Whether the child-earth system is isolated or not.

Question

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 \((-180^{\circ},180^{\circ}]\).

Answer 1

Question

Chapter 8, Problem 8.27P

(a)

To determine

Whether the child-earth system is isolated or not.

(b)

To determine

Whether there is a non-conservative force acting within the system or not.

(c)

To determine

The total energy of the earth-child system when the child is at the top of the water slide.

(d)

To determine

The expression for the total energy of the system at the launching point.

(e)

To determine

The expression for the total energy of the system at the highest point in her projectile motion.

(f)

To determine

The speed of child at launching point.

(g)

To determine

The maximum airborne height ymax in terms of h and the launch angle θ.

(h)

To determine

Whether the answers would be same if the waterslide were not frictionless.

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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 \((-180^{\circ},180^{\circ}]\).

What are the expected readings of the ammeter and voltmeter for the circuit in the figure below? (R = 5.60 Ω, ΔV = 6.30 V) ammeter I =

simple diagram to illustrate the setup for each law- coulombs law and biot savart law

Answer 2

Question

Chapter 8, Problem 8.27P

(a)

To determine

Whether the child-earth system is isolated or not.

(b)

To determine

Whether there is a non-conservative force acting within the system or not.

(c)

To determine

The total energy of the earth-child system when the child is at the top of the water slide.

(d)

To determine

The expression for the total energy of the system at the launching point.

(e)

To determine

The expression for the total energy of the system at the highest point in her projectile motion.

(f)

To determine

The speed of child at launching point.

(g)

To determine

The maximum airborne height ymax in terms of h and the launch angle θ.

(h)

To determine

Whether the answers would be same if the waterslide were not frictionless.

Expert Solution & Answer

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Answer 3

Question

Chapter 8, Problem 8.27P

(a)

To determine

Whether the child-earth system is isolated or not.

(b)

To determine

Whether there is a non-conservative force acting within the system or not.

(c)

To determine

The total energy of the earth-child system when the child is at the top of the water slide.

(d)

To determine

The expression for the total energy of the system at the launching point.

(e)

To determine

The expression for the total energy of the system at the highest point in her projectile motion.

(f)

To determine

The speed of child at launching point.

(g)

To determine

The maximum airborne height ymax in terms of h and the launch angle θ.

(h)

To determine

Whether the answers would be same if the waterslide were not frictionless.

Expert Solution & Answer

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Answer 4

Question

Chapter 8, Problem 8.27P

(a)

To determine

Whether the child-earth system is isolated or not.

(b)

To determine

Whether there is a non-conservative force acting within the system or not.

(c)

To determine

The total energy of the earth-child system when the child is at the top of the water slide.

(d)

To determine

The expression for the total energy of the system at the launching point.

(e)

To determine

The expression for the total energy of the system at the highest point in her projectile motion.

(f)

To determine

The speed of child at launching point.

(g)

To determine

The maximum airborne height ymax in terms of h and the launch angle θ.

(h)

To determine

Whether the answers would be same if the waterslide were not frictionless.

Expert Solution & Answer

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Answer 5

Chapter 8, Problem 8.27P

(a)

To determine

Whether the child-earth system is isolated or not.

(b)

To determine

Whether there is a non-conservative force acting within the system or not.

(c)

To determine

The total energy of the earth-child system when the child is at the top of the water slide.

(d)

To determine

The expression for the total energy of the system at the launching point.

(e)

To determine

The expression for the total energy of the system at the highest point in her projectile motion.

(f)

To determine

The speed of child at launching point.

(g)

To determine

The maximum airborne height ymax in terms of h and the launch angle θ.

(h)

To determine

Whether the answers would be same if the waterslide were not frictionless.

Answer 6

Chapter 8, Problem 8.27P

(a)

To determine

Whether the child-earth system is isolated or not.

Answer 7

Chapter 8, Problem 8.27P

(a)

To determine

Whether the child-earth system is isolated or not.

Answer 8

(b)

To determine

Whether there is a non-conservative force acting within the system or not.

Answer 9

(b)

To determine

Whether there is a non-conservative force acting within the system or not.

Answer 10

(c)

To determine

The total energy of the earth-child system when the child is at the top of the water slide.

Answer 11

(c)

To determine

The total energy of the earth-child system when the child is at the top of the water slide.

Answer 12

(d)

To determine

The expression for the total energy of the system at the launching point.

Answer 13

(d)

To determine

The expression for the total energy of the system at the launching point.

Answer 14

(e)

To determine

The expression for the total energy of the system at the highest point in her projectile motion.

Answer 15

(e)

To determine

The expression for the total energy of the system at the highest point in her projectile motion.

Answer 16

(f)

To determine

The speed of child at launching point.

Answer 17

(f)

To determine

The speed of child at launching point.

Answer 18

(g)

To determine

The maximum airborne height ymax in terms of h and the launch angle θ.

Answer 19

(g)

To determine

The maximum airborne height ymax in terms of h and the launch angle θ.

Answer 20

(h)

To determine

Whether the answers would be same if the waterslide were not frictionless.

Answer 21

(h)

To determine

Whether the answers would be same if the waterslide were not frictionless.

Answer 22

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Answer 23

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Answer 24

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Answer 25

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Answer 27

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Answer 33

Ch. 8 - By what transfer mechanisms does energy enter and...Ch. 8 - Consider a block sliding over a horizontal surface...Ch. 8 - A rock of mass m is dropped to the ground from a...Ch. 8 - Three identical balls are thrown from the top of a...Ch. 8 - You are traveling along a freeway at 65 mi/h. Your...Ch. 8 - You hold a slingshot at arms length, pull the...Ch. 8 - Two children stand on a platform at the top of a...Ch. 8 - At the bottom of an air track tilted at angle , a...Ch. 8 - An athlete jumping vertically on a trampoline...Ch. 8 - Answer yes or no to each of the following...

Whether the child-earth system is isolated or not.

Solution Summary: The author explains that the child-earth system is isolated as the only force that can do work on her is her weight. There is no non-conservative force acting within the system.

Concept explainers

Whether the child-earth system is isolated or not.

Whether there is a non-conservative force acting within the system or not.

The total energy of the earth-child system when the child is at the top of the water slide.

The expression for the total energy of the system at the launching point.

The expression for the total energy of the system at the highest point in her projectile motion.

The speed of child at launching point.

The maximum airborne height ymax in terms of h and the launch angle θ.

Whether the answers would be same if the waterslide were not frictionless.

Chapter 8 Solutions