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Concept explainers
(a)
Identify the positions of two particles at any instant t and explain about its motion.
(a)
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Answer to Problem 8.3P
Equation to find the position of particles at any instant t are
Explanation of Solution
Write the general expression for position coordinate of centre of mass of system.
Here¸
Rearrange the above equation as follows.
Express
Here,
Rewrite equation (II) by adding
Write the equation for linear velocity of 1st mass from the above equation.
Here,
Rewrite equation (II) by adding
Draw the diagram showing the spring- mass system.
Write the law of conservation of momentum for spring-mass system.
Here,
Rewrite the expression for
Write the equation for position of initial centre of mass.
Write the equation of motion for coordinate of centre of mass.
Rewrite the above equation by substituting equations (IV) and (V).
Write the Lagrange equation in relative coordinates.
Replace
Write the Lagrange equation with respect to
Rewrite the above equation by substituting
Write the solution for above equation.
Replace
At time t=0, r=L.
Differentiate
At t=0,
Rewrite the previous equation by substituting
Rewrite the equation
Substitute
Replace
Substitute
Conclusion:
Therefore, the equation to find the position of particles at any instant t are
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Chapter 8 Solutions
Classical Mechanics
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