What is the final velocity of a particle in a force field around point O?

[24forChromium]

A force field is maintained around point O, a particle with mass m is experiencing a force F in the force field. F as a function of the particle's distance from O is: F = cos(d/5) How does one go about looking for the final velocity of the particle if it began at rest at a negligible distance away from point O?

 

[andrewkirk]

Calculate the work done on the particle by the force in moving it to distance d away from O. Then find the velocity at which the mass has that kinetic energy.

 

[Chandra Prayaga]

Calculate the work done on the particle by the force in moving it to distance d away from O. Then find the velocity at which the mass has that kinetic energy.

Absolutely. That is the way to go. The only question I have is, what exactly does the statement of the problem mean by the word, "negligible distance".?

 

[andrewkirk]

In practice it means you can use zero as the lower limit for your integration. I expect the reason they said 'negligible distance' rather than 'start at O' is that usually when forces are symmetrically arranged around a point it's because there's a particle at that point, and two particles can't occupy the same point in classical phycics.

 

[Chandra Prayaga]

In practice it means you can use zero as the lower limit for your integration. I expect the reason they said 'negligible distance' rather than 'start at O' is that usually when forces are symmetrically arranged around a point it's because there's a particle at that point, and two particles can't occupy the same point in classical phycics.

Ah! So the particle is moving effectively from 0 to d?

 

[andrewkirk]

Yes, I think that is the intent of the question.