Pearson eText Conceptual Integrated Science -- Instant Access (Pearson+)
3rd Edition
ISBN: 9780135626573
Author: Paul Hewitt, Suzanne Lyons
Publisher: PEARSON+
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Textbook Question
Chapter 2, Problem 63TE
Which of Aristotle’s ideas did Galileo discredit with his inclined plane experiments?
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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 \((-180^{\circ},180^{\circ}]\).
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Chapter 2 Solutions
Pearson eText Conceptual Integrated Science -- Instant Access (Pearson+)
Ch. 2 - What were Aristotles two main classifications of...Ch. 2 - Did Aristotle believe that forces are necessary to...Ch. 2 - What two main ideas of Aristotle did Galileo...Ch. 2 - Which dominated Galileos way of extending...Ch. 2 - What is the name of the property of objects to...Ch. 2 - Which depends on gravity: weight or mass?Ch. 2 - Where would your weight be greater: on Earth or on...Ch. 2 - What are the units of measurement for weight and...Ch. 2 - One kg weighs 10 N on Earth. Would it weigh more...Ch. 2 - Which has the greater density: 1 kg of water or 10...
Ch. 2 - What is the net force on a box that is being...Ch. 2 - What two quantities are necessary to determine a...Ch. 2 - What is the name given to a force that occurs in a...Ch. 2 - How much rope tension holds a 20-N bag of apples...Ch. 2 - What is the meaning of F=0?Ch. 2 - What test tells us whether or not a moving object...Ch. 2 - One bowling ball sits at rest and another rolls at...Ch. 2 - Why is the support force on an object often called...Ch. 2 - When you weigh yourself, how does the support...Ch. 2 - How does the direction of a friction force compare...Ch. 2 - If you push on a heavy crate to the right and it...Ch. 2 - Suppose you push on a heavy crate, but not hard...Ch. 2 - What equation shows the relationship among speed,...Ch. 2 - Why do we say that velocity is a vector and speed...Ch. 2 - Does the speedometer on a vehicle show the average...Ch. 2 - How can you be at rest and also moving at 100,000...Ch. 2 - What equation shows the relationship among...Ch. 2 - What is the acceleration of an object in free fall...Ch. 2 - Why does the unit of time appear twice in the...Ch. 2 - When you toss a ball upward, by how much does its...Ch. 2 - Joints are places where bones meet. Many of them,...Ch. 2 - In what way does friction affect an earthquake?Ch. 2 - When during a standing jump is your speed zero?Ch. 2 - What is the record-breaking height for a standing...Ch. 2 - What are some anatomical features that affect an...Ch. 2 - Show that the average speed of a rabbit that runs...Ch. 2 - Calculate your average walking speed when you step...Ch. 2 - Show that the acceleration of a hamster is 5m/s2...Ch. 2 - Show that the acceleration of a car that can go...Ch. 2 - Show that the acceleration of a rock that reaches...Ch. 2 - Show that Careless Cary who slips from the rung of...Ch. 2 - Show that a basketball player who jumps vertically...Ch. 2 - The weights of Burl, Paul, and the scaffold...Ch. 2 - Rank the net forces on the block from greatest to...Ch. 2 - Different materials, A, B, C, and D, rest on a...Ch. 2 - Three pucks, A, B, and C, are sliding across ice...Ch. 2 - Find the strength of the net force on a crate that...Ch. 2 - Lucy Lightfoot stands with one foot on one...Ch. 2 - A ball is thrown straight up with an initial speed...Ch. 2 - The sketch shows a painters scaffold in mechanical...Ch. 2 - A different scaffold that weighs 400 N supports...Ch. 2 - A vehicle changes its velocity from 90km/h to a...Ch. 2 - Extend Table 2.2 which gives values from 0 to 5 s...Ch. 2 - An airplane starting from rest on a runway...Ch. 2 - Knowledge can be gained by philosophical logic and...Ch. 2 - Which of Aristotles ideas did Galileo discredit...Ch. 2 - Your friend says that a ball rolling down a flat...Ch. 2 - A ball at the end of a string makes a pendulum. If...Ch. 2 - Which has more mass, a 2-kg fluffy pillow or a...Ch. 2 - Gravitational force on the Moon is merely 1/6 that...Ch. 2 - A monkey hangs stationary at the end of a vertical...Ch. 2 - Suppose the monkey weighs 100 N and the vine...Ch. 2 - Nellie hangs suspended at rest from the ends of...Ch. 2 - Nellie Newton stands at rest on a bathroom scale....Ch. 2 - Can a basketball player halfway through a jump in...Ch. 2 - Little Hudson as shown in the opening photo of...Ch. 2 - An empty 50-N jug rests on a table. What is the...Ch. 2 - A book that weighs 15 N is at rest on a table. How...Ch. 2 - The falling speedometer of Figure 2.24 shows...Ch. 2 - In Figure 2.13, we see Marie pushing horizontally...Ch. 2 - Suppose that a free-falling object were somehow...Ch. 2 - For a free-falling object dropped from rest, what...Ch. 2 - What is the acceleration of a car that moves at a...Ch. 2 - Correct your friend who says, Japans bullet trains...Ch. 2 - An airplane flies horizontally at a constant...Ch. 2 - You toss a coin vertically upward in the air....Ch. 2 - Does a person on a diet more accurately lose mass...Ch. 2 - Gracie says acceleration is how fast you go. Alex...Ch. 2 - Your friend says that a ball in free fall...Ch. 2 - Harry the painter swings year after year from his...Ch. 2 - When a ballplayer throws a ball straight up, by...Ch. 2 - Someone standing on the edge of a cliff as in...Ch. 2 - For a freely falling object dropped from rest,...Ch. 2 - Two balls, A and B, are released simultaneously...Ch. 2 - According to Galileo, inertia is a a force like...Ch. 2 - An object with a very small mass must also have a...Ch. 2 - The equilibrium rule F=0 applies to a objects or...Ch. 2 - A man weighing 800 N stands at rest on two...Ch. 2 - If an object moves along a straight-line path at...Ch. 2 - What is the net force on a box of chocolates when...Ch. 2 - Neglecting air resistance, when you toss a rock...Ch. 2 - During each second of free fall, the speed of an...Ch. 2 - A freely falling object has a speed of 40 m/s at...Ch. 2 - The vertical height attained by a basketball...
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