Circular motion HELP !!! (1 Viewer)

[joelferns27]

Hey guys at our school we recently did a prac, i cant even find it in the syllabus but it was investigating circular motion.

We were trying to determine the relationship between velocity and radius (much like satellites orbiting earth).

According the v = square root(Gm/r), isnt the relationship inversly proportional, where v is inversely proportional to square root (r)??

but according to f=mv^2/r . v^2 is proportional to r??? i dont get why and how this contradicts?? dont satellites in space obey both formulas

CAN someone pls explaaaaaaain

 

[joelferns27]

thank you so much! so f=mv^2/r really just shows the relationship between force and m v r, however the relationship that v^2 vs r is proportional is invalid?

Then why did our teacher make us graph v^2 vs r?

 

[DannyBoy33]

I think you are having some slight confusion, your first formula basically is the orbital velocity formula, which all satellites adhere in travelling around their planet where gravitational force provides the centripetal force for stable orbital motion at a particular altitude, however, you have to realise your first formula states the relationship between velocity, mass of planet and radius of planet, while your second formula relates force to mass of planet, velocity and radius-hence for second formula, you can only deduce the relationship between f and another variable, the deduction of v2 proportional to r in the second formula is not valid, so essentially what I am saying is satellites in space obeys both formulas but the formulas relates different variables, hence can't be seen as equal, there are separate.... hope this kind of helps to clarify your confusion

cool, thanks

 

[strawberrye]

thank you so much! so f=mv^2/r really just shows the relationship between force and m v r, however the relationship that v^2 vs r is proportional is invalid?

Then why did our teacher make us graph v^2 vs r?

Actually, I personally don't think my previous explanation was completely right either, plotting v2/r is because in the formula, F=mv2/r, so m is a constant, v2/r essentially equals the acceleration which is the acceleration due to gravity, which should also be constant for same radius, as you need same force to keep something in same radius spinning uniformly, so by plotting v2 vs r, you will get acceleration, times by mass of object, you will be able to deduce the force keeping the object in motion, I think this apparent disparity/inconstancy may have something to do with the fact that F=mv2/r just refer to centripetal motion, however for satellite, there are just gravitational force responsible, but say for a car turning a curved corner or an electron spinning around the nucleus, there are other counteracting force with different formulas to equate to the F=mv2/r formula to get formula for different velocity at different radius, since the v= square root of GM/r formula comes from equating F=mv2/r and g=GM/r2, so it works for satellites, but the latter formula are more generalised-it may partially be because of this allowance that results in this disparity of relationship,

And I apologise for saying v2 vs r is not directly proportional in the second, it is, but right now, even after thinking about it for a while, I still don't know exactly the cause for this disparity-I think the best solution would be to ask your physics teacher for a complete clarification of the reason. I apologise again, but hoped that perhaps my explanation may have shed some light on what the answer might be...