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In 2000, NASA placed a satellite in orbit around an asteroid. Consider a spherical asteroid with a mass of 1.0 10 16 kg and a radius of 8.8 km. a. What is the speed of a satellite orbiting 5.0 km... Pluto moves in a fairly elliptical orbit around the sun. Plutos speed at its closest approach of 4.43 10 9 km is 6.12 km/s. What is Plutos speed at the most distant point in its orbit, where it is... What are the magnitude and direction of the net gravitational force on the 20.0 kg mass in FIGURE P13.36? y 10.0 kg 10.0 kg 5.0 cm 5.0 cm 20.0 cm 20.0 kg FIGURE P13.36 What is the total gravitational potential energy of the three masses in FIGURE P13.36? 10.0 kg y 10.0 kg 5.0 cm 5.0 cm 20.0 cm 20.0 kg FIGURE P13.36 Two spherical objects have a combined mass of 150 kg. The gravitational attraction between them is 8.00 10 -6 N when their centers are 20 cm apart. What is the mass of each? Two 100 kg lead spheres are suspended from 100-m-long massless cables. The tops of the cables have been carefully anchored exactly 1 m apart. By how much is the distance between the centers of the... A rogue black hole with a mass 12 times the mass of the sun drifts into the solar system on a collision course with earth. How far is the black hole from the center of the earth when objects on the... A projectile is shot straight up from the earths surface at a speed of 10,000 km/h. How high does it go? An astronaut circling the earth at an altitude of 400 km is horrified to discover that a cloud of space debris is moving in the exact same orbit as his spacecraft, but in the opposite direction. The... Suppose that on earth you can jump straight up a distance of 45 cm. Asteroids are made of material with mass density 2800 kg/m 3 . What is the maximum diameter of a spherical asteroid from which you... Two spherical asteroids have the same radius R. Asteroid 1 has mass M and asteroid 2 has mass 2M. The two asteroids are released from rest with distance 10R between their centers. What is the speed... The 75,000 kg space shuttle used to fly in a 250-km-high circular orbit. It needed to reach a 610-km-high circular orbit to service the Hubble Space Telescope. How much energy was required to boost... How much energy would be required to move the earth into a circular orbit with a radius 1.0 km larger than its current radius? NASA would like to place a satellite in orbit around the moon such that the satellite always remains in the same position over the lunar surface. What is the satellites altitude? A satellite orbiting the earth is directly over a point on the equator at 12:00 midnight every two days. It is not over that point at any time in between. What is the radius of the satellites orbit? Three stars, each with the mass of our sun, form an equilateral triangle with sides 1.0 10 12 m long. (This triangle would just about fit within the orbit of Jupiter.) The triangle has to rotate,... Comets move around the sun in very elliptical orbits. At its closet approach, in 1986, Comet Halley was 8.79 10 7 km from the sun and moving with a speed of 54.6 km/s. What was the comets speed when... A 55,000 kg space capsule is in a 28,000-km-diameter circular orbit around the moon. A brief but intense firing of its engine in the forward direction suddenly decreases its speed by 50%. This causes... Two Jupiter-size planets are released from rest 1.0 10 11 m apart. What are their speeds as they crash together? A satellite in a circular orbit of radius r has period T. A satellite in a nearby orbit with radius r + r, where r < < r, has the very slightly different period T + T. a. Show that T/T = 3/2 r/r b.... While visiting Planet Physics, you toss a rock straight up at 11 m/s and catch it 2.5 s later. While you visit the surface, your cruise ship orbits at an altitude equal to the planets radius every... A moon lander is orbiting the moon at an altitude of 1000 km. By what percentage must it decrease its speed so as to just graze the moons surface one-half period later? Lets look in more detail at how a satellite is moved from one circular orbit to another. FIGURE CP13.71 shows two circular orbits, of radii r 1 and r 2 , and an elliptical orbit that connects them.... Rank in order, from largest to smallest, the pressures at d, e, and f in FIGURE Q14.2. Explain. f d a b A 5.0 kg rock whose density is 4800 kg/m 3 is suspended by a string such that half of the rocks volume is under water. What is the tension in the string? What is the tension of the string in FIGURE EX14.21? 100 cm of aluminum, density PAI = 2700 kg/m Ethyl alcohol FIGURE EX14.21 You need to determine the density of a ceramic statue. If you suspend it from a spring scale, the scale reads 28.4 N. If you then lower the statue into a tub of water, so that it is completely... Styrofoam has a density of 150 kg/m 3 . What is the maximum mass that can hang without sinking from a 50-cm-diameter Styrofoam sphere in water? Assume the volume of the mass is negligible compared to... You and your friends are playing in the swimming pool with a 60-cm-diameter beach ball. How much force would be needed to push the ball completely under water? A 1.0-cm-diameter pipe widens to 2.0 cm, then narrows to 5.0 mm. Liquid flows through the first segment at a speed of 4.0 m/s. a. What is the speed in the second and third segments? b. What is the... An 80-cm-long, 1.0-mm-diameter steel guitar string must be tightened to a tension of 2000 N by turning the tuning screws. By how much is the string stretched? A 3.0-m-tall, 50-cm-diameter concrete column supports a 200,000 kg load. By how much is the column compressed? a. What is the pressure at a depth of 5000 m in the ocean? b. What is the fractional volume change V/V of seawater at this pressure? c. What is the density of seawater at this pressure? A large 10,000 L aquarium is supported by four wood posts (Douglas fir) at the corners. Each post has a square 4.0 cm 4.0 cm cross section and is 80 cm tall. By how much is each post compressed by... The two 60-cm-diameter cylinders in FIGURE P14.39, closed at one end, open at the other, are joined to form a single cylinder, then the air inside is removed. a. How much force does the atmosphere... a. The 70 kg student in FIGURE P14.42 balances a 1200 kg elephant on a hydraulic lift. What is the diameter of the piston the student is standing on? b. When a second student joins the first, the... A 55 kg cheerleader uses an oil-filled hydraulic lift to hold four 110 kg football players at a height of 1.0 m. If her piston is 16 cm in diameter, what is the diameter of the football players... Glycerin is poured into an open U-shaped tube until the height in both sides is 20 cm. Ethyl alcohol is then poured into one arm until the height of the alcohol column is 20 cm. The two liquids do... An aquarium of length L, width (front to back) W, and depth D is filled to the top with liquid of density . a. Find an expression for the force of the liquid on the bottom of the aquarium. b. Find an... Its possible to use the ideal-gas law to show that the density of the earths atmosphere decreases exponentially with height. That is, = 0 exp(-z/z 0 ), where z is the height above sea level, 0 is... The average density of the body of a fish is 1080 kg/m 3 . To keep from sinking, a fish increases its volume by inflating an internal air bladder, known as a swim bladder, with air. By what percent... A cylinder with cross-section area A floats with its long axis vertical in a liquid of density . a. Pressing down on the cylinder pushes it deeper into the liquid. Find an expression for the force... A 355 mL soda can is 6.2 cm in diameter and has a mass of 20 g. Such a soda can half full of water is floating upright in water. What length of the can is above the water level? A nuclear power plant draws 3.0 10 6 L/min of cooling water from the ocean. If the water is drawn in through two parallel, 3.0-m-diameter pipes, what is the water speed in each pipe? A tree loses water to the air by the process of transpiration at the rate of 110 g/h. This water is replaced by the upward flow of sap through vessels in the trunk. If the trunk contains 2000... The 1.0-m-tall cylinder in FIGURE P14.61 contains air at a pressure of 1 atm. A very thin, frictionless piston of negligible mass is placed at the top of the cylinder, to prevent any air from... Water flowing out of a 16-mm-diameter faucet fills a 2.0 L bottle in 10 s. At what distance below the faucet has the water stream narrowed to 10 mm diameter? Water from a vertical pipe emerges as a 10-cm-diameter cylinder and falls straight down 7.5 m into a bucket. The water exits the pipe with a speed of 2.0 m/s. What is the diameter of the column of... A 2.0-m-diameter vertical cylinder, open at the top, is filled with ethyl alcohol to the 2.5 m mark. A worker pulls a plug from a hole 55 cm from the bottom, causing the fluid level to begin dropping... An air-track glider attached to a spring oscillates between the 10 cm mark and the 60 cm mark on the track. The glider completes 10 oscillations in 33 s. What are the (a) Period, (b) Frequency, (c)... A block oscillating on a spring has period T = 2 s. What is the period if: a. The blocks mass is doubled? Explain. Note that you do not know the value of either m or k, so do not assume any... An object in simple harmonic motion has an amplitude of 8.0 cm, a frequency of 0.25 Hz, and a phase constant of -/2 rad. Draw a position graph showing two cycles of the motion. An object in simple harmonic motion has amplitude 4.0 cm and frequency 4.0 Hz, and at t = 0 s it passes through the equilibrium point moving to the right. Write the function x(t) that describes the... A block attached to a spring with unknown spring constant oscillates with a period of 2.0 s. What is the period if a. The mass is doubled? b. The mass is halved? c. The amplitude is doubled? d. The... A spring with spring constant 15 N/m hangs from the ceiling. A ball is attached to the spring and allowed to come to rest. It is then pulled down 6.0 cm and released. If the ball makes 30... A spring is hung from the ceiling. When a block is attached to its end, it stretches 2.0 cm before reaching its new equilibrium length. The block is then pulled down slightly and released. What is... A 100 g block attached to a spring with spring constant 2.5 N/m oscillates horizontally on a frictionless table. Its velocity is 20 cm/s when x = -5.0 cm. a. What is the amplitude of oscillation? b.... A 5.0 kg block hangs from a spring with spring constant 2000 N/m. The block is pulled down 5.0 cm from the equilibrium position and given an initial velocity of 1.0 m/s back toward equilibrium. What... Prove that the expression for x(t) in Equation 15.55 is a solution to the equation of motion for a damped oscillator, Equation 15.54, if and only if the angular frequency is given by the expression... Draw the snapshot graph D(x, t = 0 s) at t = 0 s for the wave shown in FIGURE EX16.6. D (cm) t (s) 1 2 3 4 5 6 -1| -2 1 History graph of a wave at x = 2 m Wave moving to the right at 1.0 m/s What are the amplitude, wavelength, frequency, and phase constant of the traveling wave in FIGURE Q16.7? D (cm) 24 m/s 2- rX (m) 4 8 /12 16\ 20 -2. -4- Snapshot graph at t = 0 s FIGURE Q16.7 FIGURE Q16.9 shows the wave fronts of a circular wave. What is the phase difference between (a) Points A and B (b) Points C and D (c) Points E and F? D E A' What are the amplitude, frequency, and wavelength of the wave in FIGURE EX16.14? D (cm) 6- 3- t (s) 0.2 /0.4 0.6\ 0.8 /1.0 -3- -6- History graph at x= 0 m Wave traveling left at 2.0 m/s FIGURE EX16.14 A loudspeaker on a tall pole broadcasts sound waves equally in all directions. What is the speakers power output if the sound intensity level is 90 dB at a distance of 20 m? FIGURE P16.57 shows a snapshot graph of a wave traveling to the right along a string at 45 m/s. At this instant, what is the velocity of points 1, 2, and 3 on the string? D (cm) 45 m/s 2, 3 -2- 30 cm... The string in FIGURE P16.60 has linear density μ. Find an expression in terms of M, μ, and θ for the speed of waves on the string. -Frictionless The G string on a guitar is a 0.46-mm-diameter steel string with a linear density of 1.3 g/m. When the string is properly tuned to 196 Hz, the wave speed on the string is 250 m/s. Tuning is done by... FIGURE P16.46 is a snapshot graph at t = 0 s of a 5.0 Hz wave traveling to the left. a. What is the wave speed? b. What is the phase constant of the wave? c. Write the displacement equation for this... Is the displacement D(x, t) = (0.10 - 0.10x 2 + xt - 2.5t 2 ) m, where x is in m and t is in s, a possible traveling wave? If so, what is the wave speed? If you take snapshots of a standing wave on a string, there are certain instants when the string is totally flat. What has happened to the energy of the wave at those instants? Western music uses a musical scale with equal temperament tuning, which means that any two adjacent notes have the same frequency ratio r. That is, notes n and n + 1 are related by f n+1 = rf n for... A gas undergoes the process shown in FIGURE Q18.10. By what factor does the temperature change? FIGURE Q18.10 A student is asked to sketch a pV diagram for a gas that goes through a cycle consisting of (a) An isobaric expansion, (b) A constant-volume reduction in temperature, (c) An isothermal process that... A demented scientist creates a new temperature scale, the Z scale. He decides to call the boiling point of nitrogen 0Z and the melting point of iron 1000Z. a. What is the boiling point of water on... A concrete bridge is built of 325-cm-long concrete slabs with an expansion joint between them. The slabs just touch on a 115F day, the hottest day for which the bridge is designed. What is the gap... A 20-cm-diameter cylinder that is 40 cm long contains 50 g of oxygen gas at 20C. a. How many moles of oxygen are in the cylinder? b. How many oxygen molecules are in the cylinder? c. What is the... A gas at temperature T 0 and atmospheric pressure fills a cylinder. The gas is transferred to a new cylinder with three times the volume, after which the pressure is half the original pressure. What... A gas with initial state variables p 1 , V 1 , and T 1 expands isothermally until V 2 = 2V 1 . What are (a) T 2 (b) p 2 ? 0.0040 mol of gas undergoes the process shown in FIGURE EX18.35. a. What type of process is this? b. What are the initial and final temperatures in °C? p (atm) 3- 2- V (cm) 300 0+ 100 200 FIGURE... An ideal gas starts with pressure p 1 and volume V 1 . Draw a pV diagram showing the process in which the gas undergoes an isochoric process that doubles the pressure, then an isobaric process that... An ideal gas starts with pressure p 1 and volume V 1 . Draw a pV diagram showing the process in which the gas undergoes an isothermal process during which the volume is halved, then an isochoric... On a cool morning, when the temperature is 15C, you measure the pressure in your car tires to be 30 psi. After driving 20 mi on the freeway, the temperature of your tires is 45C. What pressure will... 10,000 cm3 of 200C steam at a pressure of 20 atm is cooled until it condenses. What is the volume of the liquid water? Give your answer in cm 3 . The 50 kg circular piston shown in FIGURE P18.58 floats on 0.12 mol of compressed air.a. What is the piston height h if the temperature is 30?C?b. How far does the piston move if the temperature is... FIGURE P18.61 shows two different processes by which 1.0 g of nitrogen gas moves from state 1 to state 2. The temperature of state 1 is 25?C. What are (a) Pressure p 1 (b) Temperatures (in ?C) T 2 ,... FIGURE P18.62 shows two different processes by which 80 mol of gas move from state 1 to state 2. The dashed line is an isotherm. a. What is the temperature of the isothermal process? b. What maximum... 4.0 g of oxygen gas, starting at 820°C, follow the process 1 2 shown in FIGURE P18.63. What is temperature T 2 (in °C)? P1 P2 2 0+ V2 V1 FIGURE P18.63 You are given the equation(s) used to solve a problem. For each of these, you are to a. Write a realistic problem for which this is the correct equation(s). b. Draw a pV diagram. c. Finish the... You are given the equation(s) used to solve a problem. For each of these, you are to a. Write a realistic problem for which this is the correct equation(s). b. Draw a pV diagram. c. Finish the... You are given the equation(s) used to solve a problem. For each of these, you are to a. Write a realistic problem for which this is the correct equation(s). b. Draw a pV diagram. c. Finish the... The cylinder in FIGURE CP18.72 has a moveable piston attached to a spring. The cylinders cross-section area is 10 cm 2 , it contains 0.0040 mol of gas, and the spring constant is 1500 N/m. At... When strong winds rapidly carry air down from mountains to a lower elevation, the air has no time to exchange heat with its surroundings. The air is compressed as the pressure rises, and its... Most stars are main-sequence stars, a group of stars for which size, mass, surface temperature, and radiated power are closely related. The sun, for instance, is a yellow main sequence star with a... A satellite to reflect radar is a 2.0-m-diameter, 2.0-mm-thick spherical copper shell. While orbiting the earth, the satellite absorbs sunlight and is warmed to 50C. When it passes into the earths... 0.020 mol of a diatomic gas, with initial temperature 20C, are compressed from 1500 cm 3 to 500 cm 3 in a process in which pV 2 = constant. How much heat energy is added during this process? Physicians use high-frequency (f = 195 MHz) sound waves, called ultrasound, to image internal organs. The speed of these ultrasound waves is 1480 m/s in muscle and 344 m/s in air. We define the index... The professor once again returns the apparatus to its original setting, but now she adjusts the oscillator to produce sound waves of half the original frequency. What happens? (a) The students who... A lottery machine uses blowing air to keep 2000 Ping-Pong balls bouncing around inside a 1.0 m 1.0 m 1.0 m box. The diameter of a Ping-Pong ball is 3.0 cm. What is the mean free path between... For a monatomic gas, what is the ratio of the volume per atom (V/N) to the volume of an atom when the mean free path is ten times the atomic diameter? The molecules in a six-particle gas have velocities Calculate (a) v avg , (b) v avg , (c) v rms . V1 = (20 30) m/s V2 = (40 + 70) m/s V3 = (-80 + 20) m/s V = 30 m/s Vs = (40 407) m/s 36 = (-50 ...
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