A particle of mass m is projected vertically upwards with velocity vo from the surface ofthe Earth at z = 0. Gravity acts downwards in the negative z direction, with expressionF₁=GmM(a+z)²where a is the radius of the Earth, M its mass, and G is the gravitational constant.Suppose that the particle is also subject to a constant friction force F₂ = -mfk, withƒ>0.(a) What are the dimensions of f?(b) Write the equation of motion and use it to show that the equation for the velocity v(z)is given byv² = v₁ +2GMa+zwhere vo> 0 is the initial velocity at z = 0.(c) Show that there is no escape velocity and find the maximum height reached by theparticle. Answers should be given in terms of a, M, vo, G and f.2GMa-2fz,

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Description: A particle of mass m is projected vertically upwards with velocity vo from the surface ofthe Earth at z = 0. Gravity acts downwards in the negative z direction, with expressionF₁=GmM(a+z)²where a is the radius of the Earth, M its mass, and G is the

The initial upwards velocity: v0 The force due to gravity: F⇀1=-GmMa+z2k^ The force of friction:…

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A particle of mass m is projected vertically upwards with velocity vo from the surface of the Earth at z = 0. Gravity acts downwards in the negative z direction, with expression F₁ = where a is the radius of the Earth, M its mass, and G is the gravitational constant. Suppose that the particle is also subject to a constant friction force F2₂ = −mfk, with ƒ>0. GmM (a+z)² (a) What are the dimensions of f? (b) Write the equation of motion and use it to show that the equation for the velocity v(z) is given by v² = √√ + 2GM a+z where vo > 0 is the initial velocity at z = = 0. 2GM a -2fz, (c) Show that there is no escape velocity and find the maximum height reached by the particle. Answers should be given in terms of a, M, vo, G and f.

A particle of mass m is projected vertically upwards with velocity vo from the surface of the Earth at z = 0. Gravity acts downwards in the negative z direction, with expression F₁ = where a is the radius of the Earth, M its mass, and G is the gravitational constant. Suppose that the particle is also subject to a constant friction force F2₂ = −mfk, with ƒ>0. GmM (a+z)² (a) What are the dimensions of f? (b) Write the equation of motion and use it to show that the equation for the velocity v(z) is given by v² = √√ + 2GM a+z where vo > 0 is the initial velocity at z = = 0. 2GM a -2fz, (c) Show that there is no escape velocity and find the maximum height reached by the particle. Answers should be given in terms of a, M, vo, G and f.

Physics for Scientists and Engineers: Foundations and Connections

1st Edition

ISBN:9781133939146

Author:Katz, Debora M.

Publisher:Katz, Debora M.

Chapter7: Gravity

Section: Chapter Questions

Problem 38PQ

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