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Sesion #21-22 MekanikaKlasik Riser Fahdiran, M.Si Umiatin, M.Si JurusanFisika FakultasMatematikadanIlmuPengetahuanAlam
Outline Newton’s Law of Gravitation Potential & Potential Energy Relation Between Gravitational Field and Gravitational Potential Poisson Equation Equipotential Surfaces Ocean Tides 05/01/2011 ©  2010 Universitas Negeri Jakarta   |  www.unj.ac.id                      | 2
GRAVITATION ©  2010 Universitas Negeri Jakarta   |  www.unj.ac.id                      | 3 05/01/2011
©  2010 Universitas Negeri Jakarta   |  www.unj.ac.id                      | 4 1. Newton’s Law of Gravitation 	Each mass particle attracts every other particle in the universe with a force that varies directly as the product of two masses and inversely as the square of the distance between them.  05/01/2011
©  2010 Universitas Negeri Jakarta   |  www.unj.ac.id                      | 5 ,[object Object],05/01/2011
©  2010 Universitas Negeri Jakarta   |  www.unj.ac.id                      | 6 ,[object Object],05/01/2011
©  2010 Universitas Negeri Jakarta   |  www.unj.ac.id                      | 7 ,[object Object]
or05/01/2011
©  2010 Universitas Negeri Jakarta   |  www.unj.ac.id                      | 8 2.Potential & Potential Energy ,[object Object]
The Earth is assumed to be a uniform sphere of mass M. The corresponding gravitational field, g defined as the gravitational force per unit mass :05/01/2011
©  2010 Universitas Negeri Jakarta   |  www.unj.ac.id                      | 9 ,[object Object],05/01/2011
©  2010 Universitas Negeri Jakarta   |  www.unj.ac.id                      | 10 ,[object Object]
Wgis independent of the path taken; it depends only on A and B. Wg the work done by the field and Wext the work done by an external agent such as you.
They simply differ by a negative sign:  Wg = -Wext 05/01/2011
©  2010 Universitas Negeri Jakarta   |  www.unj.ac.id                      | 11 ,[object Object],05/01/2011
©  2010 Universitas Negeri Jakarta   |  www.unj.ac.id                      | 12 ,[object Object]
.If the path forms a closed loop, so that the object moves around and then returns to where it starts off, the net work done by the gravitational field would be zero, and we say that the gravitational force is conservative.05/01/2011
©  2010 Universitas Negeri Jakarta   |  www.unj.ac.id                      | 13 ,[object Object]
When dealing with a conservative force, it is often convenient to introduce the concept of potential energy U. The change in potential energy associated with a conservative force acting on an object as it moves from A to B is defined as: 05/01/2011
©  2010 Universitas Negeri Jakarta   |  www.unj.ac.id                      | 14 ,[object Object]
Uo is an arbitrary constant which depends on a reference point. It is often convenient to choose a reference point where Uo is equal to zero. 05/01/2011
©  2010 Universitas Negeri Jakarta   |  www.unj.ac.id                      | 15 ,[object Object],05/01/2011
©  2010 Universitas Negeri Jakarta   |  www.unj.ac.id                      | 16 ,[object Object]
Physically ΔV represents the negative of the work done per unit mass by gravity to move a particle from A to B.  05/01/2011
©  2010 Universitas Negeri Jakarta   |  www.unj.ac.id                      | 17 ,[object Object],05/01/2011
©  2010 Universitas Negeri Jakarta   |  www.unj.ac.id                      | 18 Relation Between Gravitational Field and Gravitational Potential ,[object Object],05/01/2011
©  2010 Universitas Negeri Jakarta   |  www.unj.ac.id                      | 19 ,[object Object]
The work done = potential difference05/01/2011
©  2010 Universitas Negeri Jakarta   |  www.unj.ac.id                      | 20 ,[object Object]
The force acting on a body :05/01/2011
©  2010 Universitas Negeri Jakarta   |  www.unj.ac.id                      | 21 ,[object Object],05/01/2011
©  2010 Universitas Negeri Jakarta   |  www.unj.ac.id                      | 22 illustration ,[object Object],05/01/2011
©  2010 Universitas Negeri Jakarta   |  www.unj.ac.id                      | 23 ,[object Object]
Using cosinus law :05/01/2011
©  2010 Universitas Negeri Jakarta   |  www.unj.ac.id                      | 24 ,[object Object]
Outside  the sphere :05/01/2011
©  2010 Universitas Negeri Jakarta   |  www.unj.ac.id                      | 25 ,[object Object]
So the potential outside :05/01/2011
©  2010 Universitas Negeri Jakarta   |  www.unj.ac.id                      | 26 ,[object Object]
Inside the hollow :05/01/2011
©  2010 Universitas Negeri Jakarta   |  www.unj.ac.id                      | 27 ,[object Object],05/01/2011
©  2010 Universitas Negeri Jakarta   |  www.unj.ac.id                      | 28 ,[object Object],05/01/2011
©  2010 Universitas Negeri Jakarta   |  www.unj.ac.id                      | 29 Poisson Equation ,[object Object],05/01/2011
©  2010 Universitas Negeri Jakarta   |  www.unj.ac.id                      | 30 ,[object Object]
Substitute g from the equation before :05/01/2011
©  2010 Universitas Negeri Jakarta   |  www.unj.ac.id                      | 31 ,[object Object],05/01/2011
©  2010 Universitas Negeri Jakarta   |  www.unj.ac.id                      | 32 ,[object Object],05/01/2011
©  2010 Universitas Negeri Jakarta   |  www.unj.ac.id                      | 33 3. Equipotential Surfaces ,[object Object],05/01/2011
©  2010 Universitas Negeri Jakarta   |  www.unj.ac.id                      | 34 05/01/2011
©  2010 Universitas Negeri Jakarta   |  www.unj.ac.id                      | 35 When is the concept of Potential Useful? ,[object Object],05/01/2011
©  2010 Universitas Negeri Jakarta   |  www.unj.ac.id                      | 36 ,[object Object]

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Mekanika Klasik (21 - 22)

  • 1. Sesion #21-22 MekanikaKlasik Riser Fahdiran, M.Si Umiatin, M.Si JurusanFisika FakultasMatematikadanIlmuPengetahuanAlam
  • 2. Outline Newton’s Law of Gravitation Potential & Potential Energy Relation Between Gravitational Field and Gravitational Potential Poisson Equation Equipotential Surfaces Ocean Tides 05/01/2011 © 2010 Universitas Negeri Jakarta | www.unj.ac.id | 2
  • 3. GRAVITATION © 2010 Universitas Negeri Jakarta | www.unj.ac.id | 3 05/01/2011
  • 4. © 2010 Universitas Negeri Jakarta | www.unj.ac.id | 4 1. Newton’s Law of Gravitation Each mass particle attracts every other particle in the universe with a force that varies directly as the product of two masses and inversely as the square of the distance between them. 05/01/2011
  • 5.
  • 6.
  • 7.
  • 9.
  • 10. The Earth is assumed to be a uniform sphere of mass M. The corresponding gravitational field, g defined as the gravitational force per unit mass :05/01/2011
  • 11.
  • 12.
  • 13. Wgis independent of the path taken; it depends only on A and B. Wg the work done by the field and Wext the work done by an external agent such as you.
  • 14. They simply differ by a negative sign: Wg = -Wext 05/01/2011
  • 15.
  • 16.
  • 17. .If the path forms a closed loop, so that the object moves around and then returns to where it starts off, the net work done by the gravitational field would be zero, and we say that the gravitational force is conservative.05/01/2011
  • 18.
  • 19. When dealing with a conservative force, it is often convenient to introduce the concept of potential energy U. The change in potential energy associated with a conservative force acting on an object as it moves from A to B is defined as: 05/01/2011
  • 20.
  • 21. Uo is an arbitrary constant which depends on a reference point. It is often convenient to choose a reference point where Uo is equal to zero. 05/01/2011
  • 22.
  • 23.
  • 24. Physically ΔV represents the negative of the work done per unit mass by gravity to move a particle from A to B. 05/01/2011
  • 25.
  • 26.
  • 27.
  • 28. The work done = potential difference05/01/2011
  • 29.
  • 30. The force acting on a body :05/01/2011
  • 31.
  • 32.
  • 33.
  • 34. Using cosinus law :05/01/2011
  • 35.
  • 36. Outside the sphere :05/01/2011
  • 37.
  • 38. So the potential outside :05/01/2011
  • 39.
  • 40. Inside the hollow :05/01/2011
  • 41.
  • 42.
  • 43.
  • 44.
  • 45. Substitute g from the equation before :05/01/2011
  • 46.
  • 47.
  • 48.
  • 49. © 2010 Universitas Negeri Jakarta | www.unj.ac.id | 34 05/01/2011
  • 50.
  • 51.
  • 52. A. Find Force through Potential
  • 53. B. Find Force directly05/01/2011
  • 54.
  • 55. © 2010 Universitas Negeri Jakarta | www.unj.ac.id | 38 05/01/2011
  • 56.
  • 57. © 2010 Universitas Negeri Jakarta | www.unj.ac.id | 40 05/01/2011
  • 58.
  • 59.
  • 60.
  • 61. The force on the center of earth’s mass05/01/2011
  • 62.
  • 63. The first is acceleration due to the earth, second is acceleration from tidal force which is responsible to produce ocean tides 05/01/2011
  • 64.
  • 65.
  • 66. At point A, R > D, eD predominates, so the tidal force is along the +x. At point B, because r/D << so the magnitude of tidal force is almost the same with point A but in the direction -x05/01/2011
  • 67.
  • 69.
  • 70. © 2010 Universitas Negeri Jakarta | www.unj.ac.id | 49 05/01/2011
  • 71.
  • 73. 05/01/2011 © 2010 Universitas Negeri Jakarta | www.unj.ac.id | 51