Explanation Refer example 11.6 by assuming that one dimensional elastic collision with a very massive target ( m 1 ≪ m 2 ) , since the collision is elastic so that the kinetic energy gained by the spacecraft is equal to kinetic energy lost by the Jupiter. Write the expression for change in kinetic energy. Δ K = 1 2 m ( v f 2 − v i 2 ) (I) Here, Δ K is the change in kinetic energy, m is the mass of the pioneer, v f is the final speed of spacecraft, and v i is the initial speed of the pioneer 10 spacecraft. Write the expression for Jupiter’s final speed. Δ K jup = 1 2 M ( v ′ f 2 − v ′ i 2 ) (II) Here, Δ K jup is the decrease in Jupiter’s kinetic energy, M is the mass of the Jupiter, v ′ f is the speed of the gravitational slingshot of the Jupiter planet, and v ′ i is the initial speed of the Jupiter. Rearrange the equation (II) for v ′ f . Δ K jup = 1 2 M ( v ′ f 2 − v ′ i 2 ) 2 Δ K jup M = ( v ′ f 2 − v ′ i 2 ) v ′ f 2 = 2 Δ K jup M + v ′ i 2 v ′ f = 2 Δ K jup M + v ′ i 2 (III) Conclusion: Substitute 270 kg for m , 37 km/s for v f , and 14 km/s for v i in the equation (I) to find Δ K

Physics for Scientists and Engineers: Foundations and Connections

1st Edition

ISBN: 9781133939146

Author: Katz, Debora M.

Publisher: Cengage Learning

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Chapter 11, Problem 48PQ

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The kinetic energy of the Jupiter and speed of the gravitational slingshot of the Jupiter planet.

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Chapter 11, Problem 47PQ

Chapter 11, Problem 49PQ

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Physics for Scientists and Engineers: Foundations and Connections

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The kinetic energy of the Jupiter and speed of the gravitational slingshot of the Jupiter planet.

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