- Parent Category: 02 Newtonian Mechanics
- Category: 08 Gravity
- Created: Thursday, 20 August 2015 15:00
- Last Updated: Thursday, 25 May 2017 15:35
- Published: Friday, 08 April 2016 15:00
- Hits: 5013
7.3.8 Relationship between F and U; between g and ϕ
To understand how g is related to ϕ:
- Similarly, compare and in the above table.
- If we differentiate with respect to r, we will get , which has the same expression as g.
- Hence, mathematically
- To understand the meaning of observe the two graphs carefully, on the right side where r is positive, the gradient of ϕ vs r graph is positive but the value of g will be negative. And on the left side where r is negative, the gradient of ϕ vs r graph is negative but the value of g is positive. Thus,
Similarly, it can be concluded that by multiplying both sides by test mass m.
18.104.22.168 Activity To doICT inquiry worksheet 1 (E), as well as the "G field and potential" EJS here. The HTML5 version is below, the Java worksheet customization to HTML5 is work in progress.
|units||N kg-1 or m s-2||J kg-1|
|meaning||Gravitational force per unit mass||Gravitational potential energy per unit mass|
towards the centre of the source mass
|relationship to mass||Force, = mg||Potential energy, = mϕ|
|computer model if M = 500.||-6.67*500/(abs(r)*r)||-6.67*500/abs(r)|
|relationship between g and ϕ||
|relationship between F and U||
|with best with||Chrome||Chrome||Chrome||Chrome|
|support full-screen?||Yes. Chrome/Opera No. Firefox/ Samsung Internet||Not yet||Yes||Yes|