Concept explainers
(a)
The magnitudes of the momenta of the
(a)
Answer to Problem 26P
The magnitudes of the momenta of the
Explanation of Solution
Write the formula for force
Write the formula for
Here,
Equating equation (I) and (II) and substitute
To convert
Conclusion:
Substitute
Thus, the magnitudes of the momenta of the
Substitute
Thus, the magnitudes of the momenta of the
(b)
The magnitude of the momentum of the neutron.
(b)
Answer to Problem 26P
The magnitude of the momentum of the neutron is
Explanation of Solution
Taking the direction of the momentum of the
Using the conservation of momentum parallel to the original momentum,
Using the conservation of momentum perpendicular to the original momentum,
Conclusion:
Squaring and adding equation (IV) and (V)
Thus, The magnitude of the momentum of the neutron is
(c)
The total energy of the
(c)
Answer to Problem 26P
The total energy of the
Explanation of Solution
Write the relativistic energy-momentum relation
Here,
Conclusion:
Substitute
Thus, the total energy of the
Substitute
Thus, the total energy of the neutron is
(d)
The total energy of the
(d)
Answer to Problem 26P
The total energy of the
Explanation of Solution
The total momentum is equal to the momentum of the
Substitute
Thus, the total energy of the
(e)
The mass of the
(e)
Answer to Problem 26P
The mass of the
Explanation of Solution
Using equation (VI), the relativistic energy-momentum relation to calculate the mass of the
Substitute
Thus, the mass of the
(f)
Compare the mass of the
(f)
Answer to Problem 26P
The mass of the
Explanation of Solution
The mass of the
The percentage of difference in their mass is
Thus, the mass of the
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Chapter 46 Solutions
Physics for Scientists and Engineers with Modern Physics Technology Update
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