To explain in physical terms why the bead cannot have an equilibrium position with ϕ > π 2 Concept Introduction: The supercritical pitchforkis also called forward bifurcation. It closely shows a continuous or second-order phase transition. In statistical mechanics, the subcritical bifurcation is sometimes called inverted or backward bifurcation, and it is related to discontinuous or first order phase transition. A bead of mass m slides along a wire hoop of radius r. The hoop is constrained to move at a constant angular velocity ω about its vertical axis.

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Answer 1

Question

Chapter 3.5, Problem 1E

Interpretation Introduction

Interpretation:

To explain in physical terms why the bead cannot have an equilibrium position with ϕ>π2

Concept Introduction:

The supercritical pitchforkis also called forward bifurcation. It closely shows a continuous or second-order phase transition.

In statistical mechanics, the subcritical bifurcation is sometimes called inverted or backward bifurcation, and it is related to discontinuous or first order phase transition.

A bead of mass m slides along a wire hoop of radius r. The hoop is constrained to move at a constant angular velocity ω about its vertical axis.

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Answer 2

Question

Chapter 3.5, Problem 1E

Interpretation Introduction

Interpretation:

To explain in physical terms why the bead cannot have an equilibrium position with ϕ>π2

Concept Introduction:

The supercritical pitchforkis also called forward bifurcation. It closely shows a continuous or second-order phase transition.

In statistical mechanics, the subcritical bifurcation is sometimes called inverted or backward bifurcation, and it is related to discontinuous or first order phase transition.

A bead of mass m slides along a wire hoop of radius r. The hoop is constrained to move at a constant angular velocity ω about its vertical axis.

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Answer 3

Question

Chapter 3.5, Problem 1E

Interpretation Introduction

Interpretation:

To explain in physical terms why the bead cannot have an equilibrium position with ϕ>π2

Concept Introduction:

The supercritical pitchforkis also called forward bifurcation. It closely shows a continuous or second-order phase transition.

In statistical mechanics, the subcritical bifurcation is sometimes called inverted or backward bifurcation, and it is related to discontinuous or first order phase transition.

A bead of mass m slides along a wire hoop of radius r. The hoop is constrained to move at a constant angular velocity ω about its vertical axis.

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Answer 4

Question

Chapter 3.5, Problem 1E

Interpretation Introduction

Interpretation:

To explain in physical terms why the bead cannot have an equilibrium position with ϕ>π2

Concept Introduction:

The supercritical pitchforkis also called forward bifurcation. It closely shows a continuous or second-order phase transition.

In statistical mechanics, the subcritical bifurcation is sometimes called inverted or backward bifurcation, and it is related to discontinuous or first order phase transition.

A bead of mass m slides along a wire hoop of radius r. The hoop is constrained to move at a constant angular velocity ω about its vertical axis.

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Answer 5

Chapter 3.5, Problem 1E

Interpretation Introduction

Interpretation:

To explain in physical terms why the bead cannot have an equilibrium position with ϕ>π2

Concept Introduction:

The supercritical pitchforkis also called forward bifurcation. It closely shows a continuous or second-order phase transition.

In statistical mechanics, the subcritical bifurcation is sometimes called inverted or backward bifurcation, and it is related to discontinuous or first order phase transition.

A bead of mass m slides along a wire hoop of radius r. The hoop is constrained to move at a constant angular velocity ω about its vertical axis.

Answer 6

Chapter 3.5, Problem 1E

Interpretation Introduction

Interpretation:

To explain in physical terms why the bead cannot have an equilibrium position with ϕ>π2

Concept Introduction:

The supercritical pitchforkis also called forward bifurcation. It closely shows a continuous or second-order phase transition.

In statistical mechanics, the subcritical bifurcation is sometimes called inverted or backward bifurcation, and it is related to discontinuous or first order phase transition.

A bead of mass m slides along a wire hoop of radius r. The hoop is constrained to move at a constant angular velocity ω about its vertical axis.

Answer 7

Chapter 3.5, Problem 1E

Interpretation Introduction

Interpretation:

To explain in physical terms why the bead cannot have an equilibrium position with ϕ>π2

Concept Introduction:

The supercritical pitchforkis also called forward bifurcation. It closely shows a continuous or second-order phase transition.

In statistical mechanics, the subcritical bifurcation is sometimes called inverted or backward bifurcation, and it is related to discontinuous or first order phase transition.

A bead of mass m slides along a wire hoop of radius r. The hoop is constrained to move at a constant angular velocity ω about its vertical axis.

Answer 8

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Answer 9

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Answer 10

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Answer 11

Ch. 3.1 - Prob. 1E Ch. 3.1 - Prob. 2E Ch. 3.1 - Prob. 3E Ch. 3.1 - Prob. 4E Ch. 3.1 - Prob. 5E Ch. 3.2 - Prob. 1E Ch. 3.2 - Prob. 2E Ch. 3.2 - Prob. 3E Ch. 3.2 - Prob. 4E Ch. 3.2 - Prob. 5E

Solution Summary: The author explains the supercritical pitchforkis, which closely shows a second-order phase transition, and the subcritical bifurcation.

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