Purchase Solution

Question on central force

Not what you're looking for?

Ask Custom Question

A particle of unit mass is projected with speed (see attached) at right angles to the radius vector at a distance a from a fixed point O and is subjected to a force F(r) = μ/r^2, with μ a positive constant. Show that the particle moves on a path which passes the centre at a distance of 3a at its maximum.

See attached

Attachments
Purchase this Solution

Solution Summary

The solution utilises concept of potential energy and law of conservation of angular momentum to trace the path of particle under central force.

Solution Preview

You are given mass, m = 1
Initial velocity vi = sqrt(3mu/2a)
Initial distance, ri = a

Let us assume, maximum distance rf = r (to be estimated, and to be proved to equal to 3a)
Let us assume, velocity at maximum distance vf = v [Note at the maximum distance, velocity will be perpendicular to r again)

You can visualize the problem as initially particle at one of the ends of minor axis of elliptical orbit. At maximum distance, the particle is at ...

Solution provided by:
Education
  • BEng, Allahabad University, India
  • MSc , Pune University, India
  • PhD (IP), Pune University, India
Recent Feedback
  • " In question 2, you incorrectly add in the $3.00 dividend that was just paid to determine the value of the stock price using the dividend discount model. In question 4 response, it should have also been recognized that dividend discount models are not useful if any of the parameters used in the model are inaccurate. "
  • "feedback: fail to recognize the operating cash flow will not begin until the end of year 3."
  • "Answer was correct"
  • "Great thanks"
  • "Perfect solution..thank you"
Purchase this Solution


Free BrainMass Quizzes
Solving quadratic inequalities

This quiz test you on how well you are familiar with solving quadratic inequalities.

Exponential Expressions

In this quiz, you will have a chance to practice basic terminology of exponential expressions and how to evaluate them.

Probability Quiz

Some questions on probability

Multiplying Complex Numbers

This is a short quiz to check your understanding of multiplication of complex numbers in rectangular form.

Geometry - Real Life Application Problems

Understanding of how geometry applies to in real-world contexts