What is the meaning of the equation Vgrav = constant - 1/2 v2?

[Joe09]

Hi, I did a quick search but didnt find anything relevant so I apologise if this has been covered.

My A2 Physics book says the following:

E_potential = E_total - E_kinetic

Since the kinetic energy is 1/2 mv², and the gravitational potential V_grav is E_potential/m, dividing this equation by m gives

V_grav = constant - 1/2 v²

My question is, the book does not go into any more detail and i am unsure what this equation is ment to actually be. I think it means G but i am unsure.

Appreciate any help.

 

[tiny-tim]

Welcome to PF!

Hi Joe09! Welcome to PF!

There's a slightly confusing difference between potential and potential energy …

electric potential is potential energy per charge, and gravitational potential is potential energy per mass …

that's why they divided E_potential by m.

Gravitational potential (in a uniform gravitational field) is U = gh.

(and btw I think we normally use U rather than V for potential)

 

[Joe09]

Thankyou for the welcome.

Of course how silly of me!

The equation:

E_potential = E_total - E_kinetic

is equivalent to:

GMm/R = mc² - 1/2 mv²

So when the physics book divides the equation by m we arrive at:

GM/R = c² - 1/2 v²

which is equivalent to:

V_grav = constant - 1/2 v²



I tell ya, working with integrals all day confudles the mind

U? Oh ok, it be nice if the worlds scientists/exam boards/teaching curriculums could agree on a universal symbol. Unless its only the UK which uses V