Gravitational Potential Energy: Difference between revisions
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==Connectedness== | ==Connectedness== | ||
#http://voyager.jpl.nasa.gov/ | #http://voyager.jpl.nasa.gov/ Nasa uses gravitational energy to get probes to break through the heliosphere as in the voyager mission. Gravitational energy is very important to understand when sending probes to explore planets. | ||
#Biochem majors may find this information useful in understanding how chemical potential works. | #Biochem majors may find this information useful in understanding how chemical potential works. | ||
#Actual Application: http://www.forbes.com/sites/startswithabang/2015/11/02/move-over-hubble-gravity-itself-is-the-best-cosmic-telescope-of-all/ | #Actual Application: http://www.forbes.com/sites/startswithabang/2015/11/02/move-over-hubble-gravity-itself-is-the-best-cosmic-telescope-of-all/ | ||
Revision as of 13:29, 16 November 2015
This topic covers Gravitational Potential Energy.
Gravitational Potential
Gravitational Potential energy belongs to a pair of objects in a system (for instance a ball+ Earth system, galaxies of stars interacting gravitationally) and is equal to the work done against gravity. This potential energy is the energy associated within the particles inside a system and is not the same as rest or kinetic energies of the individual particles. Traditionally potential energy is represented by the symbol U and this page describes specific examples in which U is equal to the gravitational energy learned about in earlier pages to be approximately mg near the surface of the Earth or
[math]\displaystyle{ F = - G \frac{m_1 m_2}{r^2}\ }[/math]
where:
- F is the force between the masses;
- G is the gravitational constant (6.674×10−11 N · (m/kg)2);
- m1 is the first mass;
- m2 is the second mass;
- r is the distance between the centers of the masses.
The latter case is distance dependent and can be derived since force is the negative gradient of U. The negative indicates that potential energy decreases as particles get closer together
A Mathematical Model
In a system composed of two objects that are interacting with gravitational potential:
[math]\displaystyle{ F = - G \frac{m_1 m_2}{r^2}\ }[/math]
where:
- F is the force between the masses;
- G is the gravitational constant (6.674×10−11 N · (m/kg)2);
- m1 is the first mass;
- m2 is the second mass;
- r is the distance between the centers of the masses.
Close to the Surface of the Earth:
- [math]\displaystyle{ U = mgh\! }[/math]
where U is the potential energy of the object assuming it is close to the surface of the Earth, m is the mass of the object, g is the acceleration of 9.8, and h is height.
Potential difference is derived to be:
- [math]\displaystyle{ \,\Delta U = mg \Delta h.\ }[/math]
A Computational Model
How do we visualize or predict using this topic. Consider embedding some vpython code here Teach hands-on with GlowScript
Examples
Be sure to show all steps in your solution and include diagrams whenever possible
Simple
Middling
Difficult
Connectedness
- http://voyager.jpl.nasa.gov/ Nasa uses gravitational energy to get probes to break through the heliosphere as in the voyager mission. Gravitational energy is very important to understand when sending probes to explore planets.
- Biochem majors may find this information useful in understanding how chemical potential works.
- Actual Application: http://www.forbes.com/sites/startswithabang/2015/11/02/move-over-hubble-gravity-itself-is-the-best-cosmic-telescope-of-all/
History
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See also
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Further reading
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External links
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References
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