An iron block of volume 0.20 m3 is suspended from a spring scale and immersed in a flask of water. Then the iron block is removed, and an aluminum block of the same volume replaces it. (a) In which case is the buoyant force the greatest, for the iron block or the aluminum block? (b) In which case does the spring scale read the largest value? (c) Use the known densities of these materials to calculate the quantities requested in parts (a) and (b). Are your calculations consistent with your previous answers to parts (a) and (b)?
> Find the x- and y -coordinates of the center of gravity for the boomerang in Figure P8.12a, modeling the boomerang as in Figure P8.12b, where each uniform leg of the model has a length of 0.300 m and a mass of 0.250 kg. (Note: Treat the legs like thin ro
> Find the x- and y-coordinates of the center of gravity of a 4.00-ft by 8.00-ft uniform sheet of plywood with the upper right quadrant removed as shown in Figure P8.11. Hint: The mass of any segment of the plywood sheet is proportional to the area of that
> A horizontal disk with moment of inertia I1 rotates with angular speed v1 about a vertical frictionless axle. A second horizontal disk having moment of inertia I2 drops onto the first, initially not rotating but sharing the same axis as the first disk. B
> Three solid, uniform boxes are aligned as in Figure P8.10. Find the x- and y-coordinates of the center of mass of the three boxes, measured from the bottom left corner of box A. Figure P8.10:
> Two bowling balls are at rest on top of a uniform wooden plank with their centers of mass located as in Figure P8.9. The plank has a mass of 5.00 kg and is 1.00 m long. Find the horizontal distance from the left end of the plank to the center of mass of
> Consider the following mass distribution, where x- and y-coordinates are given in meters: 5.0 kg at (0.0, 0.0) m, 3.0 kg at (0.0, 4.0) m, and 4.0 kg at (3.0, 0.0) m. Where should a fourth object of 8.0 kg be placed so that the center of mass of the four-
> A simple pendulum consists of a small object of mass 3.0 kg hanging at the end of a 2.0-m-long light string that is connected to a pivot point. (a) Calculate the magnitude of the torque (due to the force of gravity) about this pivot point when the string
> A dental bracket exerts a horizontal force of 80.0 N on a tooth at point B in Figure P8.6. What is the torque on the root of the tooth about point A? Figure P8.6:
> The density of air is 1.3 kg/m3 at sea level. From your knowledge of air pressure at ground level, estimate the height of the atmosphere. As a simplifying assumption, take the atmosphere to be of uniform density up to some height, after which the density
> Two point masses are the same distance R from an axis of rotation and have moments of inertia IA and IB. (a) If IB = 4IA, what is the ratio mB/mA of the two masses? (b) At what distance from the axis of rotation should mass A be placed so that IB = IA?
> Markings to indicate length are placed on a steel tape in a room that is at a temperature of 22°C. Measurements are then made with the same tape on a day when the temperature is 27°C. Are the measurements too long, too short, or accurate?
> A container filled with an ideal gas is connected to a reservoir of the same gas so that the number of moles in the container can change. If the pressure and volume of the container are each doubled while the temperature is held constant, what is the rat
> Calculate the net torque (magnitude and direction) on the beam in Figure P8.5 about (a) An axis through O perpendicular to the page and (b) An axis through C perpendicular to the page. Figure P8.5:
> A rubber balloon is blown up and the end tied. Is the pressure inside the balloon greater than, less than, or equal to the ambient atmospheric pressure? Explain.
> A sealed container contains a fixed volume of a monatomic ideal gas. If the gas temperature is increased by a factor of two, what is the ratio of the final to the initial (a) Pressure, (b) Average molecular kinetic energy, (c) Root-mean-square speed, and
> Figure CQ10.14 shows a metal washer being heated by a Bunsen burner. The red arrows in options a, b, and c indicate the possible directions of expansion caused by the heating. Which option correctly illustrates the washer’s expansion?
> Suppose the volume of an ideal gas is doubled while the pressure is reduced by half. Does the internal energy of the gas increase, decrease, or remain the same? Explain.
> The air we breathe is largely composed of nitrogen (N2) and oxygen (O2) molecules. The mass of an N2 molecule is less than the mass of an O2 molecule. (a) For air at 300 K, is the average kinetic energy of an N2 molecule greater than, less than, or equal
> One of the predicted problems due to global warming is that ice in the polar ice caps will melt and raise sea levels everywhere in the world. Is that more of a worry for ice (a) At the North Pole, where most of the ice floats on water; (b) At the South P
> A mouse is initially at rest on a horizontal turntable mounted on a frictionless, vertical axle. As the mouse begins to walk clockwise around the perimeter, which of the following statements must be true of the turntable? (a) It also turns clockwise. (b)
> Once ski jumpers are airborne (Fig. CQ9.14), why do they bend their bodies forward and keep their hands at their sides? Figur CQ9.14:
> A cat usually lands on its feet regardless of the position from which it is dropped. A slow-motion film of a cat falling shows that the upper half of its body twists in one direction while the lower half twists in the opposite direction. (See Fig. CQ8.14
> Will an ice cube float higher in water or in an alcoholic beverage?
> Find the net torque on the wheel in Figure P8.4 about the axle through O perpendicular to the page, taking a = 10.0 cm and b = 25.0 cm. Figure P8.4:
> (a) Give an example in which the net force acting on an object is zero, yet the net torque is nonzero. (b) Give an example in which the net torque acting on an object is zero, yet the net force is nonzero.
> An ice cube is placed in a glass of water. What happens to the level of the water as the ice melts?
> An object is acted on by a single nonzero force of magnitude F. (a) Is it possible for the object to have zero acceleration (? (b) Is it possible for the object to have zero angular acceleration (? (c) Is it possible for the object to be in mechanical eq
> During inhalation, the pressure in the lungs is slightly less than external pressure and the muscles controlling exhalation are relaxed. Under water, the body equalizes internal and external pressures. Discuss the condition of the muscles if a person und
> If you toss a textbook into the air, rotating it each time about one of the three axes perpendicular to it, you will find that it will not rotate smoothly about one of those axes. (Try placing a strong rubber band around the book before the toss so that
> Many people believe that a vacuum created inside a vacuum cleaner causes particles of dirt to be drawn in. Actually, the dirt is pushed in. Explain.
> A person stands a distance R from a door’s hinges and pushes with a force F directed perpendicular to its surface. By what factor does the applied torque change if the person’s position and force change to (a) 2R and 2F, (b) 2R and F, (c) R and F/2, (d)
> Figure CQ9.4 shows aerial views from directly above two dams. Both dams are equally long (the vertical dimension in the diagram) and equally deep (into the page in the diagram). The dam on the left holds back a very large lake, while the dam on the right
> (a) Is it possible to calculate the torque acting on a rigid object without specifying an origin? (b) Is the torque independent of the location of the origin?
> A water tank open to the atmosphere at the top has two small holes punched in its side, one above the other. The holes are 5.00 cm and 12.0 cm above the floor. How high does water stand in the tank if the two streams of water hit the floor at the same pl
> The fishing pole in Figure P8.3 makes an angle of 20.0° with the horizontal. What is the magnitude of the torque exerted by the fish about an axis perpendicular to the page and passing through the angler’s hand if the fish pu
> Oil having a density of 930 kg/m3 floats on water. A rectangular block of wood 4.00 cm high and with a density of 960 kg/m3 floats partly in the oil and partly in the water. The oil completely covers the block. How far below the interface between the two
> In about 1657, Otto von Guericke, inventor of the air pump, evacuated a sphere made of two brass hemispheres (Fig. P9.89). Two teams of eight horses each could pull the hemispheres apart only on some trials and then “with greatest diffi
> A u-tube open at both ends is partially filled with water (Fig. P9.88a). Oil (p = 750 kg/m3) is then poured into the right arm and forms a column L = 5.00 cm high (Fig. P9.88b). (a) Determine the difference h in the heights of the two liquid surfaces. (b
> A light spring of constant k = 90.0 N/m is attached vertically to a table (Fig. P9.87a). A 2.00-g balloon is filled with helium (density = 0.179 kg/m3) to a volume of 5.00 m3 and is then connected to the spring, causing the spring to stretch as shown in
> A helium-filled balloon, whose envelope has a mass of 0.25 kg, is tied to a 2.0-m-long, 0.050-kg string. The balloon is spherical with a radius of 0.40 m. When released, it lifts a length h of the string and then remains in equilibrium, as in Figure P9.8
> Figure P9.85 shows a water tank with a valve. If the valve is opened, what is the maximum height attained by the stream of water coming out of the right side of the tank? Assume h = 10.0 m, L = 2.00 m, and θ = 30.0°, and that the
> A hydrometer is an instrument used to determine liquid density. A simple one is sketched in Figure P9.84. The bulb of a syringe is squeezed and released to lift a sample of the liquid of interest into a tube containing a calibrated rod of known density.
> The human brain and spinal cord are immersed in the cerebrospinal fluid. The fluid is normally continuous between the cranial and spinal cavities and exerts a pressure of 100 to 200 mm of H2O above the prevailing atmospheric pressure. In medical work, pr
> Superman attempts to drink water through a very long vertical straw as in Figure P9.82. With his great strength, he achieves maximum possible suction. The walls of the straw don’t collapse. (a) Find the maximum height through which he c
> The approximate diameter of the aorta is 0.50 cm; that of a capillary is 10. mm. The approximate average blood flow speed is 1.0 m/s in the aorta and 1.0 cm/s in the capillaries. If all the blood in the aorta eventually flows through the capillaries, est
> A worker applies a torque to a nut with a wrench 0.500 m long. Because of the cramped space, she must exert a force upward at an angle of 60.0° with respect to a line from the nut through the end of the wrench. If the force she exerts has magnitude 80.0
> Take the density of blood to be p and the distance between the feet and the heart to be hH. Ignore the flow of blood. (a) Show that the difference in blood pressure between the feet and the heart is given by PF - PH = pghH. (b) Take the density of blood
> In most species of clingfish (family Gobiesocidae), pelvic and pectoral fins converge to form a suction cup edged by hairy structures that allow a good seal even on rough surfaces. Experiments have shown that a clingfish’s suction cup can support up to 2
> Suppose two worlds, each having mass M and radius R, coalesce into a single world. Due to gravitational contraction, the combined world has a radius of only ¾ R. What is the average density of the combined world as a multiple of p0, the average density o
> The total cross-sectional area of the load-bearing calcified portion of the two forearm bones (radius and ulna) is approximately 2.4 cm2. During a car crash, the forearm is slammed against the dashboard. The arm comes to rest from an initial speed of 80
> Determine the elongation of the rod in Figure P9.75 if it is under a tension of 5.8 x 103 N. Figure P9.75:
> The deepest point in the ocean is in the Mariana Trench, about 11 km deep. The pressure at the ocean floor is huge, about 1.13 x 108 N/m2. (a) Calculate the change in volume of 1.00 m3 of water carried from the surface to the bottom of the Pacific. (b) T
> A high-speed lifting mechanism supports an 800. -kg object with a steel cable that is 25.0 m long and 4.00 cm2 in cross-sectional area. (a) Determine the elongation of the cable. (b) By what additional amount does the cable increase in length if the obje
> A stainless-steel orthodontic wire is applied to a tooth, as in Figure P9.72. The wire has an unstretched length of 3.1 cm and a radius of 0.11 mm. If the wire is stretched 0.10 mm, find the magnitude and direction of the force on the tooth. Disregard th
> Bone has a Young’s modulus of 18 x 109 Pa. Under compression, it can withstand a stress of about 160 x 106 Pa before breaking. Assume that a femur (thigh bone) is 0.50 m long, and calculate the amount of compression this bone can withstand before breakin
> A man opens a 1.00-m wide door by pushing on it with a force of 50.0 N directed perpendicular to its surface. What magnitude of torque does he apply about an axis through the hinges if the force is applied (a) At the center of the door? (b) At the edge f
> Two spheres, one hollow and one solid, are rotating with the same angular speed around an axis through their centers. Both spheres have the same mass and radius. Which sphere, if either, has the higher rotational kinetic energy? (a) The hollow sphere. (b
> Assume that if the shear stress in steel exceeds about 4.00 x 108 N/m2, the steel ruptures. Determine the shearing force necessary to (a) Shear a steel bolt 1.00 cm in diameter and (b) Punch a 1.00-cm-diameter hole in a steel plate 0.500 cm thick.
> For safety in climbing, a mountaineer uses a nylon rope that is 50. m long and 1.0 cm in diameter. When supporting a 90. -kg climber, the rope elongates 1.6 m. Find its Young’s modulus.
> Artificial diamonds can be made using high-pressure, high-temperature presses. Suppose an artificial diamond of volume 1.00 x 10-6 m3 is formed under a pressure of 5.00 GPa. Find the change in its volume when it is released from the press and brought to
> A plank 2.00 cm thick and 15.0 cm wide is firmly attached to the railing of a ship by clamps so that the rest of the board extends 2.00 m horizontally over the sea below. A man of mass 80.0 kg is forced to stand on the very end. If the end of the board d
> A 25.0-m long steel cable with a cross-sectional area of 2.03 x 10-3 m2 is used to suspend a 3.50 x 103 -kg container. By how much will the cable stretch once bearing the load?
> A 200.- kg load is hung on a wire of length 4.00 m, cross-sectional area 0.200 x 10–4 m2, and Young’s modulus 8.00 x 1010 N/m2. What is its increase in length?
> Small spheres of diameter 1.00 mm fall through 20°C water with a terminal speed of 1.10 cm/s. Calculate the density of the spheres.
> The viscous force on an oil drop is measured to be equal to 3.0 x 10-13 N when the drop is falling through air with a speed of 4.5 x 10-4 m/s. If the radius of the drop is 2.5 x 10-6 m, what is the viscosity of air?
> Glycerin in water diffuses along a horizontal column that has a cross-sectional area of 2.0 cm2. The concentration gradient is 3.0 x 10-2 kg/m4, and the diffusion rate is found to be 5.7 x 10-15 kg/s. Determine the diffusion coefficient.
> Sucrose is allowed to diffuse along a 10.- cm length of tubing filled with water. The tube is 6.0 cm2 in cross-sectional area. The diffusion coefficient is equal to 5.0 x 10-10 m2/s, and 8.0 x 10-14 kg is transported along the tube in 15 s. What is the d
> A constant net torque is applied to an object. Which one of the following will not be constant? (a) Angular acceleration, (b) Angular velocity, (c) Moment of inertia, or (d) Center of gravity.
> The aorta in humans has a diameter of about 2.0 cm, and at certain times the blood speed through it is about 55 cm/s. Is the blood flow turbulent? The density of whole blood is 1050 kg/m3, and its coefficient of viscosity is 2.7 x 10-3 N · s/m2.
> What radius needle should be used to inject a volume of 500. cm3 of a solution into a patient in 30.0 min? Assume the length of the needle is 2.5 cm and the solution is elevated 1.0 m above the point of injection. Further, assume the viscosity and densit
> A hypodermic needle is 3.0 cm in length and 0.30 mm in diameter. What pressure difference between the input and output of the needle is required so that the flow rate of water through it will be 1 g/s? (Use 1.0 x 10-3 Pa · s as the viscosity of water.)
> Spherical particles of a protein of density 1.8 g/cm3 are shaken up in a solution of 20°C water. The solution is allowed to stand for 1.0 h. If the depth of water in the tube is 5.0 cm, find the radius of the largest particles that remain in solution at
> The pulmonary artery, which connects the heart to the lungs, has an inner radius of 2.6 mm and is 8.4 cm long. If the pressure drop between the heart and lungs is 400 Pa, what is the average speed of blood in the pulmonary artery?
> A straight horizontal pipe with a diameter of 1.0 cm and a length of 50 m carries oil with a coefficient of viscosity of 0.12 N · s/m2. At the output of the pipe, the flow rate is 8.6 x 10-5 m3/s and the pressure is 1.0 atm. Find the gauge pressure at th
> A thin 1.5-mm coating of glycerine has been placed between two microscope slides of width 1.0 cm and length 4.0 cm. Find the force required to pull one of the microscope slides at a constant speed of 0.30 m/s relative to the other slide.
> The block of ice (temperature 0°C) shown in Figure P9.53 is drawn over a level surface lubricated by a layer of water 0.10 mm thick. Determine the magnitude of the force F( needed to pull the block with a constant speed of 0.50 m/s. At 0Â
> Whole blood has a surface tension of 0.058 N/m and a density of 1050 kg/m3. To what height can whole blood rise in a capillary blood vessel that has a radius of 2.0 x 10-6 m if the contact angle is zero?
> A certain fluid has a density of 1080 kg/m3 and is observed to rise to a height of 2.1 cm in a 1.0-mm-diameter tube. The contact angle between the wall and the fluid is zero. Calculate the surface tension of the fluid.
> Using a screwdriver, you try to remove a screw from a piece of furniture, but can’t get it to turn. To increase the chances of success, you should use a screwdriver that (a) Is longer, (b) Is shorter, (c) Has a narrower handle, or (d) Has a wider handle.
> To lift a wire ring of radius 1.75 cm from the surface of a container of blood plasma, a vertical force of 1.61 x 10-2 N greater than the weight of the ring is required. Calculate the surface tension of blood plasma from this information.
> A square metal sheet 3.0 cm on a side and of negligible thickness is attached to a balance and inserted into a container of fluid. The contact angle is found to be zero, as shown in Figure P9.49a, and the balance to which the metal sheet is attached read
> The Venturi tube shown in Figure P9.48 may be used as a fluid flowmeter. Suppose the device is used at a service station to measure the flow rate of gasoline (p = 7.00 x 102 kg/m3) through a hose having an outlet radius of 1.20 cm. If the difference in p
> Old Faithful geyser in Yellowstone Park erupts at approximately 1-hour intervals, and the height of the fountain reaches 40.0 m (Fig. P9.47). (a) Consider the rising stream as a series of separate drops. Analyze the free-fall motion of one of the drops t
> Water is pumped through a pipe of diameter 15.0 cm from the Colorado River up to Grand Canyon Village, on the rim of the canyon. The river is at 564 m elevation and the village is at 2096 m. (a) At what minimum pressure must the water be pumped to arrive
> The inside diameters of the larger portions of the horizontal pipe depicted in Figure P9.45 are 2.50 cm. Water flows to the right at a rate of 1.80 x 10-4 m3/s. Determine the inside diameter of the constriction. Figure P9.45:
> A large storage tank, open to the atmosphere at the top and filled with water, develops a small hole in its side at a point 16.0 m below the water level. If the rate of flow from the leak is 2.50 x 10-3 m3/min, determine (a) The speed at which the water
> A jet of water squirts out horizontally from a hole near the bottom of the tank shown in Figure P9.43. If the hole has a diameter of 3.50 mm, what is the height h of the water level in the tank? Figure P9.43:
> Water moves through a constricted pipe in steady, ideal flow. At the lower point shown in Figure P9.42, the pressure is 1.75 x 105 Pa and the pipe radius is 3.00 cm. At the higher point located at y = 2.50 m, the pressure is 1.20 x 105 Pa and the pipe ra
> In a water pistol, a piston drives water through a larger tube of radius 1.00 cm into a smaller tube of radius 1.00 mm as in Figure P9.41. (a) If the pistol is fired horizontally at a height of 1.50 m, use ballistics to determine the time it takes water
> One container is filled with argon gas and another with helium gas. Both containers are at the same temperature. Which atoms have the higher rms speed? (a) Argon, (b) Helium, (c) They have the same speed, or (d) Not enough information to say.
> A man attaches a divider to an outdoor faucet so that water flows through a single pipe of radius 9.00 mm into two pipes, each with a radius of 6.00 mm. If water flows through the single pipe at 1.25 m/s, calculate the speed of the water in the narrower
> A jet airplane in level flight has a mass of 8.66 x 104 kg, and the two wings have an estimated total area of 90.0 m2. (a) What is the pressure difference between the lower and upper surfaces of the wings? (b) If the speed of air under the wings is 225 m
> When a person inhales, air moves down the bronchus (windpipe) at 15 cm/s. The average flow speed of the air doubles through a constriction in the bronchus. Assuming incompressible flow, determine the pressure drop in the constriction.
> A hypodermic syringe contains a medicine with the density of water (Fig. P9.37). The barrel of the syringe has a cross-sectional area of 2.50 x 10-5 m2. In the absence of a force on the plunger, the pressure everywhere is 1.00 atm. A force F( of magnitud
> A liquid (p = 1.65 g/ cm3) flows through a horizontal pipe of varying cross section as in Figure P9.36. In the first section, the cross-sectional area is 10.0 cm2, the flow speed is 275 cm/s, and the pressure is 1.20 x 105 Pa. In the second section, the
> (a) Calculate the mass flow rate (in grams per second) of blood (p = 1.0 g/cm3) in an aorta with a cross-sectional area of 2.0 cm2 if the flow speed is 40. cm/s. (b) Assume that the aorta branches to form a large number of capillaries with a combined cro
> Water flowing through a garden hose of diameter 2.74 cm fills a 25.0-L bucket in 1.50 min. (a) What is the speed of the water leaving the end of the hose? (b) A nozzle is now attached to the end of the hose. If the nozzle diameter is one-third the diamet
> A large water tank is 3.00 m high and filled to the brim, the top of the tank open to the air. A small pipe with a faucet is attached to the side of the tank, 0.800 m above the ground. If the valve is opened, at what speed will water come out of the pipe
> A horizontal pipe narrows from a radius of 0.250 m to 0.100 m. If the speed of the water in the pipe is 1.00 m/s in the larger-radius pipe, what is the speed in the smaller pipe?
> A 1.00-kg beaker containing 2.00 kg of oil (density = 916 kg/m3) rests on a scale. A 2.00-kg block of iron is suspended from a spring scale and is completely submerged in the oil (Fig. P9.31). Find the equilibrium readings of both scales. Figure P9.31:
