What are the magnitude and direction of the angular momentum relative to the origin of the 200 g particle in FIGURE EX12.42? 200 g 45 2.0 m- 3.0 m/s - 1.0 m
What is the angular momentum vector of the 2.0 kg, 4.0-cm-diameter rotating disk in FIGURE EX12.43? y 600 rpm FIGURE EX12.43
What is the angular momentum vector of the 500 g rotating bar in FIGURE EX12.44? 120 rpm 2.0 m FIGURE EX12.44
How fast, in rpm, would a 5.0 kg, 22-cm-diameter bowling ball have to spin to have an angular momentum of 0.23 kg m 2 /s?
A 2.0 kg, 20-cm-diameter turntable rotates at 100 rpm on frictionless bearings. Two 500 g blocks fall from above, hit the turntable simultaneously at opposite ends of a diameter, and stick. What is...
A 75 g, 6.0-cm-diameter solid spherical top is spun at 1200 rpm on an axle that extends 1.0 cm past the edge of the sphere. The tip of the axle is placed on a support. What is the tops precession...
A 300 g ball and a 600 g ball are connected by a 40-cm-long massless, rigid rod. The structure rotates about its center of mass at 100 rpm. What is its rotational kinetic energy?
An 800 g steel plate has the shape of the isosceles triangle shown in FIGURE P12.50. What are the x- and y-coordinates of the center of mass? y 20 cm 30 cm FIGURE P12.50
Determine the moment of inertia about the axis of the object shown in FIGURE P12.51. Rod of p , mass M Rotation axis FIGURE P12.51
What is the moment of inertia of a 2.0 kg, 20-cm-diameter disk for rotation about an axis (a) Through the center, (b) Through the edge of the disk?
Calculate the moment of inertia of the rectangular plate in FIGURE P12.54 for rotation about a perpendicular axis through the center. Rotation axis L L FIGURE P12.54
a. A disk of mass M and radius R has a hole of radius r centered on the axis. Calculate the moment of inertia of the disk. b. Confirm that your answer agrees with Table 12.2 when r = 0 and when r =...
Consider a solid cone of radius R, height H, and mass M. The volume of a cone is 1/3HR 2 . a. What is the distance from the apex (the point) to the center of mass? b. What is the moment of inertia...
A persons center of mass is easily found by having the person lie on a reaction board. A horizontal, 2.5-m-long, 6.1 kg reaction board is supported only at the ends, with one end resting on a scale...
A 40 kg, 5.0-m-long beam is supported by, but not attached to, the two posts in Figure P12.60. A 20 kg boy starts walking along the beam. How close can he get to the right end of the beam without it...
Rank in order, from largest to smallest, the angular accelerations a to d in FIGURE Q12.10. Explain. 2F 2F 2m 2r 2r 2m b d FIGURE Q12.10
A 120-cm-wide sign hangs from a 5.0 kg, 200-cm-long pole. A cable of negligible mass supports the end of the rod as shown in Figure P12.62. What is the maximum mass of the sign if the maximum tension...
A piece of modern sculpture consists of an 8.0-m-long, 150 kg stainless steel bar passing diametrically through a 50 kg copper sphere. The center of the sphere is 2.0 m from one end of the bar. To be...
The 2.0 kg, 30-cm-diameter disk in Figure P12.66 is spinning at 300 rpm. How much friction force must the brake apply to the rim to bring the disk to a halt in 3.0 s? Brake FIGURE P12.66
A 30-cm-diameter, 1.2 kg solid turntable rotates on a 1.2-cm diameter, 450 g shaft at a constant 33 rpm. When you hit the stop switch, a brake pad presses against the shaft and brings the turntable...
A hollow sphere is rolling along a horizontal floor at 5.0 m/s when it comes to a 30 incline. How far up the incline does it roll before reversing direction?
Flywheels are large, massive wheels used to store energy. They can be spun up slowly, then the wheels energy can be released quickly to accomplish a task that demands high power. An industrial...
Your engineering team has been assigned the task of measuring the properties of a new jet-engine turbine. Youve previously determined that the turbines moment of inertia is 2.6 kg m 2 . The next job...
A cylinder of radius R, length L, and mass M is released from rest on a slope inclined at angle . It is oriented to roll straight down the slope. If the slope were frictionless, the cylinder would...
A long, thin rod of mass M and length L is standing straight up on a table. Its lower end rotates on a frictionless pivot. A very slight push causes the rod to fall over. As it hits the table, what...
The marble rolls down the track shown in FIGURE P12.75 and around a loop-the-loop of radius R. The marble has mass m and radius r. What minimum height h must the track have for the marble to make it...
A satellite follows the elliptical orbit shown in FIGURE P12.77. The only force on the satellite is the gravitational attraction of the planet. The satellites speed at point a is 8000 m/s. a. Does...
A merry-go-round is a common piece of playground equipment. A 3.0-m-diameter merry-go-round with a mass of 250 kg is spinning at 20 rpm. John runs tangent to the merry go-round at 5.0 m/s, in the...
A 45 kg figure skater is spinning on the toes of her skates at 1.0 rev/s. Her arms are outstretched as far as they will go. In this orientation, the skater can be modeled as a cylindrical torso (40...
The two blocks in FIGURE CP12.86 are connected by a massless rope that passes over a pulley. The pulley is 12 cm in diameter and has a mass of 2.0 kg. As the pulley turns, friction at the axle exerts...
A rod of length L and mass M has a nonuniform mass distribution. The linear mass density (mass per length) is = cx 2 , where x is measured from the center of the rod and c is a constant. a. What are...
In FIGURE CP12.88, a 200 g toy car is placed on a narrow 60-cm-diameter track with wheel grooves that keep the car going in a circle. The 1.0 kg track is free to turn on a frictionless, vertical...
Is the earths gravitational force on the sun larger than, smaller than, or equal to the suns gravitational force on the earth? Explain.
A 1000 kg satellite and a 2000 kg satellite follow exactly the same orbit around the earth. a. What is the ratio F 1 /F 2 of the gravitational force on the first satellite to that on the second...
The International Space Station orbits 300 km above the surface of the earth. What is the gravitational force on a 1.0 kg sphere inside the International Space Station?
Two 65 kg astronauts leave earth in a spacecraft, sitting 1.0 m apart. How far are they from the center of the earth when the gravitational force between them is as strong as the gravitational force...
Why is the gravitational potential energy of two masses negative? That saying because thats what the equation gives is not an explanation.
A 20 kg sphere is at the origin and a 10 kg sphere is at x = 20 cm. At what position on the x-axis could you place a small mass such that the net gravitational force on it due to the spheres is zero?
The escape speed from Planet X is 10,000 m/s. Planet Y has the same radius as Planet X but is twice as dense. What is the escape speed from Planet Y?
a. What is the free-fall acceleration at the surface of the sun? b. What is the free-fall acceleration toward the sun at the distance of the earth?
The mass of Jupiter is 300 times the mass of the earth. Jupiter orbits the sun with T Jupiter = 11.9 yr in an orbit with r Jupiter = 5.2r earth . Suppose the earth could be moved to the distance of...
Satellites in near-earth orbit experience a very slight drag due to the extremely thin upper atmosphere. These satellites slowly but surely spiral inward, where they finally burn up as they reach the...
A sensitive gravimeter at a mountain observatory finds that the free-fall acceleration is 0.0075 m/s 2 less than that at sea level. What is the observatorys altitude?
Saturns moon Titan has a mass of 1.35 10 23 kg and a radius of 2580 km. What is the free-fall acceleration on Titan?
A newly discovered planet has a radius twice as large as earths and a mass five times as large. What is the free-fall acceleration on its surface?
Suppose we could shrink the earth without changing its mass. At what fraction of its current radius would the free-fall acceleration at the surface be three times its present value?
Planet Z is 10,000 km in diameter. The free-fall acceleration on Planet Z is 8.0 m/s 2 . a. What is the mass of Planet Z? b. What is the free-fall acceleration 10,000 km above Planet Zs north pole?
An astronaut on earth can throw a ball straight up to a height of 15 m. How high can he throw the ball on Mars?
A space station orbits the sun at the same distance as the earth but on the opposite side of the sun. A small probe is fired away from the station. What minimum speed does the probe need to escape...
Nothing can escape the event horizon of a black hole, not even light. You can think of the event horizon as being the distance from a black hole at which the escape speed is the speed of light, 3.00 ...
You have been visiting a distant planet. Your measurements have determined that the planets mass is twice that of earth but the free-fall acceleration at the surface is only one-fourth as large. a....
Two meteoroids are heading for earth. Their speeds as they cross the moons orbit are 2.0 km/s. a. The first meteoroid is heading straight for earth. What is its speed of impact? b. The second misses...
A binary star system has two stars, each with the same mass as our sun, separated by 1.0 10 12 m. A comet is very far away and essentially at rest. Slowly but surely, gravity pulls the comet toward...
The asteroid belt circles the sun between the orbits of Mars and Jupiter. One asteroid has a period of 5.0 earth years. What are the asteroids orbital radius and speed?
You are the science officer on a visit to a distant solar system. Prior to landing on a planet you measure its diameter to be 1.8 10 7 m and its rotation period to be 22.3 hours. You have previously...
Three satellites orbit a planet of radius R, as shown in FIGURE EX13.26. Satellites S 1 and S 3 have mass m. Satellite S 2 has mass 2m. Satellite S 1 orbits in 250 minutes and the force on S 1 is...
A satellite orbits the sun with a period of 1.0 day. What is the radius of its orbit?
A new planet is discovered orbiting the star Vega in a circular orbit. The planet takes 55 earth years to complete one orbit around the star. Vegas mass is 2.1 times the suns mass. What is the radius...
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...