An Introduction to Physical Science
14th Edition
ISBN: 9781305079137
Author: James Shipman, Jerry D. Wilson, Charles A. Higgins, Omar Torres
Publisher: Cengage Learning
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Chapter 4, Problem CM
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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 4 Solutions
An Introduction to Physical Science
Ch. 4.1 - Is work a vector quantity? In other words, does it...Ch. 4.1 - What are the units of work?Ch. 4.2 - By what process is energy transferred from one...Ch. 4.2 - To find the difference in gravitational potential...Ch. 4.2 - Prob. 4.1CECh. 4.3 - Overall, can energy be created or destroyed?Ch. 4.3 - What is the difference between total energy and...Ch. 4.3 - Find the kinetic energy of the stone in the...Ch. 4.4 - What is the difference in the operations of a 2-hp...Ch. 4.4 - Electric bills from power companies charge for so...
Ch. 4.4 - A student expends 7.5 W of power in lifting a...Ch. 4.4 - Prob. 4.4CECh. 4.5 - Prob. 1PQCh. 4.5 - Prob. 2PQCh. 4.6 - What is the difference between alternative and...Ch. 4.6 - Prob. 2PQCh. 4 - KEY TERMS 1. work (4.1) 2. joule 3. foot-pound 4....Ch. 4 - Prob. BMCh. 4 - Prob. CMCh. 4 - Prob. DMCh. 4 - Prob. EMCh. 4 - Prob. FMCh. 4 - Prob. GMCh. 4 - Prob. HMCh. 4 - Prob. IMCh. 4 - Prob. JMCh. 4 - Prob. KMCh. 4 - Prob. LMCh. 4 - Prob. MMCh. 4 - KEY TERMS 1. work (4.1) 2. joule 3. foot-pound 4....Ch. 4 - KEY TERMS 1. work (4.1) 2. joule 3. foot-pound 4....Ch. 4 - Work is done on an object when it is ___. (4.1)...Ch. 4 - Which of the following is a unit of work? (4.1)...Ch. 4 - Prob. 3MCCh. 4 - Which of the following objects has the greatest...Ch. 4 - A pitcher throws a fastball. When the catcher...Ch. 4 - The reference point for gravitational potential...Ch. 4 - When the height of an object is changed, the...Ch. 4 - Mechanical energy is ___. (4.2) (a) the sum of...Ch. 4 - On which of the following does the speed of a...Ch. 4 - Power is expressed by which of the following...Ch. 4 - If motor A has twice as much horsepower as motor...Ch. 4 - Prob. 12MCCh. 4 - Which one of the following would not be classified...Ch. 4 - Prob. 14MCCh. 4 - Work is equal to the force times the ___ distance...Ch. 4 - Prob. 2FIBCh. 4 - The unit N m is given the special name of ___ ....Ch. 4 - Prob. 4FIBCh. 4 - Prob. 5FIBCh. 4 - The stopping distance of an automobile on a level...Ch. 4 - Kinetic energy is commonly referred to as the...Ch. 4 - Prob. 8FIBCh. 4 - Prob. 9FIBCh. 4 - Prob. 10FIBCh. 4 - Prob. 11FIBCh. 4 - Prob. 12FIBCh. 4 - Renewable energy sources cannot be ___ . (4.6)Ch. 4 - Gasohol is gasoline mixed with ___ . (4.6)Ch. 4 - Prob. 1SACh. 4 - Do all forces do work? Explain.Ch. 4 - What does work on a shuffleboard puck as it slides...Ch. 4 - A weight lifter holds 900 N (about 200 lb) over...Ch. 4 - For the situation in Fig. 4.4a, if the applied...Ch. 4 - Car B is traveling twice as fast as car A, but car...Ch. 4 - Prob. 7SACh. 4 - If the speed of a moving object is doubled, how...Ch. 4 - A book sits on a library shelf 1.5 m above the...Ch. 4 - (a) A car traveling at a constant speed on a level...Ch. 4 - An object is said to have a negative potential...Ch. 4 - Prob. 12SACh. 4 - A ball is dropped from a height at which it has 50...Ch. 4 - Prob. 14SACh. 4 - A simple pendulum as shown in Fig. 4.24...Ch. 4 - Two students throw identical snowballs from the...Ch. 4 - Prob. 17SACh. 4 - When you throw an object into the air, is its...Ch. 4 - Prob. 19SACh. 4 - Persons A and B do the same job, but person B...Ch. 4 - What does a greater power rating mean in terms of...Ch. 4 - What do we pay the electric company for, power or...Ch. 4 - Prob. 23SACh. 4 - Prob. 24SACh. 4 - Prob. 25SACh. 4 - On average, how much energy do you radiate each...Ch. 4 - Prob. 27SACh. 4 - Prob. 28SACh. 4 - Prob. 29SACh. 4 - Prob. 30SACh. 4 - Prob. 1VCCh. 4 - A fellow student tells you that she has both zero...Ch. 4 - Two identical stones are thrown from the top of a...Ch. 4 - A person on a trampoline can go higher with each...Ch. 4 - With which of our five senses can we detect...Ch. 4 - What are three common ways to save electricity to...Ch. 4 - A worker pushes horizontally on a large crate with...Ch. 4 - While rearranging a dorm room, a student does 400...Ch. 4 - A 5.0-kilo bag of sugar is on a counter. How much...Ch. 4 - How much work is required to lift a 6.0-kg...Ch. 4 - A man pushes a lawn mower on a level lawn with a...Ch. 4 - If the man in Exercise 5 pushes the mower with 40%...Ch. 4 - How much work does gravity do on a 0.150-kg ball...Ch. 4 - A student throws the same ball straight upward to...Ch. 4 - (a) What is the kinetic energy in joules of a...Ch. 4 - A 60-kg student traveling in a car with a constant...Ch. 4 - What is the kinetic energy of a 20-kg dog that is...Ch. 4 - Which has more kinetic energy, a 0.0020-kg bullet...Ch. 4 - Prob. 13ECh. 4 - How much farther would the force in Exercise 13...Ch. 4 - What is the potential energy of a 3.00-kg object...Ch. 4 - How much work is required to lift a 3.00-kg object...Ch. 4 - An object is dropped from a height of 12 m. At...Ch. 4 - A 1.0-kg rock is dropped from a height of 6.0 m....Ch. 4 - A sled and rider with a combined weight of 60 kg...Ch. 4 - A 30.0-kg child starting from rest slides down a...Ch. 4 - If the man in Exercise 5 pushes the lawn mower 6.0...Ch. 4 - If the man in Exercise 5 expended 60 W of power in...Ch. 4 - A student who weighs 556 N climbs a stairway...Ch. 4 - A 125-lb student races up stairs with a vertical...Ch. 4 - On a particular day, the following appliances are...Ch. 4 - Prob. 26E
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