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Newton's Law of Universal Gravitation


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Introduction to Gravitation Newton's Law and an important deduction which shows relation between 'acceleration due to gravity g' and 'mass of body m'.

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Newton's Law of Universal Gravitation

  1. 1. Presented By:- Name – Akshat Saxena
  2. 2.  What is Force?  Who discovered Gravitational law?  Discovery of Gravitational Force.  Calculation used by Newton.  Calculating the constant.  Gravity- A special Case.  Effect of Gravity and its Uses.
  3. 3. Sir Issac newton gave many laws of nature. In his First law of motion, he described the inherent property of matters,qualitatively. In his second law,he wrote “A force action on a body gives it an accelaration which is in the direction of force and has a magnitude given by ma.” So,it describes force quantitatively also. In his third law,he describes how force are exerted. Therefore,we can say he discovered “Force”.
  4. 4. The force is an external effort(cause) in the form of a push or pull which either changes or tends to change the state of rest or the uniform motion of a body along a straight line. They are classified into two categories:- (i) Contact Force. - Frictional force, normal reaction,tensile force etc. (ii) Non-Contact Force. - electric,magnetic,gravitational force.
  5. 5.  Sir Isaac Newton (1642-1727)  Perhaps the greatest genius of all time  Invented the reflecting telescope  Invented calculus  Connected gravity and planetary forces Philosophiae naturalis principia mathematica
  6. 6.  In 1665, Issac Newton performed brilliant theoretical and experimental tasks in mechanics and optics.  In this year, he focused his attention on the motion of the moon about the earth.  While doing so, he had a question that what is the force that makes moon to revolve.
  7. 7. He had data that moon revolves round the earth in 27.3 days. Its distance from earth is R = 3.85 ×105 km. The acceleration of moon is ,therefore, α = ω2 R α = 2π 2 × R ( velocity = disp. ) T time = 4π2 ×(3.85 ×105 km) (27.3 days)2 Displacement and time were converted into SI units. He had a belief that earth is making the moon to revolve.But How? = 0.0027 m/s2
  8. 8. Newton was sitting under an apple tree when an apple fell down from the tree on the earth. This sparked the idea that the earth attracts all bodies towards its centre. He declared that the laws of nature are same for earthly and celestial bodies.
  9. 9. The acceleration of a body falling near the earth’s surface is about 9.8 m/s2 and moon’s acceleration is 0.0027m/s2 .Thus, aapple amoon = 9.8 m/s2 0.0027 m/s2 Also, distance of the moon from the earth distance of the apple from the earth dmoon dapple 3.85 ×105 km 6400 km = 3600. ....(i) aapple amoon = dmoon dapple 2 = = = 60 ….(ii) By comparing (i)&(ii)
  10. 10. Newton guessed that, acceleration a ∝ 1 r2 …..(1) He had, F ∝ ma ; (Newton’s second law) …..(2) . ˙ . F ∝ m . ( From (1) ) r2 …..(3) By Newton’s Third law of motion, F ∝ M …..(4) Combining 3 & 4, F ∝ Mm r2
  11. 11. F = GMm r2 where, – F = Force of attraction between the two particles. – M = mass of first particle. – m = mass of second particle. – r = distance between the centers of the first and second particle. – G = Universal gravitational constant. = 6.67 × 10-11 N·m2 /kg Dimensional formula of F is [MLT-2 ] S.I. Unit = N (Newton) C.G.S. Unit = dyne
  12. 12. m1 m2 ř12 ř21 r F12 = - Gm2m1 r2 F21 = - Gm1m2 r2 ř21 ř12 Note : -(minus) sign denotes that opposite direction of force and Distance.
  13. 13.  Always acts as “Force of Attraction”.  Form an action-reaction pair.  Central Forces.  Independent of the presence of other bodies and properties of the intervening medium.  Weakest Force.
  14. 14. The force of attraction between any two material particles is directly proportional to the product of the masses of the particles and inversely proportional to the square of the distance between them. It acts along the line joining the two particles. i.e, F ∝ Mm r2
  15. 15.  First measurement was done by Cavendish in 1798,about 71 years after the law was formulated.  The Gravitational constant G is a small quantity and its measurement needs very sensitive arrangement.  Value of G was given through Cavendish Experiment. Calculating the Gravitational Constant
  16. 16. In 1798 Sir Henry Cavendish suspended a rod with two small masses (red) from a thin wire. Two larger mass (silver) attract the small masses and cause the wire to twist slightly, since each force of attraction produces a torque in the same direction. By varying the masses and measuring the separations and the amount of twist, Cavendish was the first to calculate G. G = 6.67 × 10-11 N·m2 /kg2 Cavendish’s Experiment
  17. 17.  Earth was treated as a single particle placed at its centre.  Newton spent several years to prove that a spherically symmetric body can be replaced by a point particle as its centre.  In this process he discovered the methods of Calculus.  He did it by use of Calculus.  It was then, applicable for the bodies if their entire mass were concentrated at their centre of mass.  Hence, it is applicable to all, whatever the size may be. Assumptions
  18. 18.  It is a Universal Law. It explains motion of heavenly bodies.  The predictions of eclipses comes true.  Tides in oceans because of attraction between moon and ocean water.  The predictions about orbits and time periods of artificial satellites found to be correct.
  19. 19. Gravity is the force by which earth attracts a body towards its centre. F e= GMem Re 2 where, – Fe = forces of attraction between Earth and particle of mass m. – Me = mass of Earth. – m = mass of particle. – Re = distance between the centers of the Earth and particle. – G = Universal gravitational constant. = 6.67 × 10-11 N·m2 /kg
  20. 20.  Follows Newton's Law of Universal Gravitation  By Newton’s second law , F = mg  Compare with F = mg so g = GM/r2  g depends inversely on the square of the distance  g depends on the mass of the planet  Nominally, g = 9.81 m/s2 or 32.2 ft/s2 • At the equator g = 9.78 m/s2 • -At the North pole g = 9.83 m/s2 • g on the Moon is 1/6 of g on Earth.
  21. 21.  Provides necessary centripetal force to moon to revolve.  Provides force to Satellites to revolve round the earth.  To make the bodies fall from height.  Formation of Tides in the ocean.
  22. 22. Fg,lead = GMEarthMlead REarth 2 Fg,wood = GMEarthMwood REarth 2 22 , 1 • Earth earth leadEarth leadearth lead leadg lead R GM MR MGM M F a === 22 , 1 • Earth earth woodEarth woodearth wood woodg wood R GM MR MGM M F a === Lead Wood aawoodwood aaleadlead Q. If two bodies one of lead and other of wood of same volume are fallen from same height from the state of rest. Then which will strike to the ground first?(Neglect air-resistance) Sol. …..(a) …..(b)
  23. 23. Let, h be their height above the ground. By second equation of motion, S = ut + 1/2at2 For lead, h = 1/2aleadt1 2 ; …..(c) For wood, h = 1/2awoodt2 2 ; ..…(d) Equating (c)&(d), 1/2aleadt1 2 = 1/2awoodt2 2 t1 2 = t2 2 Or, t1 = t2 Thus, they will reach earth at same instant. (From (a) &(b))
  24. 24.    Books Prof. H.C.Verma : Concept of Physics Vol. I Kumar,Mittal : ISC PHYSICS Class XI Modern ABC : Physics Vol.I
  25. 25. THANK YOU