Classical Dynamics of Particles and Systems

5th Edition

ISBN: 9780534408961

Author: Stephen T. Thornton, Jerry B. Marion

Publisher: Cengage Learning

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Textbook Question

Chapter 2, Problem 2.52P

A particle of mass m moving in one dimension has potential energy U(x) = U₀[2(x/a)² − (x/a)⁴], where U₀ and a are positive constants. (a) Find the force F(x), which acts on the particle. (b) Sketch U(x). Find the positions of stable and unstable equilibrium. (c) What is the angular frequency ω of oscillations about the point of stable equilibrium? (d) What is the minimum speed the particle must have at the origin to escape to infinity? (e) At t = 0 the particle is at the origin and its velocity is positive and equal in magnitude to the escape speed of part (d). Find x(t) and sketch the result.

Expert Solution & Answer

Chapter 2 Solutions

Classical Dynamics of Particles and Systems

Ch. 2 - Prob. 2.1P Ch. 2 - Prob. 2.2P Ch. 2 - If a projectile is fired from the origin of the...Ch. 2 - A clown is juggling four balls simultaneously....Ch. 2 - A jet fighter pilot knows he is able to withstand...Ch. 2 - In the blizzard of ’88, a rancher was forced to...Ch. 2 - Prob. 2.7P Ch. 2 - A projectile is fired with a velocity 0 such that...Ch. 2 - Consider a projectile fired vertically in a...Ch. 2 - Prob. 2.11P

Ch. 2 - A particle is projected vertically upward in a...Ch. 2 - A particle moves in a medium under the influence...Ch. 2 - A projectile is fired with initial speed 0 at an...Ch. 2 - A particle of mass m slides down an inclined...Ch. 2 - A particle is projected with an initial velocity 0...Ch. 2 - A strong softball player smacks the ball at a...Ch. 2 - Prob. 2.19P Ch. 2 - A gun fires a projectile of mass 10 kg of the type...Ch. 2 - Prob. 2.21P Ch. 2 - Prob. 2.22P Ch. 2 - A skier weighing 90 kg starts from rest down a...Ch. 2 - A block of mass m = 1.62 kg slides down a...Ch. 2 - A child slides a block of mass 2 kg along a slick...Ch. 2 - A rope having a total mass of 0.4 kg and total...Ch. 2 - A superball of mass M and a marble of mass m are...Ch. 2 - An automobile driver traveling down an 8% grade...Ch. 2 - A student drops a water-filled balloon from the...Ch. 2 - Prob. 2.31P Ch. 2 - Two blocks of unequal mass are connected by a...Ch. 2 - A particle is released from rest (y = 0) and falls...Ch. 2 - Perform the numerical calculations of Example 2.7...Ch. 2 - Prob. 2.36P Ch. 2 - A particle of mass m has speed υ = α/x, where x is...Ch. 2 - The speed of a particle of mass m varies with the...Ch. 2 - A boat with initial speed υ0 is launched on a...Ch. 2 - A train moves along the tracks at a constant speed...Ch. 2 - Prob. 2.42P Ch. 2 - Prob. 2.45P Ch. 2 - Prob. 2.46P Ch. 2 - Consider a particle moving in the region x > 0...Ch. 2 - Prob. 2.48P Ch. 2 - Prob. 2.49P Ch. 2 - According to special relativity, a particle of...Ch. 2 - Let us make the (unrealistic) assumption that a...Ch. 2 - A particle of mass m moving in one dimension has...Ch. 2 - A potato of mass 0.5 kg moves under Earth’s...Ch. 2 - Prob. 2.55P

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