(a)
To draw: The graph of the relativistic kinetic energy and the classical kinetic energy, both as a function of speed for an object.
(a)
Answer to Problem 54P
The graph of the classical kinetic energy and the speed is given in figure I and the graph of the relativistic kinetic energy and the speed is given in figure II.
Explanation of Solution
Consider the mass of the object is
The formula for the classical kinetic energy is,
Here,
Substitute
The table for the classical kinetic energy with respective values of the speed, by substitute the values of
|
|
0.000 | 0.000 |
0.100 | 0.045E16 |
0.200 | 0.180E16 |
0.300 | 0.405E16 |
0.400 | 0.720E16 |
0.500 | 1.13E16 |
0.600 | 1.62E16 |
0.700 | 2.21E16 |
0.800 | 2.88E16 |
0.900 | 3.65E16 |
0.990 | 4.41E16 |
Table 1
The graph for classical kinetic energy as a function of speed for an object is given below.
Figure I
The formula for the relativistic kinetic energy is,
Substitute
The table for the relativistic kinetic energy with respective values of the speed, by substitute the values of
|
|
0.000 | 0.000 |
0.100 | 0.0453E16 |
0.200 | 0.186E16 |
0.300 | 0.435E16 |
0.400 | 0.820E16 |
0.500 | 1.39E16 |
0.600 | 2.25E16 |
0.700 | 3.60E16 |
0.800 | 6.00E16 |
0.900 | 11.6E16 |
0.990 | 54.8E16 |
Table 2
The graph for relativistic kinetic energy as a function of speed for an object is given below.
Figure II
Conclusion:
Therefore, the graph of the classical kinetic energy and the speed is given in figure I and the graph of the relativistic kinetic energy and the speed is given in figure II.
(b)
The speed at which the classical kinetic energy underestimate the experimental value by
(b)
Answer to Problem 54P
The speed at which the classical kinetic energy underestimate the experimental value by
Explanation of Solution
As the classical kinetic energy is underestimate the experimental value by
Substitute
Conclusion:
Therefore, the speed at which the classical kinetic energy underestimate the experimental value by
(c)
The speed at which the classical kinetic energy underestimate the experimental value by
(c)
Answer to Problem 54P
The speed at which the classical kinetic energy underestimate the experimental value by
Explanation of Solution
As the classical kinetic energy is underestimate the experimental value by
Substitute
Conclusion:
Therefore, the speed at which the classical kinetic energy underestimate the experimental value by
(d)
The speed at which the classical kinetic energy underestimate the experimental value by
(d)
Answer to Problem 54P
The speed at which the classical kinetic energy underestimate the experimental value by
Explanation of Solution
As the classical kinetic energy is underestimate the experimental value by
Substitute
Conclusion:
Therefore, the speed at which the classical kinetic energy underestimate the experimental value by
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