used to measure atmospheric conditions at high attitudes, are normally released while filled to only 10-20% of their maximum volume.

Problem 15CQ Suppose a child gets off a rotating merry-go-round. Does the angular velocity of the merry-go-round increase, decrease, or remain the same if: (a) He jumps off radially? (b) He jumps backward to land motionless? (c) He jumps straight up and hangs onto an overhead tree branch? (d) He jumps off forward, tangential to the edge? Explain your answers. (Refer to Figure 10.34).

Problem 15PE Consider the 12.0 kg motorcycle wheel shown in Figure 10.38. Assume it to be approximately an annular ring with an inner radius of 0.280 m and an outer radius of 0.330 m. The motorcycle is on its center stand, so that the wheel can spin freely. (a) If the drive chain exerts a force of 2200 N at a radius of 5.00 cm, what is the angular acceleration of the wheel? (b) What is the tangential acceleration of a point on the outer edge of the tire? (c) How long, starting from rest, does it take to reach an angular velocity of 80.0 rad/s?

Problem 16PE Zorch, an archenemy of Superman, decides to slow Earth’s rotation to once per 28.0 h by exerting an opposing force at and parallel to the equator. Superman is not immediately concerned, because he knows Zorch can only exert a force of 4.00×107 N (a little greater than a Saturn V rocket’s thrust). How long must Zorch push with this force to accomplish his goal? (This period gives Superman time to devote to other villains.) Explicitly show how you follow the steps found in Problem-Solving Strategy for Rotational Dynamics.

Problem 16Q Why do you float higher in salt water than in fresh water?

Problem 17PE An automobile engine can produce 200 N · m of torque. Calculate the angular acceleration produced if 95.0% of this torque is applied to the drive shaft, axle, and rear wheels of a car, given the following information. The car is suspended so that the wheels can turn freely. Each wheel acts like a 15.0 kg disk that has a 0.180 m radius. The walls of each tire act like a 2.00-kg annular ring that has inside radius of 0.180 m and outside radius of 0.320 m. The tread of each tire acts like a 10.0-kg hoop of radius 0.330 m. The 14.0-kg axle acts like a rod that has a 2.00-cm radius. The 30.0-kg drive shaft acts like a rod that has a 3.20-cm radius.

If you dangle two pieces of paper vertically, a few inches apart (Fig. ), and blow between them, how do you think the papers will move? Try it and see. Explain. FIGURE 10-46 Question 17.

Problem 18PE Starting with the formula for the moment of inertia of a rod rotated around an axis through one end perpendicular to its l?engt?h (?I = M ? l2 / 3), prove that the moment of inertia of a rod rotated about an axis through its center perpendicular to its? leng?th is ?I? l2 / 12 . You will find the graphics in Figure 10.12 useful in visualizing these rotations.

Problem 18Q Why does the canvas top of a convertible bulge out when the car is traveling at high speed? [Hint: The windshield deflects air upward, pushing streamlines closer together.)

Unreasonable Results A gymnast doing a forward flip lands on the mat and exerts a \(\text{500-N} \cdot \mathrm m\) torque to slow and then reverse her angular velocity. Her initial angular velocity is 10.0 rad/s, and her moment of inertia is \(\mathrm{0.050 ~kg \cdot m^2}\). (a) What time is required for her to exactly reverse her spin? (b) What is unreasonable about the result? (c) Which premises are unreasonable or inconsistent?

Problem 19Q Roofs of houses are sometimes "blown" off (or are they pushed off?) during a tornado or hurricane. Explain using Bernoulli's principle.

Problem 20PE Unreasonable Results An advertisement claims that an 800-kg car is aided by its 20.0-kg flywheel, which can accelerate the car from rest to a speed of 30.0 m/s. The flywheel is a disk with a 0.150-m radius. (a) Calculate the angular velocity the flywheel must have if 95.0% of its rotational energy is used to get the car up to speed. (b) What is unreasonable about the result? (c) Which premise is unreasonable or which premises are inconsistent?

Problem 20Q Children are told to avoid standing too close to a rapidly moving train because they might get sucked under it. Is this possible? Explain.

Problem 21Q A tall Styrofoam cup is filled with water. Two holes are punched in the cup near the bottom, and water begins rushing out. If the cup is dropped so it falls freely, will the water continue to flow from the holes? Explain.

Problem 22PE What is the final velocity of a hoop that rolls without slipping down a 5.00-m-high hill, starting from rest?

Problem 22Q Why do airplanes normally take off into the wind?

Problem 23CQ Competitive divers pull their limbs in and curl up their bodies when they do flips. Just before entering the water, they fully extend their limbs to enter straight down. Explain the effect of both actions on their angular velocities. Also explain the effect on their angular momenta.

Problem 23PE (a) Calculate the rotational kinetic energy of Earth on its axis. (b) What is the rotational kinetic energy of Earth in its orbit around the Sun?

Why does the stream of water from a faucet become narrower as it falls (Fig. 10-47)?

Problem 24CQ Draw a free body diagram to show how a diver gains angular momentum when leaving the diving board.

Problem 24PE Calculate the rotational kinetic energy in the motorcycle wheel (Figure 10.38) if its angular velocity is 120 rad/s. Assume M = 12.0 kg, R1 = 0.280 m, and R2 = 0.330 m.

Problem 24P (II) A crane lifts the 13,000-kg steel hull of a sunken ship out of the water. Determine (a) the tension in the crane's cable when the hull is fully submerged in the water, and (b) the tensior when the hull is completely out of the water.

Problem 24Q Two ships moving in parallel paths close to one another risk colliding. Why?

Problem 25PE A baseball pitcher throws the ball in a motion where there is rotation of the forearm about the elbow joint as well as other movements. If the linear velocity of the ball relative to the elbow joint is 20.0 m/s at a distance of 0.480 m from the joint and the moment of inertia of the forearm is 0.500 kg ? m2 , what is the rotational kinetic energy of the forearm?

Problem 26CQ Describe two different collisions—one in which angular momentum is conserved, and the other in which it is not. Which condition determines whether or not angular momentum is conserved in a collision?

Problem 26PE While punting a football, a kicker rotates his leg about the hip joint. The moment of inertia of the leg is 3.75 kg ? m2 and its rotational kinetic energy is 175 J. (a) What is the angular velocity of the leg? (b) What is the velocity of tip of the punter’s shoe if it is 1.05 m from the hip joint? (c) Explain how the football can be given a velocity greater than the tip of the shoe (necessary for a decent kick distance).

Problem 27CQ Suppose an ice hockey puck strikes a hockey stick that lies flat on the ice and is free to move in any direction. Which quantities are likely to be conserved: angular momentum, linear momentum, or kinetic energy (assuming the puck and stick are very resilient)?

Problem 27PE A bus contains a 1500 kg flywheel (a disk that has a 0.600 m radius) and has a total mass of 10,000 kg. (a) Calculate the angular velocity the flywheel must have to contain enough energy to take the bus from rest to a speed of 20.0 m/s, assuming 90.0% of the rotational kinetic energy can be transformed into translational energy. (b) How high a hill can the bus climb with this stored energy and still have a speed of 3.00 m/s at the top of the hill? Explicitly show how you follow the steps in the Problem-Solving Strategy for Rotational Energy.

Problem 28CQ While driving his motorcycle at highway speed, a physics student notices that pulling back lightly on the right handlebar tips the cycle to the left and produces a left turn. Explain why this happens.

Problem 28PE A ball with an initial velocity of 8.00 m/s rolls up a hill without slipping. Treating the ball as a spherical shell, calculate the vertical height it reaches. (b) Repeat the calculation for the same ball if it slides up the hill without rolling.

Problem 29CQ While driving his motorcycle at highway speed, a physics student notices that pulling back lightly on the right handlebar tips the cycle to the left and produces a left turn. Explain why this happens.

Problem 29PE While exercising in a fitness center, a man lies face down on a bench and lifts a weight with one lower leg by contacting the muscles in the back of the upper leg. (a) Find the angular acceleration produced given the mass lifted is 10.0 kg at a distance of 28.0 cm from the knee joint, the moment of inertia of the lower leg is 0.900 kg ? m2 , the muscle force is 1500 N, and its effective perpendicular lever arm is 3.00 cm. (b) How much work is done if the leg rotates through an angle of 20.0º with a constant force exerted by the muscle?

Problem 30CQ Gyroscopes used in guidance systems to indicate directions in space must have an angular momentum that does not change in direction. Yet they are often subjected to large forces and accelerations. How can the direction of their angular momentum be constant when they are accelerated?

To develop muscle tone, a woman lifts a 2.00-kg weight held in her hand. She uses her biceps muscle to flex the lower arm through an angle of \(60.0^\circ\). (a) What is the angular acceleration if the weight is 24.0 cm from the elbow joint, her forearm has a moment of inertia of \(\mathrm{0.250~kg \cdot m^2}\), and the net force she exerts is 750 N at an effective perpendicular lever arm of 2.00 cm? (b) How much work does she do?

Problem 31PE Consider two cylinders that start down identical inclines from rest except that one is frictionless. Thus one cylinder rolls without slipping, while the other slides frictionlessly without rolling. They both travel a short distance at the bottom and then start up another incline. (a) Show that they both reach the same height on the other incline, and that this height is equal to their original height. (b) Find the ratio of the time the rolling cylinder takes to reach the height on the second incline to the time the sliding cylinder takes to reach the height on the second incline. (c) Explain why the time for the rolling motion is greater than that for the sliding motion.

Problem 32PE What is the moment of inertia of an object that rolls without slipping down a 2.00-m-high incline starting from rest, and has a final velocity of 6.00 m/s? Express the moment of inertia as a multip ? le of ?MR2, where ? M is the mass of the obj? ect and ?R is its radius.

Suppose a 200-kg motorcycle has two wheels like the one described in 10.15 and is heading toward a hill at a speed of 30.0 m/s. (a) How high can it coast up the hill, if you neglect friction? (b) How much energy is lost to friction if the motorcycle only gains an altitude of 35.0 m before coming to rest? Reference 10.15: Consider the 12.0 kg motorcycle wheel shown in Figure 10.38. Assume it to be approximately an annular ring with an inner radius of 0.280 m and an outer radius of 0.330 m. The motorcycle is on its center stand, so that the wheel can spin freely. (a) If the drive chain exerts a force of 2200 N at a radius of 5.00 cm, what is the angular acceleration of the wheel? (b) What is the tangential acceleration of a point on the outer edge of the tire? (c) How long, starting from rest, does it take to reach an angular velocity of 80.0 rad/s?

In softball, the pitcher throws with the arm fully extended (straight at the elbow). In a fast pitch the ball leaves the hand with a speed of 139 km/h. (a) Find the rotational kinetic energy of the pitcher’s arm given its moment of inertia is \(\mathrm{0.720~ kg \cdot m^2}\) and the ball leaves the hand at a distance of 0.600 m from the pivot at the shoulder. (b) What force did the muscles exert to cause the arm to rotate if their effective perpendicular lever arm is 4.00 cm and the ball is 0.156 kg?

Problem 35PE Construct Your Own Problem Consider the work done by a spinning skater pulling her arms in to increase her rate of spin. Construct a problem in which you calculate the work done with a “force multiplied by distance” calculation and compare it to the skater’s increase in kinetic energy.

Problem 37PE (a) What is the angular momentum of the Moon in its orbit around Earth? (b) How does this angular momentum compare with the angular momentum of the Moon on its axis? Remember that the Moon keeps one side toward Earth at all times. (c) Discuss whether the values found in parts (a) and (b) seem consistent with the fact that tidal effects with Earth have caused the Moon to rotate with one side always facing Earth.

Problem 38PE Suppose you start an antique car by exerting a force of 300 N on its crank for 0.250 s. What angular momentum is given to the engine if the handle of the crank is 0.300 m from the pivot and the force is exerted to create maximum torque the entire time?

Problem 39PE A playground merry-go-round has a mass of 120 kg and a radius of 1.80 m and it is rotating with an angular velocity of 0.500 rev/s. What is its angular velocity after a 22.0-kg child gets onto it by grabbing its outer edge? The child is initially at rest.

Problem 40PE Three children are riding on the edge of a merry-go-round that is 100 kg, has a 1.60-m radius, and is spinning at 20.0 rpm. The children have masses of 22.0, 28.0, and 33.0 kg. If the child who has a mass of 28.0 kg moves to the center of the merry-go-round, what is the new angular velocity in rpm?

Problem 41PE (a) Calculate the angular momentum of an ice skater spinning at 6.00 rev/s given his moment of inertia is 0.400 kg ? m2 . (b) He reduces his rate of spin (his angular velocity) by extending his arms and increasing his moment of inertia. Find the value of his moment of inertia if his angular velocity decreases to 1.25 rev/s. (c) Suppose instead he keeps his arms in and allows friction of the ice to slow him to 3.00 rev/s. What average torque was exerted if this takes 15.0 s?

Problem 42PE Consider the Earth-Moon system. Construct a problem in which you calculate the total angular momentum of the system including the spins of the Earth and the Moon on their axes and the orbital angular momentum of the Earth-Moon system in its nearly monthly rotation. Calculate what happens to the Moon’s orbital radius if the Earth’s rotation decreases due to tidal drag. Among the things to be considered are the amount by which the Earth’s rotation slows and the fact that the Moon will continue to have one side always facing the Earth.

Problem 46PE Suppose a 0.250-kg ball is thrown at 15.0 m/s to a motionless person standing on ice who catches it with an outstretched arm as shown in Figure 10.40. (a) Calculate the final linear velocity of the person, given his mass is 70.0 kg. (b) What is his angular velocity if each arm is 5.00 kg? You may treat the ball as a point mass and treat the person's arms as uniform rods (each has a length of 0.900 m) and the rest of his body as a uniform cylinder of radius 0.180 m. Neglect the effect of the ball on his center of mass so that his center of mass remains in his geometrical center. (c) Compare the initial and final total kinetic energies.

(III) In Fig. , take into account the speed of the top surface of the tank and show that the speed of fluid leaving the opening at the bottom is \(v_{1}=\sqrt{\frac{2 g h}{\left(1-A_{1}^{2} / A_{2}^{2}\right)}}\) where \(h=y_{2}-y_{1}, \text { and } A_{1} \text { and } A_{2}\) are the areas of the opening and of the top surface, respectively. Assume \(A_{1} \ll A_{2}\) so that the flow remains nearly steady and laminar. FIGURE 10-54 Problems 48 and 49 Equation Transcription: Text Transcription: v_1=\sqrt{\frac{2 g h(1-A_1^2 / A_2^2) h=y_2-y_1, and A_1 and A_2 A_1 \ll A_2

(I) A gardener feels it is taking him too long to water a garden with a \(\frac{3}{8}\) -in.-diameter hose. By what factor will his time be cut if he uses a \(\frac{5}{8}\) -in.-diameter hose? Assume nothing else is changed. Equation Transcription: Text Transcription: \frac{3}{8} \frac{5}{8}

Problem 48PE The axis of Earth makes a 23.5° angle with a direction perpendicular to the plane of Earth’s orbit. As shown in Figure 10.41, this axis precesses, making one complete rotation in 25,780 y. (a) Calculate the change in angular momentum in half this time. (b) What is the average torque producing this change in angular momentum? (c) If this torque were created by a single force (it is not) acting at the most effective point on the equator, what would its magnitude be?

(II) Calculate the pressure drop per along the aorta using the data of Example and Table .

Problem 61P (II) If the base of an insect's leg has a radius of about 3.0 X10-5 m and the insect's mass is 0.016 g, would you expect the six-legged insect to remain on top of the water? Why or why not?

Problem 69GP Giraffes are a wonder of cardiovascular engineering. Calculate the difference in pressure (in atmospheres) that the blood vessels in a giraffe's head must accommodate as the head is lowered from a full upright position to ground level for a drink. The height of an average giraffe is about 6 m.

A simple model (Fig. ) considers a continent as a block (density \(\approx 2800 \mathrm{~kg} / \mathrm{m}^{3}\) ) floating in the mantle rock ?round it (density \(\approx 3300 \mathrm{~kg} / \mathrm{m}^{3}\)). Assuming the continent is thick (the average thickness of the Earth's continental crust), estimate the height of the continent above the surrounding rock. FIGURE 10-56 Problem 72. Equation Transcription: Text Transcription: \approx 2800 kg/m3 \approx 3300 kg/m3

Problem 73GP The contraction of the left ventricle (chamber) of the heart pumps blood to the body. Assuming that the inner surface of the left ventricle has an area of 82 cm2 and the maximum pressure in the blood is 120 mm-Hg, estimate the force exerted by that ventricle at maximum pressure.

Problem 74GP Estimate the total mass of the Earth's atmosphere, using the known value of atmospheric pressure at sea level.

Problem 11P (II) The gauge pressure in each of the four tires of an automobile is 240 kPa. If each tire has a "footprint" of 190 cm2 (area touching the ground), estimate the mass of the car.

Problem 11CQ A ball of putty is dropped from a height of 2 m onto a hard floor, where it sticks. What object or objects need to be included within the system if the system is to be isolated during this process?

Problem 8CQ For Question, give a specific example of a system with the energy transformation shown. In these questions, W is the work done on the system, and are the kinetic, potential, and thermal energies of the system, respectively. Any energy not mentioned in the transformation is assumed to remain constant; if work is not mentioned, it is assumed to be zero.

Problem 7P Estimate the pressure exerted on a floor by (a) one pointed chair leg (60 kg on all four legs) of area = 0.020 cm2, and (b) a 1500-kg elephant standing on one foot (area = 800 cm2).

Problem 7CQ For Question, give a specific example of a system with the energy transformation shown. In these questions, W is the work done on the system, and are the kinetic, potential, and thermal energies of the system, respectively. Any energy not mentioned in the transformation is assumed to remain constant; if work is not mentioned, it is assumed to be zero. U ?? ?K

Problem 6CQ For Question, give a specific example of a system with the energy transformation shown. In these questions, W is the work done on the system, and are the kinetic, potential, and thermal energies of the system, respectively. Any energy not mentioned in the transformation is assumed to remain constant; if work is not mentioned, it is assumed to be zero. ? K ? ?W

Problem 5P A bottle has a mass of 35.00 g when empty and 98.44 g when filled with water. When filled with another fluid, the mass is 88.78 g. What is the specific gravity of this other fluid?

Problem 5CQ For Question, give a specific example of a system with the energy transformation shown. In these questions, W is the work done on the system, and are the kinetic, potential, and thermal energies of the system, respectively. Any energy not mentioned in the transformation is assumed to remain constant; if work is not mentioned, it is assumed to be zero. ? K ? ?U

Problem 4P (I) State your mass and then estimate your volume. [Hint Because you can swim on or just under the surface of the water in a swimming pool, you have a pretty good idea of your density.)

Problem 3P If you tried to smuggle gold bricks by filling your backpack, whose dimensions are 60 cm × 28 cm × 18 cm, what would its mass be?

Problem 3CQ For Question, give a specific example of a system with the energy transformation shown. In these questions, W is the work done on the system, and are the kinetic, potential, and thermal energies of the system, respectively. Any energy not mentioned in the transformation is assumed to remain constant; if work is not mentioned, it is assumed to be zero. W ?? ?K

Problem 2P What is the approximate mass of air in a living room 4.8 m × 3.8 m × 2.8 m?

Problem 30P A scuba diver and her gear displace a volume of 65.0 L and have a total mass of 68.0 kg. (a) What is the buoyant force on the diver in sea water? (b) Will the diver sink or float?

Problem 29P (II) An undersea research chamber is spherical with an external diameter of 5.20 m. The mass of the chamber, when occupied, is 74,400 kg. It is anchored to the sea bottom by a cable. What is (a) the buoyant force on the chamber, and (b) the tension in the cable?

Problem 27P (II) What is the likely identity of a metal (see Table 10-1) if a sample has a mass of 63.5 g when measured in air and an apparent mass of 55.4 g when submerged in water?

Problem 32P (II) A 0.43-kg piece of wood floats in water but is found to sink in alcohol (SG =0.79), in which it has an apparent mass of 0.047 kg. What is the SG of the wood?

(II) Archimedes' principle can be used not only to determine the specific gravity of a solid using a known liquid (Example 10-8); the reverse can be done as well. (a) As an example, a \(3.40-\mathrm{kg}\) aluminum ball has an apparent mass of \(2.10 \mathrm{~kg}\) when submerged in a particular liquid: calculate the density of the liquid. (b) Derive a formula for determining the density of a liquid using this procedure.

Problem 34P A 5.25-kg piece of wood (SG = 0.50) floats on water. What minimum mass of lead, hung from the wood by a string, will cause it to sink?

Problem 33P (II) The specific gravity of ice is 0.917, whereas that of seawater is 1.025. What percent of an iceberg is above the surface of the water?

Problem 36P A 15-cm-radius air duct is used to replenish the air of a room 9.2 m × 5.0 m × 4.5 m every 16 min. How fast does air flow in the duct?

Problem 33P (II) The specific gravity of ice is 0.917, whereas that of seawater is 1.025. What percent of an iceberg is above the surface of the water?

(II) A \(\frac{5}{8}\) -inch (inside) diameter garden hose is used to fill a round swimming pool in diameter. How long will it take to fill the pool to a depth of if water issues from the hose at a speed of \(0.40 \mathrm{~m} / \mathrm{s}\)? Equation Transcription: Text Transcription: 5 over 8 0.40 m/s

(I) Show that Bernoulli's equation reduces to the hydrostatic variation of pressure with depth (Eq. 10-3b) when there is no flow \(\left(v_1=v_2=0\right)\).

Problem 38P How fast does water flow from a hole at the bottom of a very wide, 4.6-m-deep storage tank filled with water? Ignore viscosity.

Problem 41P A 6.0-cm-diameter horizontal pipe gradually narrows to 4.0 cm. When water flows through this pipe at a certain rate, the gauge pressure in these two sections is 32.0 kPa and 24.0 kPa, respectively. What is the volume rate of flow?

Problem 42P What is the volume rate of flow of water from a 1.85-cm-diameter faucet if the pressure head is 15.0 m?

Problem 40P What gauge pressure in the water mains is necessary if a firehose is to spray water to a height of 15 m?

Problem 43P If wind blows at 35 m/s over a house, what is the net force on the roof if its area is 240 m2 and is flat?

Problem 44P What is the lift (in newtons) due to Bernoulli’s principle on a wing of area 78 m2 if the air passes over the top and bottom surfaces at speeds of 260 m/s and 150 m/s, respectively?

(II) Water at a gauge pressure of atm at street level flows into an office building at a speed of through a pipe in diameter. The pipe tapers down to in diameter by the top floor, above (Fig. ), where the faucet has been left open. Calculate the flow velocity and the gauge pressure in such a pipe on the top floor. Assume no branch pipes and ignore viscosity.

(II) Estimate the air pressure inside a category 5 hurricane, where the wind speed is \(300 \mathrm{~km} / \mathrm{h}\) (Fig. ). Equation Transcription: Text Transcription: 300 km/h

(III) (a) Show that the flow velocity measured by a venturi meter (see Fig. ) is given by the relation \(v_{1}=A_{2} \sqrt{\frac{2\left(P_{1}-P_{2}\right)}{\rho\left(A_{1}^{2}-A_{2}^{2}\right)}}\) (b) A venturi tube is measuring the flow of water; it has a main diameter of tapering down to a throat diameter of . If the pressure difference is measured to be , what is the velocity of the water? Equation Transcription: Text Transcription: v_1=A_2 \sqrt{\frac{2(P_1-P_2)\rho(A_1^2-A_2^2)

(I) The approximate volume of the granite monolith known as El Capitan in Yosemite National Park (Fig. 10-48) is about \(10^{8} \mathrm{~m}^{3}\) .What is its approximate mass? Equation Transcription: Text Transcription: 10^8 m^3

Problem 8P What is the difference in blood pressure (mm-Hg) between the top of the head and bottom of the feet of a 1.60-m-tall person standing vertically?

(a) Calculate the total force of the atmosphere acting on the top of a table that measures \(\mathrm{1.6 ~m \times 2.9 ~m}\). (b) What is the total force acting upward on the underside of the table?

The maximum gauge pressure in a hydraulic lift is 17.0 atm. What is the largest size vehicle (kg) it can lift if the diameter of the output line is 28.0 cm?

Problem 13P (II) How high would the level be in an alcohol barometer at normal atmospheric pressure?

Problem 14P (a) What are the total force and the absolute pressure on the bottom of a swimming pool 22.0 m by 8.5 m whose uniform depth is 2.0 m? (b) What will be the pressure against the side of the pool near the bottom?

(II) How high would the atmosphere extend if it were of uniform density throughout, equal to half the present density at sea level?

Water and then oil (which don’t mix) are poured into a U-shaped tube, open at both ends. They come to equilibrium as shown in Fig. 10–49. What is the density of the oil? [Hint: Pressures at points a and b are equal. Why?]

Problem 19P An open-tube mercury manometer is used to measure the pressure in an oxygen tank. When the atmospheric pressure is 1040 mbar, what is the absolute pressure (in Pa) in the tank if the height of the mercury in the open tube is (a) 28.0 cm higher, (b) 4.2 cm lower, than the mercury in the tube connected to the tank?

In working out his principle, Pascal showed dramatically how force can be multiplied with fluid pressure. He placed a long, thin tube of radius \(r=0.30 \mathrm{~cm} \) vertically into a wine barrel of radius \(R=21 \mathrm{~cm}\), Fig. 10-51. He found that when the barrel was filled with water and the tube filled to a height of 12 m, the barrel burst. Calculate (a) the mass of water in the tube, and (b) the net force exerted by the water in the barrel on the lid just before rupture. Equation Transcription: Text Transcription: r=0.30 cm R=21 cm

Estimate the density of the water 6.0 km deep in the sea. (See Table 9–1 and Section 9–5 regarding bulk modulus.) By what fraction does it differ from the density at the surface?

Problem 22P (II) A geologist finds that a Moon rock whose mass is 9.28 kg has an apparent mass of 6.18 kg when submerged in water. What is the density of the rock?

Problem 23P (II) What fraction of a piece of iron will be submerged when it floats in mercury?

Problem 25P (II) A spherical balloon has a radius of 7.15 m and is filled with helium. How large a cargo cai it lift, assuming that the skin and structure of the balloon have a mass of 930 kg? Neglect the buoyant force on the cargo volume itself.

Problem 26P A 78-kg person has an apparent mass of 54 kg (because of buoyancy) when standing in water that comes up to the hips. Estimate the mass of each leg. Assume the body has SG = 1.00.

Problem 2Q Airplane travelers sometimes note that their cosmetics bottles and other containers have leaked during a flight. What might cause this?

The three containers in Fig. are filled with water to the same height and have the same surface area at the base; hence the water pressure, and the total force on the base of each, is the same. Yet the total weight of water is different for each. Explain this "hydrostatic paradox."

(II) If \(5.0 \mathrm{~L}\) of antifreeze solution (specific gravity =0.80 ) is added to \(4.0 \mathrm{~L}\) of water to make a 9.0-L mixture, what is the specific gravity of the mixture?

Problem 15Q A small wooden boat floats in a swimming pool, and the level of the water at the edge of the pool is marked. Consider the following situations and explain whether the level of the water will rise, fall, or stay the same. (a) The boat is removed from the water. (b) The boat in the water holds an iron anchor which is removed from the boat and placed on the shore. (c) The iron anchor is removed from the boat and dropped in the pool.

(II) A house at the bottom of a hill is fed by a full tank of water deep and connected to the house by a pipe that is long at an angle of from the horizontal (Fig. ). (a) Determine the water gauge pressure at the house. (b) How high could the water shoot if it came vertically out of a broken pipe in front of the house?

Problem 18P Determine the minimum gauge pressure needed in the water pipe leading into a building if water is to come out of a faucet on the twelfth floor, 38 m above that pipe.

Problem 28P Calculate the true mass (in vacuum) of a piece of aluminum whose apparent mass is 2.0000 kg when weighed in air.

(III) Suppose the opening in the tank of Fig. 10-54is a height \(h_{1}\) above the base and the liquid surface is a height \(h_{2}\) above the base. The tank rests on level ground. (a) At what horizontal distance from the base of the tank will the fluid strike the ground? (b) At what other height, \(h_{1}^{\prime}\), can a hole be placed so that the emerging liquid will have the same "range"? Assume \(v_{2} \approx 0\).

Problem 50P A viscometer consists of two concentric cylinders, 10.20 cm and 10.60 cm in diameter. A particular liquid fills the space between them to a depth of 12.0 cm. The outer cylinder is fixed, and a torque of 0.024 m · N keeps the inner cylinder turning at a steady rotational speed of 62 rev/min. What is the viscosity of the liquid?

(II) What must be the pressure difference between the two ends of a 1.9-km section of pipe, 29 cm in diameter, if it is to transport oil \(\left(\rho=950 \mathrm{~kg} / \mathrm{m}^3, \eta=0.20 \mathrm{~Pa} \cdot \mathrm{s}\right)\) at a rate of \(450 \mathrm{~cm}^3 / \mathrm{s}\)$ ?

(II) Engine oil (assume SAE 10, Table 10-3) passes through a \(1.80-\mathrm{mm}\)-diameter tube in a prototype engine. The tube is \(5.5 \mathrm{~cm}\) long. What pressure difference is needed to maintain a flow rate of \(5.6 \mathrm{~mL} / \mathrm{min}\)?

(II) What diameter must a \(21.0-\mathrm{m}\)-long air duct have if the ventilation and heating system is to replenish the air in a room \(9.0 \mathrm{~m} \times 12.0 \mathrm{~m} \times 4.0 \mathrm{~m}\) every \(10 \mathrm{~min}\) ? Assume the pump can exert a gauge pressure of \(0.71 \times 10^{-3} \mathrm{~atm}\).

Problem 56P Assuming a constant pressure gradient, if blood flow is reduced by 75%, by what factor is a blood vessel decreased in radius?

(II) Poiseuille's equation does not hold if the flow velocity is high enough that turbulence sets in. The onset of turbulence occurs when the Reynolds number, , exceeds approximately Re is defined as \(R e=\frac{2 v^{-} r \rho}{\eta}\) where \(v^{-}\) is the average speed of the fluid, \(\rho\) is its density, \(\eta\) is its viscosity, and is the radius of the tube in which the fluid is flowing. () Determine if blood flow through the aorta is laminar or turbulent when the average speed of blood in the aorta \((r=1.2 \mathrm{~cm})\) during the resting part of the heart's cycle is about \(40 \mathrm{~cm} / \mathrm{s}\) During exercise, the blood-flow speed approximately doubles. Calculate the Reynolds number in this case, and determine if the flow is laminar or turbulent. Equation Transcription: Text Transcription: R e=\frac{2 v^- r \rho \eta v^- \rho \eta (r=1.2 cm) 40 cm/s

(III) A patient is to be given a blood transfusion. The blood is to flow through a tube from a raised bottle to a needle inserted in the vein (Fig. 10-55 ). The inside diameter of the 4.0-cm -long needle is 0.40 mm, and the required flow rate is \(4.0 \mathrm{~cm}^{3}\) of blood per minute. How high h should the bottle be placed above the needle? Obtain \(\rho\) and \(\eta\) from the Tables. Assume the blood pressure is 18 torr above atmospheric pressure.

(I) If the force F needed to move the wire in Fig. 10-35 is \(5.1 \times 10^{-3} \mathrm{~N}\), calculate the surface tension \(\gamma\) of the enclosed fluid. Assume \(L=0.070 \mathrm{~m}\).

(I) Calculate the force needed to move the wire in Fig. if it is immersed in a soapy solution and the wire is long.

Problem 62P The surface tension of a liquid can be determined by measuring the force F needed to just lift a circular platinum ring of radius r from the surface of the liquid. (a) Find a formula for ? in terms of F and r. (b) At 30°C, if F = 8.40 × 10?3N and r = 2.8 cm, calculate ? for the tested liquid.

Intravenous infusions are often made under gravity, as shown in Fig. . Assuming the fluid has a density of \(1.00 \mathrm{~g} / \mathrm{cm}^{3}\), at what height should the bottle be placed so the liquid pressure is (a) \(55 \mathrm{~mm}-\mathrm{Hg}\), and (b) \(650 \mathrm{~mm}-\mathrm{H}_{2} \mathrm{O}\)? If the blood pressure is \(18 \mathrm{~mm}-\mathrm{Hg}\) above atmospheric pressure, how high should the bottle be placed so that the fluid just barely enters the vein? Equation Transcription: Text Transcription: 1.00 g/cm^3 55 mm - Hg 650 mm - H_2O 18 mm - Hg

A 2.4-N force is applied to the plunger of a hypodermic needle. If the diameter of the plunger is 1.3 cm and that of the needle 0.20 mm, (a) with what force does the fluid leave the needle? (b) What force on the plunger would be needed to push fluid into a vein where the gauge pressure is 18 mm-Hg? Answer for the instant just before the fluid starts to move.

Problem 65GP A bicycle pump is used to inflate a tire. The initial tire (gauge) pressure is 210kPa (30 psi). At the end of the pumping process, the final pressure is 310 kPa (45 psi). If the diameter of the plunger in the cylinder of the pump is 3.0 cm, what is the range of the force that needs to be applied to the pump handle from beginning to end?

Problem 66GP Estimate the pressure on the mountains underneath the Antarctic ice sheet, which is typically 3 km thick.

What is the approximate difference in air pressure between the top and the bottom of the Empire State building in New York City? It is \(380 \mathrm{~m}\) tall and is located at sea level. Express as a fraction of atmospheric pressure at sea level.

A hydraulic lift is used to jack a \(970-\mathrm{kg}\) car \(12 \mathrm{~cm}\) off the floor. The diameter of the output piston is \(18 \mathrm{~cm}\), and the input force is \(250 \mathrm{~N}\). (a) What is the area of the input piston? (b) What is the work done in lifting the car \(12 \mathrm{~cm}\)? (c) If the input piston moves \(13 \mathrm{~cm}\) in each stroke, how high does the car move up for each stroke? (d) How many strokes are required to jack the car up \(12 \mathrm{~cm}\)? (e) Show that energy is conserved.

Problem 70GP When you ascend or descend a great deal when driving in a car, your ears “pop,” which means that the pressure behind the eardrum is being equalized to that outside. If this did not happen, what would be the approximate force on an eardrum of area 0.50 cm2 if a change in altitude of 950 m takes place?

One arm of a U-shaped tube (open at both ends) contains water, and the other alcohol. If the two fluids meet at exactly the bottom of the U, and the alcohol is at a height of 18.0 cm, at what height will the water be?

Suppose a person can reduce the pressure in his lungs to ?80mm-Hg gauge pressure. How high can water then be sucked up a straw?

A ship, carrying fresh water to a desert island in the Caribbean, has a horizontal cross-sectional area of \(2650 \mathrm{~m}^2\) at the waterline. When unloaded, the ship rises \(8.50 \mathrm{~m}\) higher in the sea. How much water was delivered?

A copper (Cu) weight is placed on top of a block of wood (density \(=0.60 \times 10^{3} \mathrm{~kg} / \mathrm{m}^{3}\)) floating in water, as shown in Fig. . What is the mass of the copper if the top of the wood block is exactly at the water's surface? Equation Transcription: Text Transcription: =0.60 x 10^3 kg/m^3

Problem 78GP A raft is made of 10 logs lashed together. Each is 56 cm in diameter and has a length of 6.1 m. How many people can the raft hold before they start getting their feet wet, assuming the average person has a mass of 68 kg? Do not neglect the weight of the logs. Assume the specific gravity of wood is 0.60.

Problem 79GP During each heartbeat, approximately 70 cm3 of blood is pushed from the heart at an average pressure of 105 mm-Hg. Calculate the power output of the heart, in watts, assuming 70 beats per minute.

Problem 80GP A bucket of water is accelerated upward at 2.4g. What is the buoyant force on a 3.0-kg granite rock (SG = 2.7) submerged in the water? Will the rock float? Why or why not?

How high should the pressure head be if water is to come from a faucet at a speed of \(9.5 \mathrm{~m} / \mathrm{s}\)? Ignore viscosity.

Problem 83GP Four lawn sprinkler heads are fed by a 1.9-cm-diameter pipe. The water comes out of the heads at an angle of 35° to the horizontal and covers a radius of 8.0 m. (a) What is the velocity of the water coming out of each sprinkler head? (Assume zero air resistance.) (b) If the output diameter of each head is 3.0 mm, how many liters of water do the four heads deliver per second? (c) How fast is the water flowing inside the 1.9-cm-diameter pipe?

The stream of water from a faucet decreases in diameter as it falls (Fig. 10-47 ). Derive an equation for the diameter of the stream as a function of the distance below the faucet, given that the water has speed \(v_{0}\) when it leaves the faucet, whose diameter is d.

You need to siphon water from a clogged sink. The sink has an area of \(0.48 \mathrm{~m}^{2}\) and is filled to a height of \(4.0 \mathrm{~cm}\).. Your siphon tube rises \(50 \mathrm{~cm}\) above the bottom of the and then descends \(100 \mathrm{~cm}\) to a pail as shown in Fig. . The siphon tube has a diameter of \(2.0 \mathrm{~cm}\). Assuming that the water enters the siphon tube with almost zero velocity, calculate its velocity when it enters the pail. ( ) Estimate how long it will take to empty the sink. Equation Transcription: Text Transcription: 0.48 m^2 4.0 cm 50 cm 100 cm 2.0 cm

Consider a siphon which transfers water from one vessel to a second (lower) one, as in Fig. . Determine the rate of flow if the tube has a diameter of and the difference in water levels of the two containers is .

An airplane has a mass of \(2.0 \times 10^6 \mathrm{~kg}\), and the air flows past the lower surface of the wings at \(95 \mathrm{~m} / \mathrm{s}\). If the wings have a surface area of \(1200 \mathrm{~m}^2\), how fast must the air flow over the upper surface of the wing if the plane is to stay in the air? Consider only the Bernoulli effect.

Blood from an animal is placed in a bottle 1.70 m above a 3.8-cm-long needle, of inside diameter 0.40 mm, from which it flows at a rate of \(4.1 \ \mathrm {cm}^3/\mathrm {min}\). What is the viscosity of this blood?

If cholesterol build-up reduces the diameter of an artery by 15%, what will be the effect on blood flow?