Find the differential equation and velocity

Alexiy · Jan 15, 2016

Homework Statement

Diagram of a particle P on a horizontal chord AB of a circle centred at O, with radius R, perpendicular distance d from O to the chord, and a force F directed from P toward O; C is the midpoint of the chord on the y-axis.

Homework Equations

3. The Attempt at a Solution [/B]

Handwritten-style typed derivation of horizontal motion: y = d constant, force F = f(r) r/|r| with r = sqrt(x^2+d^2) and r vector = -(x i + d j), leading to mx'' = -kx/(x^2+d^2).

Hello guys,I posted images since its easier to write equations.Please can someone help me check this, if this is correct so far, then i should be able to find the velocity at C, using kinetic energy?

Chestermiller · Jan 15, 2016

Looks good to me.

Alexiy · Jan 16, 2016

Chestermiller said:

Looks good to me.

Typed mathematical derivation of kinetic energy and work done from A to C, computing an integral of -kx/(x^2+d^2) and concluding v_c = sqrt((2k/m) ln(R/d)).

Edit: Work done from A to C is the difference of the potential energy between these two points, am i wrong?

Alexiy · Jan 16, 2016

By the way in the problems text i translated R as circumference, but its actually a radius R.

Chestermiller · Jan 16, 2016

In my judgment, you did all this correctly. I think you should have more confidence in your ability. Your analysis was very nice, perceptive, and mathematically talented.

Chet

Alexiy · Jan 17, 2016

Chestermiller said:

In my judgment, you did all this correctly. I think you should have more confidence in your ability. Your analysis was very nice, perceptive, and mathematically talented.

Chet

Thank you very much Chet, I can't help it,I always had some difficulties to translate "physics thoughts" into math language so maybe I am overly cautious, sometimes i even waste time writing code for motion simulations to make sure something behaves like its supposed to, but it seems I'm getting the hang of it.Thanks again for your support.

Find the differential equation and velocity

Homework Statement

Homework Equations

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