College Physics
11th Edition
ISBN: 9781305952300
Author: Raymond A. Serway, Chris Vuille
Publisher: Cengage Learning
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Chapter 7, Problem 10CQ
A car of mass m follows a truck of mass 2m around a circular turn. Both vehicles move at speed v. (a) What is the ratio of the truck’s net
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A planar double pendulum consists of two point masses \[m_1 = 1.00~\mathrm{kg}, \qquad m_2 = 1.00~\mathrm{kg}\]connected by massless, rigid rods of lengths \[L_1 = 1.00~\mathrm{m}, \qquad L_2 = 1.20~\mathrm{m}.\]The upper rod is hinged to a fixed pivot; gravity acts vertically downward with\[g = 9.81~\mathrm{m\,s^{-2}}.\]Define the generalized coordinates \(\theta_1,\theta_2\) as the angles each rod makes with thedownward vertical (positive anticlockwise, measured in radians unless stated otherwise).At \(t=0\) the system is released from rest with \[\theta_1(0)=120^{\circ}, \qquad\theta_2(0)=-10^{\circ}, \qquad\dot{\theta}_1(0)=\dot{\theta}_2(0)=0 .\]Using the exact nonlinear equations of motion (no small-angle or planar-pendulumapproximations) and assuming the rods never stretch or slip, determine the angle\(\theta_2\) at the instant\[t = 10.0~\mathrm{s}.\]Give the result in degrees, in the interval \((-180^{\circ},180^{\circ}]\).
Chapter 7 Solutions
College Physics
Ch. 7.1 - A rigid body is rotating counterclockwise about a...Ch. 7.1 - Suppose the change in angular position for each of...Ch. 7.2 - Consider again the pairs of angular positions for...Ch. 7.3 - Andrea and Chuck are riding on a merry-go-round....Ch. 7.3 - When the merry-go-round of Quick Quiz 7.4 is...Ch. 7.3 - A racetrack is constructed such that two arcs of...Ch. 7.3 - An object moves in a circular path with constant...Ch. 7.5 - A ball is falling toward the ground. Which of the...Ch. 7.5 - A planet has two moons with identical mass. Moon 1...Ch. 7.5 - Suppose an asteroid has a semimajor axis of 4 AU....
Ch. 7 - A disk rotates about an axis through its center....Ch. 7 - Suppose an alien civilization has a space station...Ch. 7 - If a cars wheels are replaced with wheels of...Ch. 7 - Objects moving along a circular path have a...Ch. 7 - A pendulum consists of a small object called a bob...Ch. 7 - Because of Earths rotation about its axis, you...Ch. 7 - It has been suggested that rotating cylinders...Ch. 7 - Describe the path of a moving object in the event...Ch. 7 - A pail of water can be whirled in a vertical...Ch. 7 - A car of mass m follows a truck of mass 2m around...Ch. 7 - Is it possible for a car to move in a circular...Ch. 7 - A child is practicing for a BMX race. His speed...Ch. 7 - An object executes circular motion with constant...Ch. 7 - Convert (a) 47.0 to radians, (b) 12.0 rad to...Ch. 7 - A bicycle tire is spinning clockwise at 2.50...Ch. 7 - The tires on a new compact car have a diameter of...Ch. 7 - A potters wheel moves uniformly from rest to an...Ch. 7 - A dentists drill starts from rest. After 3.20 s of...Ch. 7 - A centrifuge in a medical laboratory rotates at an...Ch. 7 - A bicyclist starting at rest produces a constant...Ch. 7 - A bicycle is turned upside down while its owner...Ch. 7 - The diameters of the main rotor and tail rotor of...Ch. 7 - The tub of a washer goes into its spin-dry cycle,...Ch. 7 - A car initially traveling at 29.0 m/s undergoes a...Ch. 7 - A 45.0-cm diameter disk rotates with a constant...Ch. 7 - A rotating wheel requires 3.00 s to rotate 37.0...Ch. 7 - An electric motor rotating a workshop grinding...Ch. 7 - A car initially traveling eastward turns north by...Ch. 7 - It has been suggested that rotating cylinders...Ch. 7 - (a) What is the tangential acceleration of a bug...Ch. 7 - An adventurous archeologist (m = 85.0 kg) tries to...Ch. 7 - One end of a cord is fixed and a small 0.500-kg...Ch. 7 - Human centrifuges are used to train military...Ch. 7 - A 55.0-kg ice skater is moving at 4.00 m/s when...Ch. 7 - A 40.0-kg child swings in a swing supported by two...Ch. 7 - A certain light truck can go around a flat curve...Ch. 7 - A sample of blood is placed in a centrifuge of...Ch. 7 - A 50.0-kg child stands at the rim of a...Ch. 7 - A space habitat for a long space voyage consists...Ch. 7 - An air puck of mass m1 = 0.25 kg is tied to a...Ch. 7 - A snowboarder drops from rest into a halfpipe of...Ch. 7 - A woman places her briefcase on the backseat of...Ch. 7 - A pail of water is rotated in a vertical circle of...Ch. 7 - A 40.0-kg child takes a ride on a Ferris wheel...Ch. 7 - Prob. 32PCh. 7 - (a) Find the magnitude of the gravitational force...Ch. 7 - The International Space Station has a mass of 4.19...Ch. 7 - A coordinate system (in meters) is constructed on...Ch. 7 - Prob. 36PCh. 7 - Objects with masses of 200. kg and 500. kg are...Ch. 7 - Use the data of Table 7.3 to find the point...Ch. 7 - Prob. 39PCh. 7 - Two objects attract each other with a...Ch. 7 - Prob. 41PCh. 7 - Prob. 42PCh. 7 - A satellite of Mars, called Phoebus, has an...Ch. 7 - Prob. 44PCh. 7 - A comet has a period of 76.3 years and moves in an...Ch. 7 - Additional Problems A synchronous satellite. which...Ch. 7 - (a) One of the moons of Jupiter, named Io, has an...Ch. 7 - Neutron stars are extremely dense objects that are...Ch. 7 - One method of pitching a softball is called the...Ch. 7 - A digital audio compact disc (CD) carries data...Ch. 7 - An athlete swings a 5.00-kg ball horizontally on...Ch. 7 - The dung beetle is known as one of the strongest...Ch. 7 - Prob. 53APCh. 7 - A 0.400-kg pendulum bob passes through the lowest...Ch. 7 - A car moves at speed v across a bridge made in the...Ch. 7 - Keratinocytes are the most common cells in the...Ch. 7 - Because of Earths rotation about its axis, a point...Ch. 7 - A roller coaster travels in a circular path, (a)...Ch. 7 - In Robert Heinleins The Moon Is a Harsh Mistress,...Ch. 7 - A model airplane of mass 0.750 kg flies with a...Ch. 7 - In a home laundry dryer, a cylindrical tub...Ch. 7 - Casting of molten metal is important in many...Ch. 7 - A skier starts at rest at the top of a large...Ch. 7 - A stuntman whose mass is 70 kg swings from the end...Ch. 7 - Suppose a 1 800-kg car passes over a bump in a...Ch. 7 - The pilot of an airplane executes a constant-speed...Ch. 7 - Prob. 67APCh. 7 - A coin rests 15.0 cm from the center of a...Ch. 7 - A 4.0-kg object is attached to a vertical rod by...Ch. 7 - A 0.275-kg object is swung in a vertical circular...Ch. 7 - (a) A luggage carousel at an airport has the form...Ch. 7 - The maximum lift force on a bat is proportional to...Ch. 7 - In a popular amusement park ride, a rotating...Ch. 7 - A massless spring of constant k = 78.4 N/m is...Ch. 7 - A 0.50-kg ball that is tied to the end of a 1.5-m...
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