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## Homework Statement

A particle with mass=m moves in the xy plane. It is under the influence of a repulsive central force described by:

F(r)={A[itex]\hat{r}[/itex] if r<R

_{0}and 0 if r>R

_{0}}

[itex]\hat{r}[/itex] is the unit radial vector and R

_{0}is the range of the force

The initial conditions are x=-3 R

_{0}, y=0.5 R

_{0}, V

_{x}=w, v

_{y}=0

(A) Calculate energy and angular momentum in terms of the parameters A, R

_{0}, and w.

(B) Calculate the approximate distance of closest approach to the origin in terms of A, R

_{0}, and w, accurate to the order A assuming A is small.

## Homework Equations

Energy=U+K=[itex]\frac{1}{2}[/itex]mv

^{2}+Force*Distance

Angular momentum=mvrsin[itex]\theta[/itex]

## The Attempt at a Solution

I am having a hard time visualizing this problem. My current take is represented in the linked image:

http://imgur.com/8btZdls (I forgot the negative on -3R

_{0})

Does that look correct?

(A)

You could represent the energy of the particle by [itex]\frac{1}{2}[/itex]mv

^{2}+A(R

_{0}-r) if the particle is within the range of the force (r<R

_{0}) but it starts outside that range meaning it only has kinetic energy. Am I to answer with regard to its current energy or generally?

Currently energy = [itex]\frac{1}{2}[/itex]mw

^{2}

Angular Momentum=mwrsin(theta) but I am asked to represent this value in terms of the parameters A, R

_{0}, and w. I can write in terms of R

_{0}by providing a variable multiple of R

_{0}as r where R

_{0}*[itex]\alpha[/itex]=r thus:

mw[itex]\alpha[/itex]R

_{0}sin[itex]\theta[/itex]

Does that seem like the answer I am looking for?

(B)

Is this asking, given the initial velocity w and its initial position, how close would the particle come to the origin? i.e. it travels in the positive x direction until reaching the range of affect of the force A and then takes a curved path away from the origin. Find the nearest distance along that path to the origin?

Thank you for your help!