Concept explainers
(a)
The time period of the satellite.
(a)
Answer to Problem 45P
The time period of the satellite is
Explanation of Solution
Write the expression for time period.
Here,
Write the expression for circular motion.
Here,
Rewrite the above expression for speed.
Here,
Rewrite the equation (I) by using (II).
Conclusion:
Substitute,
Thus, the time period of the satellite is
(b)
The speed of the satellite.
(b)
Answer to Problem 45P
The speed of the satellite is
Explanation of Solution
Write the expression for speed.
Conclusion:
Substitute,
Thus, the speed of the satellite is
(c)
The minimum energy required to place satellite in orbit.
(c)
Answer to Problem 45P
The minimum energy required to place satellite in orbit is
Explanation of Solution
Write the expression for minimum energy by using the conservation of energy formula.
Here,
Write the expression for the final kinetic energy.
Here,
Write the expression for the initial kinetic energy.
Here,
Write the expression for the initial speed of satellite.
Here,
Write the expression for the initial potential energy,
Write the expression for the final potential energy,
Rewrite the expression for the minimum energy from equation (V) by using (VI), (VII), (VIII), (IX) and (X).
Conclusion:
Substitute,
Thus, the minimum energy required to place satellite in orbit is
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Chapter 13 Solutions
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