Transcribed TextTranscribed Text

Chapter 6= Problem 17 & 18 Chapter 9= problem 3 only 6.17 A smooth wire has the form of the helix x - a cosé, y = a sine, : = be, where 6 is a real parameter, and de b are positive constants. The wire is fixed with the axis Or pointing vertically upwards. A particle P. which can slide freely on the wire, is released from rest at the point (a, 0, 2mb). Find the speed of P when it reaches the point (a,0,0) and the time taken for il to do so. 6.18 A smooth wire has the form of the parabola : = x /2b, y = 0. where b is a positive constant. The wire is fixed with the axis Oz pointing vertically upwards. A particle P. which can slide freely on the wire, is performing oscillations with x in the range - sisa Show that the period T of these oscillations is given by b² + x 2 1/2 dx. T= (gb) a? - x 2 By the above integral, obtain a new formula small. for T. Use this formula to tind a two-term approximation to T. valid when the ratio a/b is making the substitution x = a sin * in 9.3 The internal potential energy function for a diatomic molecule is approximated by the Morse potential V(r) = Vo 2 - Vo. where / is the distance of separation of the two atoms, and Vo. a, b are positive constants. lake 3 sketch of the Morse potential. Suppose the molecule is restricted to vibrational motion in which the centre of mass G of the molecule is fixed, and the atoms move on a fixed straight line through G. Show that there is a single equilibrium configuration for the molecule and that it is stable. If the atoms each have mass m, find the angular frequency of small vibrational oscillations of the molecule.

Solution PreviewSolution Preview

These solutions may offer step-by-step problem-solving explanations or good writing examples that include modern styles of formatting and construction of bibliographies out of text citations and references. Students may use these solutions for personal skill-building and practice. Unethical use is strictly forbidden.

    By purchasing this solution you'll be able to access the following files:

    for this solution

    PayPal, G Pay, ApplePay, Amazon Pay, and all major credit cards accepted.

    Find A Tutor

    View available Classical Mechanics Tutors

    Get College Homework Help.

    Are you sure you don't want to upload any files?

    Fast tutor response requires as much info as possible.

    Upload a file
    Continue without uploading

    We couldn't find that subject.
    Please select the best match from the list below.

    We'll send you an email right away. If it's not in your inbox, check your spam folder.

    • 1
    • 2
    • 3
    Live Chats