Physics for Scientists and Engineers: Foundations and Connections
1st Edition
ISBN: 9781133939146
Author: Katz, Debora M.
Publisher: Cengage Learning
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Chapter 6, Problem 72PQ
To determine
The minimum period of rotation if the block is to remain stationary.
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a) Show that the torque on a planet orbiting the Sun due to the gravitational attraction of the
Sun is zero.
b) Show that the area swept out by a planet in time dt is proportional to its angular momentum.
c) Using your answers above derive Kepler’s 2nd law.
d) If a planet is in a circular orbit of radius, R, determine the potential energy due to gravity,
its kinetic energy due to the motion of the planet, and the total energy.
e) A satelite is in geostationary orbit. How much energy is required to move it to a circular
orbit where it orbits the Earth once in 8 days? You may express your answer in terms of
the total energy of the initial geostationary orbit.
**Only answer part D and E, answers to previous questions have been provided in the image.**
a) Show that the torque on a planet orbiting the Sun due to the gravitational attraction of theSun is zero.b) Show that the area swept out by a planet in time dt is proportional to its angular momentum.c) Using your answers above derive Kepler’s 2nd law.d) If a planet is in a circular orbit of radius, R, determine the potential energy due to gravity,its kinetic energy due to the motion of the planet, and the total energy.e) A satelite is in geostationary orbit. How much energy is required to move it to a circularorbit where it orbits the Earth once in 8 days? You may express your answer in terms ofthe total energy of the initial geostationary orbit.
In the Pirate Boat ride at the amusement park, riders swing back and forth in a pendulumlike “boat.” The distance from the boat to the pivot point is 13m, and the maximum angle the boat reaches is 40°.a. What is the maximum speed the boat attains?b. What is the apparent weight of a 55 kg rider at the bottom of the arc?
Chapter 6 Solutions
Physics for Scientists and Engineers: Foundations and Connections
Ch. 6.1 - CASE STUDY Skydiving Arguments Take a moment to...Ch. 6.3 - A box rests on a steel surface. Four sides of the...Ch. 6.3 - Prob. 6.3CECh. 6.4 - Imagine trying to push a heavy sofa across the...Ch. 6.4 - Prob. 6.5CECh. 6.4 - Prob. 6.6CECh. 6.4 - What forces act on you as you walk across a room?...Ch. 6.5 - Figure 6.20 shows four objects moving downward....Ch. 6.5 - Prob. 6.9CECh. 6.5 - Prob. 6.10CE
Ch. 6.6 - The following objects are moving in uniform...Ch. 6 - In many textbook problems, we ignore certain...Ch. 6 - Prob. 2PQCh. 6 - Prob. 3PQCh. 6 - Prob. 4PQCh. 6 - Prob. 5PQCh. 6 - Draw a free-body diagram for the burglar, who is...Ch. 6 - The shower curtain rod in Figure P6.7 is called a...Ch. 6 - A rectangular block has a length that is five...Ch. 6 - A man exerts a force of 16.7 N horizontally on a...Ch. 6 - A makeshift sign hangs by a wire that is extended...Ch. 6 - In Problem 10, the mass of the sign is 25.4 kg,...Ch. 6 - Prob. 12PQCh. 6 - A motorcyclist is traveling at 55.0 mph on a flat...Ch. 6 - A small steel I-beam (Fig. P6.14) is at rest with...Ch. 6 - A box is at rest with respect to the surface of a...Ch. 6 - A filled treasure chest of mass m with a long rope...Ch. 6 - A filled treasure chest (m = 375 kg) with a long...Ch. 6 - Rochelle holds her 2.80-kg physics textbook by...Ch. 6 - Prob. 19PQCh. 6 - A sled and rider have a total mass 56.8 kg. They...Ch. 6 - Prob. 21PQCh. 6 - Prob. 22PQCh. 6 - Prob. 23PQCh. 6 - Lisa measured the coefficient of static friction...Ch. 6 - An ice cube with a mass of 0.0507 kg is placed at...Ch. 6 - Prob. 26PQCh. 6 - Curling is a game similar to lawn bowling except...Ch. 6 - Prob. 28PQCh. 6 - A sled and rider have a total mass of 56.8 kg....Ch. 6 - A sled and rider have a total mass of 56.8 kg....Ch. 6 - A cart and rider have a total mass of 56.8 kg. The...Ch. 6 - Prob. 32PQCh. 6 - Prob. 33PQCh. 6 - Prob. 34PQCh. 6 - Prob. 35PQCh. 6 - Prob. 36PQCh. 6 - A racquetball has a radius of 0.0285 m. The drag...Ch. 6 - Prob. 38PQCh. 6 - Prob. 39PQCh. 6 - Prob. 40PQCh. 6 - An inflated spherical beach ball with a radius of...Ch. 6 - CASE STUDY In the train collision case study...Ch. 6 - Your sailboat has capsized! Fortunately, you are...Ch. 6 - Prob. 44PQCh. 6 - The drag coefficient C in FD=12CAv2 (Eq. 6.5)...Ch. 6 - Prob. 46PQCh. 6 - The speed of a 100-g toy car at the bottom of a...Ch. 6 - Prob. 48PQCh. 6 - Artificial gravity is produced in a space station...Ch. 6 - Escaping from a tomb raid gone wrong, Lara Croft...Ch. 6 - Harry Potter decides to take Pottery 101 as an...Ch. 6 - Harry sets some clay (m = 3.25 kg) on the edge of...Ch. 6 - A small disk of mass m is attached by a rope to a...Ch. 6 - Prob. 54PQCh. 6 - Prob. 55PQCh. 6 - Prob. 56PQCh. 6 - When a star dies, much of its mass may collapse...Ch. 6 - A satellite of mass 16.7 kg in geosynchronous...Ch. 6 - Banked curves are designed so that the radial...Ch. 6 - A block lies motionless on a horizontal tabletop....Ch. 6 - A car with a mass of 1453 kg is rolling along a...Ch. 6 - Prob. 62PQCh. 6 - Prob. 63PQCh. 6 - A box rests on a surface (Fig. P6.64). A force...Ch. 6 - A box of mass m rests on a rough, horizontal...Ch. 6 - A cylinder of mass M at rest on the end of a...Ch. 6 - Problems 67. 70. 71. and 72 are grouped. A A block...Ch. 6 - Instead of moving back and forth, a conical...Ch. 6 - Prob. 69PQCh. 6 - A Suppose you place a block of mass M on a plane...Ch. 6 - Prob. 71PQCh. 6 - Prob. 72PQCh. 6 - A car is driving around a flat, circularly curved...Ch. 6 - Prob. 74PQCh. 6 - Two children, with masses m1 = 35.0 kg and m2 =...Ch. 6 - Chris, a recent physics major, wanted to design...Ch. 6 - Prob. 77PQCh. 6 - Prob. 78PQCh. 6 - The radius of circular electron orbits in the Bohr...Ch. 6 - A particle of dust lands 45.0 mm from the center...Ch. 6 - Since March 2006, NASAs Mars Reconnaissance...
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- Consider the Earth and the Moon as a two-particle system, a. How far from the center of the Earth is the gravitational field of this two-particle system zero? b. Sketch gravitational field vectors g along the line joining the Earth and the Moon. Indicate the point at which g=0 (Do not consider positions inside either object.)arrow_forward(a) Determine the kinetic energy per unit mass that a missile must have after being fired from the surface of the earth if it is to reach an infinite distance from the earth. (b) What is the initial velocity of the missile (called the escape velocity)? Give your answers in SI units and show that the answer to part b is independent of the firing angle.arrow_forward(a) What is the escape speed on a spherical asteroid whose radius is 274 km and whose gravitational acceleration at the surface is 0.444 m/s2? (b) How far from the surface will a particle go if it leaves the asteroid's surface with a radial speed of 311 m/s? (c) With what speed will an object hit the asteroid if it is dropped from 289.4 km above the surface?arrow_forward
- (a) At what height above Earth’s surface is the energy required to lift a satellite to that height equal to the kinetic energy required for the satellite to be in orbit at that height? (b) For greater heights, which is greater, the energy for lifting or the kinetic energy for orbiting?arrow_forwardDuring the eclipse of the sun, the moon, the earth, and the sun lie in a straight line, so that the moon is between the earth and the sun. a. What is the power of the sun on the moon? b. What is the power that the Earth makes on the moon? c. How strong is the sun on Earth? , d. Compare the answers a and b. Why doesn't the sun catch the moon far from Earth? M(moon)= 7.36 x 10^22 kg M(earth) = 5.98 x 10^24 kg M(sun) = 1.99 x 10^30 kg (distance between Earth and the moon)= 3.84x10^8m (distance between the sun and the earth)= 1.496 x 10^11 marrow_forwardDuring the eclipse of the sun, the moon, the earth, and the sun lie in a straight line, so that the moon is between the earth and the sun. a. What is the power of the sun on the moon? b. What is the power that the Earth makes on the moon? c. How strong is the sun on Earth? , d. Compare the answers a and b. Why doesn't the sun catch the moon far from Earth? M(moon)= 7.36 x 10^22 kg M(earth) = 5.98 x 10^24 kg M(sun) = 1.99 x 10^30 kg (distance between Earth and the moon)= 3.84x10^8m (distance between the sun and the earth)= 1.496 x 10^11 m ReplyForwardarrow_forward
- a. At what height above the earth is the free-fall acceleration 10% of its value at the surface?arrow_forward(a) What is the speed of the roller coaster, in meters per second, at the top of the loop if the radius of curvature there is 15 m and the downward acceleration of the car is 1.9g? Note that g here is the acceleration due to gravity. (b) The beginning of this roller coaster is at the top of a high hill. If it started from rest at the top of this hill, how high, in meters, above the top of the loop is this initial starting point? You may assume there is no friction anywhere on the track. (c) If it actually starts 6.5 m higher than your answer to the previous part (yet still reaches the top of the loop with the same velocity), how much energy, in joules, did it lose to friction? Its mass is 1400 kg.arrow_forwardA) A student throws a dart horizontally toward the center of a target, X, at a speed of 20 m/s as shown. The dart flies for 0.1 s and then hits below the center, at Y. How much lower, in m, does it hit? B) A drone at too great a height drops a box. The box drops straight down the ground and hits at 100 m/s smashing the contents. Neglecting air friction, approximately, how high, in m was the drone? C) is in the picturearrow_forward
- A 2,000 kg rocket is launched 12 km straight up at a constant acceleration into the sky at which point the rocket is traveling at 750 m/s. a) How much work was done by the rocket? b) What is the magnitude of the acceleration of the rocket? c) How long did the flight take?arrow_forwardn an amusement park, group of thrill seeking students decides to ride a circular roller coaster and wants to determine the force on the coaster by the track. From researching the internet site, the lead group determines that the radius of the roller coaster is 24 m and will travel with a speed of 18 m/s at the lowest point. What is the force exerted by the track if the mass of the group and the coaster is 2000 kg? a. 2.3 x10^4N b. 1x10^4N c. 4.7x10^4N d. 3.0x10^4Narrow_forwarda) Derive the escape speed vII (sometimes called the second cosmic speed) from the surface of body of radius R and mass M, using energy conservation. Assume that the planet does not move or spin, so that the total mechanical energy E of a test particle both on the surface and at infinity is equal to zero, and the speed at infinity is zero. Use the formula come up in the last part, Compute this escape speed (in km/s) from Venus, Mars, Jupiter and Neptune. b) Evaluate vIII from the heliocentric orbit of the 4 planets (Venus, Mars, Jupiter and Neptune) mentioned above, assuming circularity of their orbits. Compare the computed speeds with the escape speeds from their surfaces (vII). Notice a big difference in the situation around the inner and the outer planets. What is it due to? A fly-by’s of small bodies near a planet can result in the small particle being accelerated to a final speed close to vII w.r.t. the planet. Draw conclusions as to which planets are able to accelerate small…arrow_forward
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