(a)
The magnitude of the speed of each planets and relative speed.
(a)
Answer to Problem 61AP
The magnitude of speed of each planet respectively
Explanation of Solution
Initially both planets will have zero potential and kinetic energy.
Write expression for the conservation of energy.
Here,
The initial momentum of the both planet is zero.
Write the expression for the conservation of momentum.
Rewrite the above equation in terms of
Write the expression to calculate the relative velocity of the two planets.
Here, V is the relative velocity of the planets.
Conclusion:
Substitute the equation (II) in (I) to rewrite in terms of
Use the above expression in the equation (II) to rewrite in terms of
Substitute the expression for
Therefore, the magnitude of speed of each planet respectively
(b)
The kinetic energy of each planet.
(b)
Answer to Problem 61AP
The kinetic energy of each planet is respectively
Explanation of Solution
Write the expression to calculate relative distance between the two planets before collision.
Write the expression to calculate the velocity of the planet of mass
Write the expression to calculate the velocity of the planet of mass
Write the expression to calculate the kinetic energy of the planet of mass
Here,
Write the expression to calculate the kinetic energy of the planet with mass
Here,
Conclusion:
Substitute
Substitute
Substitute
Substitute
Substitute
Therefore, the kinetic energy of each planet is respectively
Want to see more full solutions like this?
Chapter 13 Solutions
Bundle: Physics for Scientists and Engineers with Modern Physics, Loose-leaf Version, 9th + WebAssign Printed Access Card, Multi-Term
- A 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_forwardIn a laboratory experiment, an electron with a kinetic energy of 50.5 keV is shot toward another electron initially at rest (Fig. P11.50). (1 eV = 1.602 1019 J) The collision is elastic. The initially moving electron is deflected by the collision. a. Is it possible for the initially stationary electron to remain at rest after the collision? Explain. b. The initially moving electron is detected at an angle of 40.0 from its original path. What is the speed of each electron after the collision? FIGURE P11.50arrow_forwardRank the following quantities of energy from largest to the smallest. State if any are equal. (a) the absolute value of the average potential energy of the SunEarth system (b) the average kinetic energy of the Earth in its orbital motion relative to the Sun (c) the absolute value of the total energy of the SunEarth systemarrow_forward
- A single-stage rocket of mass 308 metric tons (not including fuel) carries a payload of 3150 kg to low-Earth orbit. The exhaust speed of the rockets cryogenic propellant is 3.20 103 m/s. a. If the speed of the rocket as it enters orbit is 8.00 km/s, what is the mass of propellant used during the rockets burn? b. The rocket is redesigned to boost its exhaust speed by a factor of two. What is the mass of propellant used in the redesigned rocket to carry the same payload to low-Earth orbit? c. Because the exhaust speed of the redesigned rocket is increased by a factor of two, why is the fuel consumption of the redesigned rocket not exactly half that of the original rocket?arrow_forwardA particle of mass m moving along the x-axis with a velocity component +u collides head-on and sticks to a particle of mass m/3 moving along the x-axis with the velocity component −u. What is the mass M of the resulting particle?arrow_forwardTwo astronauts with masses m1 and m2 are moving with the velocity u together. They push each other off in the direction perpendicular to u,spending the energy ΔE. What is the angle between the velocities of the astronauts after the push-off?arrow_forward
- The mass of particle 1 is 11kg and the mass of particle 2 is 15kg. The initial velocity for particle 1 is (-104m/s)i + (216m/s)j and the initial velocity of particle 2 is (75m/s)i + (-152m/s)j.arrow_forwardBlock A and block B collide and the impact is such that energy is conserved. Just before impact their velocities are vA = (5.1i) m/s and vB = (-2.1i) m/s respectively. If the masses of the blocks are the same, what is the speed of block A just after the collision?arrow_forwardConsider two objects/particles: Object 1 has mass 3m and speed v and Object 1 has mass 2m and speed 2v, respectively. In each of the three different scenarios, the objects collide inelastically and stick together after the collision. Scenario A: The objects move toward each other and collide head-on. Scenario B: Object 2m chases Object 3m and collides with from behind. Scenario C: The objects move at right angles before the collision. Rank these three scenarios from highest to lowest speed after the collision. (Circle ONLY ONE answer) a. B>A>C b. C>A>B c. C>B>A d. B>C>A e. A>B>C f. A>C>Barrow_forward
- If a particle of mass 100 g initially had a speed of 100 cm/s, what would be its approximate kinetic energy at the end of its 10 cm fall? The correct answer is 15 x 10⁵ ergsarrow_forwardThe carbon isotope 14C is used for carbon dating of archeological artifacts. 14C (mass 2.34 x 10-26 kg) decays by the process known as beta decay in which the nucleus emits an electron (the beta particle) and a subatomic particle called a neutrino. In one such decay, the electron and the neutrino are emitted at right angles to each other. The electron (mass 9.11 x 10-31 kg) has a speed of 5.00 x 107 m/s and the neutrino has a momentum of 8.00 x 10-24 kg • m/s. What is the recoil speed of the nucleus?arrow_forwardOne newly discovered light particle has a mass of m and property q. Suppose it moves within the vicinity of an extremely heavy (fixed in place) particle with a property Q and mass M. When the light particle is xi distance from the heavy particle, it is moving directly away from the heavy particle with a speed of vi. a) What is the lighter particle's speed when it is xf away from the heavy particle?arrow_forward
- Principles of Physics: A Calculus-Based TextPhysicsISBN:9781133104261Author:Raymond A. Serway, John W. JewettPublisher:Cengage LearningGlencoe Physics: Principles and Problems, Student...PhysicsISBN:9780078807213Author:Paul W. ZitzewitzPublisher:Glencoe/McGraw-HillPhysics for Scientists and Engineers: Foundations...PhysicsISBN:9781133939146Author:Katz, Debora M.Publisher:Cengage Learning
- Modern PhysicsPhysicsISBN:9781111794378Author:Raymond A. Serway, Clement J. Moses, Curt A. MoyerPublisher:Cengage LearningClassical Dynamics of Particles and SystemsPhysicsISBN:9780534408961Author:Stephen T. Thornton, Jerry B. MarionPublisher:Cengage LearningCollege PhysicsPhysicsISBN:9781285737027Author:Raymond A. Serway, Chris VuillePublisher:Cengage Learning