(a) The mathematical proof of the statement stating that "If c n is the centre of mass of the first n identical books of mass m and unit length placed one above the other in a stack, measured along x-axis and if (n+1)st book is placed with its right edge at c n , then its centre of mass is located at c n +1/2."

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Answer 1

Question

Chapter 11.3, Problem 88E

To determine

(a)

The mathematical proof of the statement stating that "If c_n is the centre of mass of the first n identical books of mass m and unit length placed one above the other in a stack, measured along x-axis and if (n+1)st book is placed with its right edge at c_n, then its centre of mass is located at c_n +1/2."

To determine

(b)

The mathematical proof of the statement stating that "If c_n is the centre of mass of the first n identical books considered as a single object of mass mn placed one above the other in a stack, and if (n+1)st book considered as a second object is placed with its right edge at c_n, then $c_{n + 1} = c_{n} + \frac{1}{2 (n + 1)}$ ."

To determine

(c)

The mathematical proof of $\lim_{n \to \infty} c_{n} = \infty$ which implies that the stack of books can be extended as far as desired without tipping over.

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Answer 2

Question

Chapter 11.3, Problem 88E

To determine

(a)

The mathematical proof of the statement stating that "If c_n is the centre of mass of the first n identical books of mass m and unit length placed one above the other in a stack, measured along x-axis and if (n+1)st book is placed with its right edge at c_n, then its centre of mass is located at c_n +1/2."

To determine

(b)

The mathematical proof of the statement stating that "If c_n is the centre of mass of the first n identical books considered as a single object of mass mn placed one above the other in a stack, and if (n+1)st book considered as a second object is placed with its right edge at c_n, then $c_{n + 1} = c_{n} + \frac{1}{2 (n + 1)}$ ."

To determine

(c)

The mathematical proof of $\lim_{n \to \infty} c_{n} = \infty$ which implies that the stack of books can be extended as far as desired without tipping over.

Expert Solution & Answer

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See solution

Answer 3

Question

Chapter 11.3, Problem 88E

To determine

(a)

The mathematical proof of the statement stating that "If c_n is the centre of mass of the first n identical books of mass m and unit length placed one above the other in a stack, measured along x-axis and if (n+1)st book is placed with its right edge at c_n, then its centre of mass is located at c_n +1/2."

To determine

(b)

The mathematical proof of the statement stating that "If c_n is the centre of mass of the first n identical books considered as a single object of mass mn placed one above the other in a stack, and if (n+1)st book considered as a second object is placed with its right edge at c_n, then $c_{n + 1} = c_{n} + \frac{1}{2 (n + 1)}$ ."

To determine

(c)

The mathematical proof of $\lim_{n \to \infty} c_{n} = \infty$ which implies that the stack of books can be extended as far as desired without tipping over.

Expert Solution & Answer

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Check out a sample textbook solution

See solution

Answer 4

Question

Chapter 11.3, Problem 88E

To determine

(a)

The mathematical proof of the statement stating that "If c_n is the centre of mass of the first n identical books of mass m and unit length placed one above the other in a stack, measured along x-axis and if (n+1)st book is placed with its right edge at c_n, then its centre of mass is located at c_n +1/2."

To determine

(b)

The mathematical proof of the statement stating that "If c_n is the centre of mass of the first n identical books considered as a single object of mass mn placed one above the other in a stack, and if (n+1)st book considered as a second object is placed with its right edge at c_n, then $c_{n + 1} = c_{n} + \frac{1}{2 (n + 1)}$ ."

To determine

(c)

The mathematical proof of $\lim_{n \to \infty} c_{n} = \infty$ which implies that the stack of books can be extended as far as desired without tipping over.

Expert Solution & Answer

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Answer 5

Chapter 11.3, Problem 88E

To determine

(a)

The mathematical proof of the statement stating that "If c_n is the centre of mass of the first n identical books of mass m and unit length placed one above the other in a stack, measured along x-axis and if (n+1)st book is placed with its right edge at c_n, then its centre of mass is located at c_n +1/2."

To determine

(b)

The mathematical proof of the statement stating that "If c_n is the centre of mass of the first n identical books considered as a single object of mass mn placed one above the other in a stack, and if (n+1)st book considered as a second object is placed with its right edge at c_n, then $c_{n + 1} = c_{n} + \frac{1}{2 (n + 1)}$ ."

To determine

(c)

The mathematical proof of $\lim_{n \to \infty} c_{n} = \infty$ which implies that the stack of books can be extended as far as desired without tipping over.

Answer 6

Chapter 11.3, Problem 88E

To determine

(a)

The mathematical proof of the statement stating that "If c_n is the centre of mass of the first n identical books of mass m and unit length placed one above the other in a stack, measured along x-axis and if (n+1)st book is placed with its right edge at c_n, then its centre of mass is located at c_n +1/2."

Answer 7

Chapter 11.3, Problem 88E

To determine

(a)

The mathematical proof of the statement stating that "If c_n is the centre of mass of the first n identical books of mass m and unit length placed one above the other in a stack, measured along x-axis and if (n+1)st book is placed with its right edge at c_n, then its centre of mass is located at c_n +1/2."

Answer 8

To determine

(b)

The mathematical proof of the statement stating that "If c_n is the centre of mass of the first n identical books considered as a single object of mass mn placed one above the other in a stack, and if (n+1)st book considered as a second object is placed with its right edge at c_n, then $c_{n + 1} = c_{n} + \frac{1}{2 (n + 1)}$ ."

Answer 9

To determine

(b)

The mathematical proof of the statement stating that "If c_n is the centre of mass of the first n identical books considered as a single object of mass mn placed one above the other in a stack, and if (n+1)st book considered as a second object is placed with its right edge at c_n, then $c_{n + 1} = c_{n} + \frac{1}{2 (n + 1)}$ ."

Answer 10

To determine

(c)

The mathematical proof of $\lim_{n \to \infty} c_{n} = \infty$ which implies that the stack of books can be extended as far as desired without tipping over.

Answer 11

To determine

(c)

The mathematical proof of $\lim_{n \to \infty} c_{n} = \infty$ which implies that the stack of books can be extended as far as desired without tipping over.

Answer 12

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Answer 13

Expert Solution & Answer

Answer 14

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Answer 15

Ch. 11.1 - Prob. 1PQ Ch. 11.1 - Prob. 2PQ Ch. 11.1 - Prob. 3PQ Ch. 11.1 - Prob. 4PQ Ch. 11.1 - Prob. 5PQ Ch. 11.1 - Prob. 1E Ch. 11.1 - Prob. 2E Ch. 11.1 - Prob. 3E Ch. 11.1 - Prob. 4E Ch. 11.1 - Prob. 5E

Solution Summary: The author explains the mathematical proof of the statement stating that if c n is the centre of mass of a book, it is located at the right edge.

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(c)

The mathematical proof of $\lim_{n \to \infty} c_{n} = \infty$ which implies that the stack of books can be extended as far as desired without tipping over.

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Chapter 11 Solutions

Solution Summary: The author explains the mathematical proof of the statement stating that if c n is the centre of mass of a book, it is located at the right edge.

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(c) The mathematical proof of limn→∞cn=∞ which implies that the stack of books can be extended as far as desired without tipping over.

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Chapter 11 Solutions

(c)

The mathematical proof of $\lim_{n \to \infty} c_{n} = \infty$ which implies that the stack of books can be extended as far as desired without tipping over.