Verify the expression m g [ ( r + b ) cos θ + r θ sin θ ] for the potential energy of the cube balanced on a cylinder.

Question

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Answer 1

Question

Chapter 4, Problem 4.33P

(a)

To determine

Verify the expression mg[(r+b)cosθ+rθsinθ] for the potential energy of the cube balanced on a cylinder.

(b)

To determine

Sketch the plot of U(θ) for b=0.9r and b=1.1r.

(c)

To determine

Using the plot in the part (b), verify the stability of the equilibrium at θ=0 in the example 4.7, and whether any other equilibrium point exist or not.

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Answer 2

Question

Chapter 4, Problem 4.33P

(a)

To determine

Verify the expression mg[(r+b)cosθ+rθsinθ] for the potential energy of the cube balanced on a cylinder.

(b)

To determine

Sketch the plot of U(θ) for b=0.9r and b=1.1r.

(c)

To determine

Using the plot in the part (b), verify the stability of the equilibrium at θ=0 in the example 4.7, and whether any other equilibrium point exist or not.

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Answer 3

Question

Chapter 4, Problem 4.33P

(a)

To determine

Verify the expression mg[(r+b)cosθ+rθsinθ] for the potential energy of the cube balanced on a cylinder.

(b)

To determine

Sketch the plot of U(θ) for b=0.9r and b=1.1r.

(c)

To determine

Using the plot in the part (b), verify the stability of the equilibrium at θ=0 in the example 4.7, and whether any other equilibrium point exist or not.

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Answer 4

Question

Chapter 4, Problem 4.33P

(a)

To determine

Verify the expression mg[(r+b)cosθ+rθsinθ] for the potential energy of the cube balanced on a cylinder.

(b)

To determine

Sketch the plot of U(θ) for b=0.9r and b=1.1r.

(c)

To determine

Using the plot in the part (b), verify the stability of the equilibrium at θ=0 in the example 4.7, and whether any other equilibrium point exist or not.

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Answer 5

Chapter 4, Problem 4.33P

(a)

To determine

Verify the expression mg[(r+b)cosθ+rθsinθ] for the potential energy of the cube balanced on a cylinder.

(b)

To determine

Sketch the plot of U(θ) for b=0.9r and b=1.1r.

(c)

To determine

Using the plot in the part (b), verify the stability of the equilibrium at θ=0 in the example 4.7, and whether any other equilibrium point exist or not.

Answer 6

Chapter 4, Problem 4.33P

(a)

To determine

Verify the expression mg[(r+b)cosθ+rθsinθ] for the potential energy of the cube balanced on a cylinder.

Answer 7

Chapter 4, Problem 4.33P

(a)

To determine

Verify the expression mg[(r+b)cosθ+rθsinθ] for the potential energy of the cube balanced on a cylinder.

Answer 8

(b)

To determine

Sketch the plot of U(θ) for b=0.9r and b=1.1r.

Answer 9

(b)

To determine

Sketch the plot of U(θ) for b=0.9r and b=1.1r.

Answer 10

(c)

To determine

Using the plot in the part (b), verify the stability of the equilibrium at θ=0 in the example 4.7, and whether any other equilibrium point exist or not.

Answer 11

(c)

To determine

Using the plot in the part (b), verify the stability of the equilibrium at θ=0 in the example 4.7, and whether any other equilibrium point exist or not.

Answer 12

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Answer 13

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Answer 14

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Answer 15

Ch. 4 - Prob. 4.1P Ch. 4 - Prob. 4.2P Ch. 4 - Prob. 4.3P Ch. 4 - Prob. 4.4P Ch. 4 - Prob. 4.5P Ch. 4 - Prob. 4.6P Ch. 4 - Prob. 4.7P Ch. 4 - Prob. 4.8P Ch. 4 - Prob. 4.9P Ch. 4 - Prob. 4.10P

Verify the expression m g [ ( r + b ) cos θ + r θ sin θ ] for the potential energy of the cube balanced on a cylinder.

Verify the expression mg[(r+b)cosθ+rθsinθ] for the potential energy of the cube balanced on a cylinder.

Sketch the plot of U(θ) for b=0.9r and b=1.1r.

Using the plot in the part (b), verify the stability of the equilibrium at θ=0 in the example 4.7, and whether any other equilibrium point exist or not.

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Chapter 4 Solutions