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Physics 2011

Physics 2011. Lecture 5: Gravitation and Applying Newton's Laws. Chapter 12: Gravitation. Gravity: Action at a distance. Gravitation (According to Newton, Anyway). Newton determined that a moon / g = 0.000278 and noticed that R E 2 / R 2 = 0.000273

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Physics 2011

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  1. Physics 2011 Lecture 5: Gravitation and Applying Newton's Laws

  2. Chapter 12: Gravitation • Gravity: Action at a distance

  3. Gravitation(According to Newton, Anyway) • Newton determined that amoon/g= 0.000278 • and noticed that RE2 / R2= 0.000273 • This inspired him to propose the Universal Law of Gravitation:|FMm|= GMm / R2 amoon g R RE where G = 6.67 x 10 -11 m3 kg-1 s-2

  4. Gravity... • The magnitude of the gravitational force F12 exerted on an object having mass m1 by another object having mass m2 a distance R12 away is: • The direction of F12 is attractive, and lies along the line connecting the centers of the masses. m1 m2 F12 F21 R12

  5. Gravity... • Near the Earth’s surface: • R12 = RE • Won’t change much if we stay near the Earth's surface. • i.e. since RE >> h, RE + h ~ RE. m Fg h M RE

  6. Gravity... • Near the Earth’s surface...  • So |Fg|= mg=ma • a= g =g All objects accelerate with acceleration g, regardless of their mass! Where:

  7. Example gravity problem: • What is the force of gravity exerted by the earth on a typical physics student? • Typical student mass m = 55kg • g = 9.8 m/s2. • Fg = mg = (55 kg)x(9.8 m/s2 ) • Fg = 539 N Fg • The force that gravity exerts on any object is called its Weight W= 539 N

  8. Force and acceleration • Suppose you are standing on a bathroom scale on Earth and it says that your weight is W. What will the same scale say your weight is on the surface of the mysterious Planet X ? • You are told that RX ~ 20 REarth and MX ~ 300 MEarth. (a)0.75W (b)1.5 W(c)2.25 W E X

  9. Ratio of weights = ratio of forces: Solution • The gravitational force on a person of mass m by another object (for instance a planet) having mass M is given by:

  10. Newton’s Third Law: • Forces occur in pairs: FA ,B = - FB ,A. • For every “action” there is an equal and opposite “reaction”. • This is consistent with the discussion of gravitation: m1 m2 F12 F21 R12

  11. Fm,w Fw,m Ff,m Fm,f Newton's Third Law... • FA ,B = - FB ,A. is true for contact forces as well:

  12. Particles in Equilibrium (2-D) • A particle is in Equilibrium when the sum of all forces on the body is Zero (FNET = 0) • By Superposition, Equilibrium can be computed for each dimensional component separately ( ΣFx = 0, Σ Fy = 0)

  13. Dynamics in 2-D • When a body is not in Equilibrium, a Net Force exists in at least one dimensional component: ΣFi = Finet = mai (Note that the Normal Force, n, is perpendicular to the 15 degree Plane)

  14. Friction • The friction force is proportional to the Normal Force: f = μN

  15. Static vs. Kinetic Friction • As the names imply, Static friction is present only when a body is not moving with respect to the surface it is contacting. • Kinetic friction is moving friction. • Static friction, representing the force required to ‘break free’ and start movement is generally greater than its Kinetic counterpart. fs > fk

  16. Friction in Fluids • At low speeds, f = kV • At high speeds, f = DV2

  17. Dynamics of Angular Motion • In angular motion, the Net Force is in the same direction as the Centripetal Acceleration

  18. In UCM, Centripetal Acceleration is the only game at the Fair:

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