Physics of Everyday Phenomena
9th Edition
ISBN: 9781259894008
Author: W. Thomas Griffith, Juliet Brosing Professor
Publisher: McGraw-Hill Education
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Chapter 4, Problem 5CQ
Did Galileo develop a more complete theory of motion than that of Newton? Explain.
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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
Physics of Everyday Phenomena
Ch. 4 - Did Galileos work on motion precede in time that...Ch. 4 - Why did Aristotle believe that heavier objects...Ch. 4 - Aristotle believed that a force was necessary to...Ch. 4 - How did Aristotle explain the continued motion of...Ch. 4 - Did Galileo develop a more complete theory of...Ch. 4 - Two equal forces act on two different objects, one...Ch. 4 - A 3-kg block is observed to accelerate at a rate...Ch. 4 - Two equal-magnitude horizontal forces act on a box...Ch. 4 - Is it possible for the final temperature of the...Ch. 4 - Suppose that a bullet is fired from a rifle in...
Ch. 4 - Two equal forces act on an object in the...Ch. 4 - An object moving horizontally across a table is...Ch. 4 - A car goes around a curve traveling at constant...Ch. 4 - Is Newtons first law of motion explained by the...Ch. 4 - Is the mass of an object the same thing as its...Ch. 4 - The gravitational force acting on a lead ball is...Ch. 4 - The acceleration due to gravity on the moon is...Ch. 4 - Is mass a force? Explain.Ch. 4 - Two identical cans, one filled with lead shot and...Ch. 4 - A boy sits at rest on the floor. What two vertical...Ch. 4 - The engine of a car is part of the car and cannot...Ch. 4 - It is difficult to stop a car on an icy road...Ch. 4 - A ball hangs from a string attached to the...Ch. 4 - Would the tablecloth trick (see everyday...Ch. 4 - When a magician performs the tablecloth trick (see...Ch. 4 - A sprinter accelerates at the beginning of a...Ch. 4 - A mule is attempting to move a cart loaded with...Ch. 4 - The upward normal force exerted by the floor on a...Ch. 4 - A toy battery-powered tractor pushes a book across...Ch. 4 - If you get into an elevator on the top floor of a...Ch. 4 - If the elevator cable breaks and you find yourself...Ch. 4 - Two masses, m1 and m2, connected by a string, are...Ch. 4 - Two blocks with the same mass are connected by a...Ch. 4 - Suppose that a skydiver wears a specially...Ch. 4 - Prob. 35CQCh. 4 - Prob. 36CQCh. 4 - A single force of 42 N acts upon a 6-kg block....Ch. 4 - A heavy ball with a mass of 4.5 kg is observed to...Ch. 4 - A net force of 32 N acting on a wooden block...Ch. 4 - A 4.0-kg block being pulled across a table by a...Ch. 4 - A pulled tablecloth exerts a frictional force of...Ch. 4 - A 5-kg block being pushed across a table by a...Ch. 4 - Two forces, one of 70 N and the other of 30 N, act...Ch. 4 - A 5-kg block is acted upon by three horizontal...Ch. 4 - A 9-kg sled sliding freely on an icy surface...Ch. 4 - What is the weight of a 45-kg mass?Ch. 4 - What is the mass of a 735-N weight?Ch. 4 - Patricia has a weight of 125 lb. a. What is her...Ch. 4 - One of the authors of this text has a weight of...Ch. 4 - Who has the larger mass, a woman weighing 160 lb...Ch. 4 - At a given instant in time, a 6-kg rock that has...Ch. 4 - At a given instant in time, a 12-kg rock is...Ch. 4 - A 0.8-kg book rests on a table. A downward force...Ch. 4 - An upward force of 32.6 N is applied via a string...Ch. 4 - A 75-kg woman in an elevator is accelerating...Ch. 4 - A constant horizontal force of 28 N is exerted by...Ch. 4 - A rope exerts a constant horizontal force of 350 N...Ch. 4 - A dish with a mass of 0.3 kg has a force of...Ch. 4 - A 60-kg crate is lowered from a loading dock to...Ch. 4 - Two blocks tied together by a horizontal string...Ch. 4 - A 85-kg man is in an elevator that is accelerating...Ch. 4 - A skydiver has a weight of 850 N. Suppose that the...
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