Concept explainers
The oldest artificial satellite still in orbit is Vanguard I, launched March 3, 1958. It mass is 1.60 kg. Neglecting atmospheric drag, the satellite would still be in its initial orbit, with a minimum distance from the center of Earth of 7.02 Mm and a speed at this perigee point of 8.23 km/s. For this orbit, find (a) the total energy of the satellite–Earth system and (b) the magnitude of the
(a)
The total energy of the satellite earth system.
Answer to Problem 13.79CP
The total energy of the satellite earth system is
Explanation of Solution
Given info: Mass of the satellite is
Write the expression for total energy of the satellite earth system.
Here,
Substitute
Conclusion:
Therefore, the total energy of the satellite earth system is
(b)
The magnitude of angular momentum of the satellite.
Answer to Problem 13.79CP
The magnitude of angular momentum of the satellite is
Explanation of Solution
Given info: Mass of the satellite is
Write the expression for angular momentum.
Here,
Substitute
Conclusion:
Therefore, the magnitude of angular momentum of the satellite is
(c)
The satellite’s speed and it’s distanced from the centre of the earth at apogee.
Answer to Problem 13.79CP
The satellite’s speed is
Explanation of Solution
Given info: Mass of the satellite is
Write the expression for total energy at apogee.
Here,
Write the expression for angular momentum at apogee.
Rearrange the expression for distanced from the centre of the earth at apogee.
Substitute
Rearrange the above equation to get a quadratic equation of
Substitute
Find the smaller roots of the above equation.
Substitute
Conclusion:
Therefore, the satellite’s speed is
(d)
The semi major axis of its orbit.
Answer to Problem 13.79CP
The semi major axis of its orbit is
Explanation of Solution
Given info: Mass of the satellite is
Write the expression for length of major axis.
Substitute
Conclusion:
Therefore, the semi major axis of its orbit is
(e)
The period of the satellite.
Answer to Problem 13.79CP
The period of the satellite is
Explanation of Solution
Given info: Mass of the satellite is
Write the expression for time period.
Substitute
Conclusion:
Therefore, the period of the satellite is
Want to see more full solutions like this?
Chapter 13 Solutions
Physics For Scientists And Engineers, Volume 2
- A satellite is spinning at 6.0 rev/s. The satellite consists of a main body in the shape of a sphere of radius 2.0 m and mass 10,000 kg, and two antennas projecting out from the center of mass of the main body that can be approximated with rods of length 3.0 m each and mass 10 kg. The antenna’s lie in the plane of rotation. What is the angular momentum of the satellite?arrow_forwardThe perihelion of Halley’s comet is 0.586 AU and the aphelion is 17.8 AU. Given that its speed at perihelion is 55 km/s, what is the speed at aphelion ( IAU=1.4961011m )? (Hint: You may use either conservation of energy or angular momentum, but the latter is much easier.)arrow_forwardA thin rod of length 2.65 m and mass 13.7 kg is rotated at anangular speed of 3.89 rad/s around an axis perpendicular to therod and through its center of mass. Find the magnitude of therods angular momentum.arrow_forward
- The position vector of a particle of mass 2.00 kg as a function of time is given by r=(6.00i+5.00tj), where r is in meters and t is in seconds. Determine the angular momentum of the particle about the origin as a function of time.arrow_forwardFor a particle traveling in a straight line, are there any points about which the angular momentum is zero? Assume the line intersects the origin.arrow_forwardThe velocity of a particle of mass m = 2.00 kg is given by v= 5.10 + 2.40 m /s. What is the angular momentumof the particle around the origin when it is located atr= 8.60 3.70 m?arrow_forward
- Can you assign an angular momentum to a particle without first defining a reference point?arrow_forwardA space probe is fired as a projectile from the Earths surface with an initial speed of 2.00 104 m/s. What will its speed be when it is very far from the Earth? Ignore atmospheric friction and the rotation of the Earth. P11.26 Ki+Ui=Kf+Uf12mvi2+GMEm(1rf1ri)=12mvf212vi2+GME(01RE)=12vf2orvf2=v122GMEREandvf=(v122GMERE)1/2,vf=[(2.00104)21.25108]1/2m/s=1.66104m/sarrow_forwardIf you know the velocity of a particle, can you say anything about the particle’s angular momentum?arrow_forward
- A solid cylinder of mass 2.0 kg and radius 20 cm is rotating counterclockwise around a vertical axis through its center at 600 rev/min. A second solid cylinder of the same mass and radius is rotating clockwise around the same vertical axis at 900 rev/min. If the cylinders couple so that they rotate about the same vertical axis, what is the angular velocity of the combination?arrow_forwardA buzzard (m = 9.29 kg) is flying in circular motion with aspeed of 8.44 m/s while viewing its meal below. If the radius ofthe buzzards circular motion is 8.00 m, what is the angularmomentum of the buzzardaround the center of its motion?arrow_forwardA bird flies overhead from where you stand at an altitude of 300.0 m and at a speed horizontal to the ground of 20.0 m/s. The bird has a mass of 2.0 kg. The radius vector to the bird makes an angle with respect to the ground. The radius vector to the bird and its momentum vector lie in the xy-plane. What is the bird’s angular momentum about the point where you are standing?arrow_forward
- Physics for Scientists and Engineers, Technology ...PhysicsISBN:9781305116399Author:Raymond A. Serway, John W. JewettPublisher:Cengage LearningPrinciples of Physics: A Calculus-Based TextPhysicsISBN:9781133104261Author:Raymond A. Serway, John W. JewettPublisher:Cengage LearningClassical Dynamics of Particles and SystemsPhysicsISBN:9780534408961Author:Stephen T. Thornton, Jerry B. MarionPublisher:Cengage Learning
- University Physics Volume 1PhysicsISBN:9781938168277Author:William Moebs, Samuel J. Ling, Jeff SannyPublisher:OpenStax - Rice UniversityModern PhysicsPhysicsISBN:9781111794378Author:Raymond A. Serway, Clement J. Moses, Curt A. MoyerPublisher:Cengage LearningPhysics for Scientists and Engineers: Foundations...PhysicsISBN:9781133939146Author:Katz, Debora M.Publisher:Cengage Learning