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An astronaut, whose mission is to go where no one has gone before, lands on a spherical planet in a distant galaxy. As she stands on the surface of the planet, she releases a small rock from rest and... An object in the shape of a thin ring has radius a and mass M. A uniform sphere with mass m and radius R is placed with its center at a distance x to the right of the center of the ring, along a line... In Example 13.10 (Section 13.6) we saw that inside a planet of uniform density (not a realistic assumption for the earth) the acceleration due to gravity increases uniformly with distance from the... In 2004 astronomers reported the discovery of a large Jupiter-sized planet orbiting very close to the star HD 179949 (hence the term hot Jupiter). The orbit was 1/9 just the distance of Mercury from... Two satellites are in circular orbits around a planet that has radius 9.00 10 6 m. One satellite has mass 68.0 kg, orbital radius 5.00 10 7 m, and orbital speed 4800 m s. The second satellite has... If a satellite is in a sufficiently low orbit, it will encounter air drag from the earths atmosphere. Since air drag does negative work (the force of air drag is directed opposite the motion), the... Find the gravitational force that the earth exerts on a 10.0-kg mass if it is placed at the following locations. Consult Fig. 13.9, and assume a constant density through each of the interior regions... A spacecraft is to be launched from the surface of the earth so that it will escape from the solar system altogether. (a) Find the speed relative to the center of the earth with which the spacecraft... Jupiters moon Io has active volcanoes (in fact, it is the most volcanically active body in the solar system) that eject material as high as 500 km (or even higher) above the surface. Io has a mass of... Titania, the largest moon of the planet Uranus, has 1/8 the radius of the earth and 1/1700 the mass of the earth. (a) What is the acceleration due to gravity at the surface of Titania? (b) What is... Find the magnitude and direction of the net gravitational force on mass A due to masses B and C in Fig. E13.6. Each mass is 2.00 kg. Figure E13.6: (a) 10 -* 40 cm (b) K10 cm- 40 cm cm- A car travels in the +x-direction on a straight and level road. For the first 4.00 s of its motion, the average velocity of the car is u av-x = 6.25 m/s. How far does the car travel in 4.00 s? The 0.100-kg sphere in Fig. P13.62 is released from rest at the position shown in the sketch, with its center 0.400 m from the center of the 5.00-kg mass. Assume that the only forces on the 0.100-kg... Your starship, the Aimless Wanderer, lands on the mysterious planet Mongo. As chief scientist-engineer, you make the following measurements: A 2.50-kg stone thrown upward from the ground at 12.0 m/s... An experiment is performed in deep space with two uniform spheres, one with mass 50.0 kg and the other with mass 100.0 kg. They have equal radii, r = 0.20 m. The spheres are released from rest with... Use the results of Example 13.5 (Section 13.3) to calculate the escape speed for a spacecraft (a) From the surface of Mars and (b) From the surface of Jupiter. Use the data in Appendix F. (c) Why is... Starting from the front door of your ranch house, you walk 60.0 m due east to your windmill, and then you turn around and slowly walk 40.0 m west to a bench where you sit and watch the sunrise. It... A couple of astronauts agree to rendezvous in space after hours. Their plan is to let gravity bring them together. One of them has a mass of 65 kg and the other a mass of 72 kg, and they start from... In the Cavendish balance apparatus shown in Fig. 13.4, suppose that m 1 = 1.10 kg, m 2 = 25.0 kg, and the rod connecting the pairs is 30.0 cm long. If, in each pair, m 1 and m 2 are 12.0 cm apart... Prevention of Hip Fractures. Falls resulting in hip fractures are a major cause of injury and even death to the elderly. Typically, the hips speed at impact is about 2.0 m/s. If this can be reduced... A remote-controlled car is moving in a vacant parking lot. The velocity of the car as a function of time is given by v = [5.00 m/s (0.0180 m/s 3 )t 2 ]i + [2.00 m/s + (0.550 m/s 2 )t]j. (a) What are... A rookie quarterback throws a football with an initial upward velocity component 12.0 m/s of and a horizontal velocity component of 20.0 m/s. Ignore air resistance. (a) How much time is required for... Dizziness. Our balance is maintained, at least in part, by the endolymph fluid in the inner ear. Spinning displaces this fluid, causing dizziness. Suppose a dancer (or skater) is spinning at a very... An athlete starts at point A and runs at a constant speed 6.0 m/s of around a circular track 100 m in diameter, as shown in Fig. P3.40. Find the x and y-components of this runners average velocity... The position of a dragonfly that is flying parallel to the ground is given as a function of time by r = [2.90 m + (0.0900 m/s 2 )t 2 ]i (0.0150 m/s 3 )t 3 j. (a) At what value of t does the velocity... Spiraling Up. It is common to see birds of prey rising upward on thermals. The paths they take may be spiral-like. You can model the spiral motion as uniform circular motion combined with a constant... A jungle veterinarian with a blow-gun loaded with a tranquilizer dart and a sly 1.5-kg monkey are each 25 m above the ground in trees 70 m apart. Just as the hunter shoots horizontally at the monkey,... A toy rocket is launched with an initial velocity of 12.0 m s in the horizontal direction from the roof of a 30.0-m-tall building. The rockets engine produces a horizontal acceleration of (1.60 m/s 3... An Errand of Mercy. An airplane is dropping bales of hay to cattle stranded in a blizzard on the Great Plains. The pilot releases the bales at 150 m above the level ground when the plane is flying at... A grasshopper leaps into the air from the edge of a vertical cliff, as shown in Fig. P3.63. Use information from the figure to find (a) The initial speed of the grasshopper and (b) The height of the... A World Record. In the shot put, a standard track and-field event, a 7.3-kg object (the shot) is thrown by releasing it at approximately 40 over a straight left leg. The world record for distance,... Two soccer players, Mia and Alice, are running as Alice passes the ball to Mia. Mia is running due north with a speed of 6.00 m s. The velocity of the ball relative to Mia is 5.00 m/s in a direction... Jaw Injury. Due to a jaw injury, a patient must wear a strap (Fig. E4.3) that produces a net upward force of 5.00 N on his chin. The tension is the same throughout the strap. To what tension must the... Boxes A and B are in contact on a horizontal, friction less surface, as shown in Fig. E4.23. Box A has mass 20.0 kg and box B has mass 5.0 kg. A horizontal force of 100 N is exerted on box A. What is... A 4.80-kg bucket of water is accelerated upward by a cord of negligible mass whose breaking strength is 75.0 N. If the bucket starts from rest, what is the minimum time required to raise the bucket a... Human Biomechanics. The fastest pitched baseball was measured at Typically, a baseball has a mass of 145 g. If the pitcher exerted his force (assumed to be horizontal and constant) over a distance of... Human Biomechanics. The fastest served tennis ball, served by Big Bill Tilden in 1931, was measured at 73.14 m/s. The mass of a tennis ball is 57 g, and the ball is typically in contact with the... Are We Martians? It has been suggested, and not facetiously, that life might have originated on Mars and been carried to the earth when a meteor hit Mars and blasted pieces of rock (perhaps... Two stones are thrown vertically upward from the ground, one with three times the initial speed of the other. (a) If the faster stone takes 10 s to return to the ground, how long will it take the... A uniform sphere with mass 28.0 kg and radius 0.380 m is rotating at constant angular velocity about a stationary axis that lies along a diameter of the sphere. If the kinetic energy of the sphere is... Given two vectors and A = 4.00i + 7.00i and B = 5.00i 2.00i, (a) Find the magnitude of each vector; (b) Write an expression for the vector difference A B using unit vectors; (c) Find the magnitude... Calculate the moment of inertia of each of the following uniform objects about the axes indicated. Consult Table 9.2 as needed. (a) A thin 2.50-kg rod of length 75.0 cm, about an axis perpendicular... A hollow spherical shell has mass 8.20 kg and radius 0.220 m. It is initially at rest and then rotates about a stationary axis that lies along a diameter with a constant acceleration of 0.890 rad/s 2... Suppose the solid cylinder in the apparatus described in Example 9.8 (Section 9.4) is replaced by a thin-walled, hollow cylinder with the same mass M and radius R. The cylinder is attached to the... A bucket of mass m is tied to a massless cable that is wrapped around the outer rim of a frictionless uniform pulley of radius R, similar to the system shown in Fig. E9.47. In terms of the stated... A flywheel has angular acceleration z (t) = 8.60 rad/s 2 (2.30 rads/s 3 )t, where counterclockwise rotation is positive. (a) If the flywheel is at rest at t = 0, what is its angular velocity at... A uniform disk with radius R = 0.400 and mass 30.0 kg rotates in a horizontal plane on a frictionless vertical axle that passes through the center of the disk. The angle through which the disk has... A disk of radius 25.0 cm is free to turn about an axle perpendicular to it through its center. It has very thin but strong string wrapped around its rim, and the string is attached to a ball that is... A classic 1957 Chevrolet Corvette of mass 1240 kg starts from rest and speeds up with a constant tangential acceleration of 2.00 m/s 2 on a circular test track of radius 60.0 m. Treat the car as a... A vacuum cleaner belt is looped over a shaft of radius 0.45 cm and a wheel of radius 1.80 cm. The arrangement of the belt, shaft, and wheel is similar to that of the chain and sprockets in Fig. Q9.4.... A meter stick with a mass of 0.180 kg is pivoted about one end so it can rotate without friction about a horizontal axis. The meter stick is held in a horizontal position and released. As it swings... A sphere with radius R = 0.200 m has density that decreases with distance r from the center of the sphere according to = 3.00 10 3 kg/m 3 (9.00 10 3 kg/m 4 )r. (a) Calculate the total mass of the... As an intern with an engineering firm, you are asked to measure the moment of inertia of a large wheel, for rotation about an axis through its center. Since you were a good physics student, you know... In the system shown in Fig. 9.17, a 12.0-kg mass is released from rest and falls, causing the uniform 10.0-kg cylinder of diameter 30.0 cm to turn about a frictionless axle through its center. How... A dancer is spinning at 72 rpm about an axis through her center with her arms outstretched, as shown in Fig. P9.92. From biomedical measurements, the typical distribution of mass in a human body is... In Fig. E10.7, forces A, B, C, and D each have magnitude 50 N and act at the same point on the object. (a) What torque (magnitude and direction) does each of these forces exert on the object about... A uniform disk with mass 40.0 kg and radius 0.200 m is pivoted at its center about a horizontal, frictionless axle that is stationary. The disk is initially at rest, and then a constant force F =... A bicycle racer is going downhill at 11.0 m/s when, to his horror, one of his 2.25-kg wheels comes off as he is 75.0 m above the foot of the hill. We can model the wheel as a thin-walled cylinder... If a person of mass M simply moved forward with speed V, his kinetic energy would be 1/2 MV 2 , However, in addition to possessing a forward motion, various parts of his body (such as the arms and... Using Problem 9.93 as a guide, apply it to a person running at 12 km h, with his arms and legs each swinging through 30 in s. As before, assume that the arms and legs are kept straight. Problem... A size-5 soccer ball of diameter 22.6 cm and mass 426 g rolls up a hill without slipping, reaching a maximum height of 5.00 m above the base of the hill. We can model this ball as a thin-walled... (a) Calculate the magnitude of the angular momentum of the earth in a circular orbit around the sun. Is it reasonable to model it as a particle? (b) Calculate the magnitude of the angular momentum of... A uniform, 4.5-kg, square, solid wooden gate 1.5 m on each side hangs vertically from a frictionless pivot at the center of its upper edge. A 1.1-kg raven flying horizontally at 5.0 m/s flies into... Tarzan has foolishly gotten himself into another scrape with the animals and must be rescued once again by Jane. The 60.0-kg Jane starts from rest at a height of 5.00 m in the trees and swings down... A small block on a frictionless, horizontal surface has a mass of 0.0250 kg. It is attached to a massless cord passing through a hole in the surface (Fig. E10.42). The block is originally revolving... In November 2003, the now-most-distant-known object in the solar system was discovered by observation with a telescope on Mt. Palomar. This object, known as Sedna, is approximately 1700 km in... A uniform rod is 2.00 m long and has mass 1.80 kg. A 2.40-kg clamp is attached to the rod. How far should the center of gravity of the clamp be from the left-hand end of the rod in order for the... End A of the bar AB in Fig. P11.53 rests on a frictionless horizontal surface, and end B is hinged. A horizontal force F of magnitude 160 N is exerted on end A. You can ignore the weight of the bar.... A uniform, 7.5-m-long beam weighing 5860 N is hinged to a wall and supported by a thin cable attached 1.5 m from the free end of the beam. The cable runs between the beam and the wall and makes a 40... A block with mass m is revolving with linear speed v 1 in a circle of radius r 1 on a frictionless horizontal surface (see Fig. E10.42). The string is slowly pulled from below until the radius of the... The bulk modulus for bone is 15 GPa. (a) If a diver-in-training is put into a pressurized suit, by how much would the pressure have to be raised (in atmospheres) above atmospheric pressure to... In the Challenger Deep of the Marianas Trench, the depth of seawater is 10.9 km and the pressure is (about 1.15 Ã 10 3 atm). (a) If a cubic meter of water is taken from the surface to this... A copper cube measures 6.00 cm on each side. The bottom face is held in place by very strong glue to a flat horizontal surface, while a horizontal force F is applied to the upper face parallel to one... A cube 5.0 cm on each side is made of a metal alloy. After you drill a cylindrical hole 2.0 cm in diameter all the way through and perpendicular to one face, you find that the cube weighs 7.50 N. (a)... (a) What is the difference between the pressure of the blood in your brain when you stand on your head and the pressure when you stand on your feet? Assume that you are 1.85 m tall. The density of... A claw hammer is used to pull a nail out of a board (Fig. P11.52). The nail is at an angle of 60 to the board, and a force F 1 of magnitude 400 N applied to the nail is required to pull it from the... At a point where an irrigation canal having a rectangular cross section is 18.5 m wide and 3.75 m deep, the water flows at 2.50 cm s. At a point downstream, but on the same level, the canal is 16.5 m... A pressure difference of 6.00 10 4 Pa is required to maintain a volume flow rate of 0.800 m 3 /s for a viscous fluid flowing through a section of cylindrical pipe that has radius 0.210 m? What... A wire of length I 0 and cross-sectional area A supports a hanging weight W. (a) Show that if the wire obeys Eq. (11.7), it behaves like a spring of force constant AY/I 0 , where Y is Youngs modulus... If the force on the tympanic membrane (eardrum) increases by about 1.5 N above the force from atmospheric pressure, the membrane can be damaged. When you go scuba diving in the ocean, below what... (a) As you can tell by watching them in an aquarium, fish are able to remain at any depth in water with no effort. What does this ability tell you about their density? (b) Fish are able to inflate... A 0.180-kg cube of ice (frozen water) is floating in glycerine. The gylcerine is in a tall cylinder that has inside radius 3.50 cm. The level of the glycerine is well below the top of the cylinder.... A plastic ball has radius 12.0 cm and floats in water with 24.0% of its volume submerged. (a) What force must you apply to the ball to hold it at rest totally below the surface of the water? (b) If... A block of balsa wood placed in one scale pan of an equalarm balance is exactly balanced by a 0.115-kg brass mass in the other scale pan. Find the true mass of the balsa wood if its density is 150... A medical technician is trying to determine what percentage of a patients artery is blocked by plaque. To do this, she measures the blood pressure just before the region of blockage and finds that it... A cylindrical container of an in-compressible liquid with density Ï rotates with constant angular speed Ï about its axis of symmetry, which we take to be the y-axis (Fig. P12.86). (a) Show... Block A in Fig. P12.74 hangs by a cord from spring balance D and is submerged in a liquid C contained in beaker B. The mass of the beaker is 1.00 kg; the mass of the liquid is 1.80 kg. Balance D... A firehose must be able to shoot water to the top of a building 28.0 m tall when aimed straight up. Water enters this hose at a steady rate of and shoots out of a round nozzle. (a) What is the... An open cylindrical tank of acid rests at the edge of a table 1.4 m above the floor of the chemistry lab. If this tank springs a small hole in the side at its base, how far from the foot of the table... When an open-faced boat has a mass of 5750 kg, including its cargo and passengers, it floats with the water just up to the top of its gunwales (sides) on a freshwater lake. (a) What is the volume of... A piece of wood is 0.600 m long, 0.250 m wide, and 0.080 m thick. Its density is 700 kg/m 3 . What volume of lead must be fastened underneath it to sink the wood in calm water so that its top is just... A rifle bullet with mass 8.00 g and initial horizontal velocity 280 m/s strikes and embeds itself in a block with mass 0.992 kg that rests on a friction-less surface and is attached to one end of an... As shown in Fig. E10.20, a string is wrapped several times around the rim of a small hoop with radius 0.0800 m and mass 0.180 kg. The free end of the string is pulled upward in just the right way so... (a) Use data from Appendix F to calculate the acceleration due to gravity on the moon. (b) Calculate the friction force on a walking 65-kg astronaut carrying a 43-kg instrument pack on the moon if... The asteroid Toro has a radius of about 5.0 km. Consult Appendix F as necessary. (a) Assuming that the density of Toro is the same as that of the earth (5.5 g/cm 3 ), find its total mass and find the... A child with poor table manners is sliding his 250-g dinner plate back and forth in SHM with an amplitude of 0.100 m on a horizontal surface. At a point 0.060 m away from equilibrium, the speed of... Four passengers with combined mass 250 kg compress the springs of a car with worn-out shock absorbers by 4.00 cm when they get in. Model the car and passengers as a single body on a single ideal... An unmanned spacecraft is in a circular orbit around the moon, observing the lunar surface from an altitude of 50.0 km (see Appendix F). To the dismay of scientists on earth, an electrical fault... Tarzan spies a 35-kg chimpanzee in severe danger, so he swings to the rescue. He adjusts his strong, but very light, vine so that he will first come to rest 4.0 s after beginning his swing, at which... A mass is vibrating at the end of a spring of force constant 225 N/m. Figure E14.62 shows a graph of its position x as a function of time t. (a) At what times is the mass not moving? (b) How much...
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