(a)
ToCalculate: The ratio of spin angular momenta of Mars and Earth.
(a)
Answer to Problem 21P
Explanation of Solution
Given information :
Mars and Earth have nearly identical lengths of days.
Earth’s mass is
Radius is
Mars’ orbital radius is on an average
The Martian year is
Formula used :
The
Where, I is the moment of inertia and
Moment of inertia of sphere is
Where, M is the mass and R is the radius of the sphere.
Calculation:
As Mars and Earth have nearly identical lengths of days.
The ratio of spin angular momenta of Mars and Earth is:
Conclusion:
The ratio of spin angular momenta of Mars and Earth is 33:1.
(b)
ToCalculate: The ratio of spin kinetic energies of Mars and Earth.
(b)
Answer to Problem 21P
Explanation of Solution
Given information :
Mars and Earth have nearly identical lengths of days.
Earth’s mass is
Radius is
Mars’ orbital radius ison an average
The Martian year is
Formula used :
Rotational kinetic energy is:
Where, I is the moment of inertia and
Moment of inertia of sphere is
Where, M is the mass and R is the radius of the sphere.
Calculation:
As Mars and Earth have nearly identical lengths of days.
Conclusion:
The ratio of spin kinetic energies of Mars and Earth is 33:1.
(c)
ToCalculate: The ratioorbital angular momenta of Mars and Earth.
(c)
Answer to Problem 21P
Explanation of Solution
Given information :
Mars and Earth have nearly identical lengths of days.
Earth’s mass is
Radius is
Mars’ orbital radius ison an average
The Martian year is
Formula used :
The angular momentum is given by:
Where, I is the moment of inertia and
Moment of inertia of sphere is
Where, M is the mass and R is the radius of the sphere.
Calculation:
Treating Earth and Mars as point objects, the ratio of their orbital angular momenta is
Substituting for the moments of inertia and angular speeds yields
Where
Substitute numerical values for the three ratios and evaluate
Conclusion:
The ratioorbital angular momenta of Mars and Earth is,
(d)
ToCalculate: The ratio of orbital kinetic energies of Mars and Earth.
(d)
Answer to Problem 21P
Explanation of Solution
Given information :
Mars and Earth have nearly identical lengths of days.
Earth’s mass is
Radius is
Mars’ orbital radius is, on average
The Martian year is
Formula used :
Rotational kinetic energy is:
Where, I is the moment of inertia and
Moment of inertia of sphere is
Where, M is the mass and R is the radius of the sphere.
Calculation:
Conclusion:
The ration of orbital kinetic energies of Mars and Earth is
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Chapter 10 Solutions
Physics for Scientists and Engineers
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