Precalculus: Mathematics for Calculus - 6th Edition
Precalculus: Mathematics for Calculus - 6th Edition
6th Edition
ISBN: 9780840068071
Author: Stewart, James, Redlin, Lothar, Watson, Saleem
Publisher: Cengage Learning
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Textbook Question
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Chapter 2.1, Problem 75E

Relativity According to the Theory of Relativity, the length L of an object is a function of its velocity v with respect to an observer. For an object whose length at rest is 10 m, the function is given by

L ( v ) = 10 1 − v 2 c 2

where c is the speed of light (300,000 km/s).

  1. (a) Find L(0.5c), L(0.75c), and L(0.9c).
  2. (b) How does the length of an object change as its velocity increases?

(a)

Expert Solution
Check Mark
To determine

The length of object when the velocity of the object is 0.5c , 0.75c and 0.9c .

Answer to Problem 75E

The length of object when the velocity of the object is 0.5c , 0.75c and 0.9c are 8.66 m , 6.61 m and 4.34 m .

Explanation of Solution

Given:

The length of the object is a function of its velocity and the length of the object at rest is 10 m .

The length of the object at velocity v is given by,

L(v)=101−v2c2

Calculation:

The length of the object at velocity v is given by,

L(v)=101−v2c2 (1)

Substitute 0.5c for v in equation (1) to find L(0.5c) ,

L(0.5c)=101−(0.5c)2c2=101−0.52=8.66 m

Substitute 0.75c for v in equation (1) to find L(0.75c) ,

L(0.75c)=101−(0.75c)2c2=101−0.752=6.61 m

Substitute 0.9c for v in equation (1) to find L(0.9c) ,

L(0.9c)=101−(0.9c)2c2=101−0.92=4.34 m

Thus, the length of object when the velocity of the object is 0.5c , 0.75c and 0.9c are 8.66 m , 6.61 m and 4.34 m .

(b)

Expert Solution
Check Mark
To determine

The variation of length of object according to the increase in velocity.

Answer to Problem 75E

The length of the object decreases as the velocity of object increases.

Explanation of Solution

Given:

The length of the object is a function of its velocity and the length of the object at rest is 10 m .

The length of the object at velocity v is given by,

L(v)=101−v2c2

Calculation:

The length of the object at velocity v is given by,

L(v)=101−v2c2

If the velocity of object increase then the term 1−v2c2 decreases due to which the length decreases.

Thus, as the velocity increases the length of the object decreases.

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Chapter 2.1, Problem 74E
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Chapter 2.1, Problem 76E

Chapter 2 Solutions

Precalculus: Mathematics for Calculus - 6th Edition

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