Concept explainers
(a)
Speed of first particle before collision.
(a)
Explanation of Solution
Given:
Particle of mass
The particles stick together after collision.
Formula used:
Write the expression of total energy of particle
Here,
Write the expression of total energy in terms of gamma factor
Here,
Substitute
Simplify the above expression for
Write the expression of gamma factor
Here,
Simplify above expression for
Calculation:
The value of
Substitute
Substitute 3 for
Conclusion:
Thus, the speed of first particle before collision is
(b)
Total energy of first particle before collision.
(b)
Explanation of Solution
Given:
Particle of mass
The particles stick together after collision.
Formula used:
Write the expression of total energy of particle
Here,
Calculation:
Substitute 3 for
Conclusion:
Thus, the total energy of first particle before collision is
(c)
Initial total momentum of system.
(c)
Explanation of Solution
Given:
Particle of mass
The particles stick together after collision.
Formula used:
Write the expression of the total relativistic energy
Here,
Rearrange the above expression
Calculation:
Substitute
Conclusion:
Thus, the initial total momentum of system is
(d)
Total kinetic energy after collision.
(d)
Explanation of Solution
Given:
Particle of mass
The particles stick together after collision.
Formula used:
Since the total energy is conserved during collision therefore
Here,
Since the momentum is conserved during the collision therefore
Here,
Write the expression for rest mass energy
Write the expression for total kinetic energy
Calculation:
Substitute
Substitute
Conclusion:
Thus, the total kinetic energy after collision is
(e)
Mass of system after collision.
(e)
Explanation of Solution
Given:
Particle of mass
The particles stick together after collision.
Formula used:
Write the expression of mass of system
Here, is mass of the system after collision
Calculation:
Substitute
Conclusion:
Thus, the mass of system after collision is
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Chapter 39 Solutions
Physics for Scientists and Engineers, Vol. 3
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