Concept explainers
A proton in a high-energy accelerator moves with a speed of c/2. Use the work-kinetic energy theorem to find the work required to increase its speed to (a) 0.750c and (b) 0.995c
(a)
The work required to increase the speed of the particle to
Answer to Problem 39.49P
The work required to increase the sped of the particle is
Explanation of Solution
Given Info: The initial speed of the particle is
The rest mass of the proton is
The speed of the light is
The final kinetic energy of the proton is,
Here,
The initial kinetic energy of the proton is,
Here,
Form the work energy theorem.
Substitute
Substitute
Substitute
Conclusion:
Therefore, the work required to increase the sped of the particle is
(b)
The work required to increase the speed of the particle to
Answer to Problem 39.49P
The work required to increase the sped of the particle is
Explanation of Solution
Given Info: The initial speed of the particle is
The rest mass of the proton is
The speed of the light is
The work done is,
Substitute
Substitute
Conclusion:
Therefore, the work required to increase the sped of the particle is
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Chapter 39 Solutions
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