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Physics 201

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  1. Physics 201 5: Some Application of Newtons Laws • Newtons Second law and Uniform Circular Motion • Newtons Second law and Nonuniform Circular Motion • Motion in Accelerated Frames of Reference • Motion in the Presence of resistive Forces.

  2. In uniform circular motion the acceleration of the object is v 2 ˆ a = - r r c ˆ r is the unit vector pointing from the center of motion to the object What causes this acceleration? It must be a force 2 m v ˆ F = - r r c where m is the mass of the object. This force is called the CENTRIPETAL force

  3. Where do centripetal forces come from? • gravity • tension • friction

  4. v W W = ma = mg ( r ) c ¯ mM v 2 ( ) G = m G is Newtons Gravitational constant e r r 2 ¯ GM v = in order that gravitational force e r sustains uniform circular motion

  5. The force of gravity continually changes the direction of motion of the object, thus keeping it a constant orbit at constant speed as long as the speed is given by • If the speed increases the radius of the orbit increases • If the speed decreases the radius of the orbit decreases

  6. T v If speed increases and length of string is fixed then the tension increases

  7. Car turning on flat road Ff v • If the speed increases and the force of friction does not the radius of turning increases (skidding outward)

  8. Car turning on banked road • 3 situations • 1: Force of friction plays no role and banking provides necessary centripetal force • 2: Banking too great and need outward force of friction • 3: Banking not enough and thus need force of friction to stop outward motion N Ff,out Fc Ff,in  W

  9. For turning speed v , total centripetal force required toward center of motion m v 2 ˆ F = - r c r this force continually deflects velocity to turn car in circle of radius r N Ff direction of Ff is determined by the speed v radius r and banking  Fc  W Forces on car

  10. Motion in Accelerated Frames of Reference N noninertial observer T Ffict W inertial observer only seen by noninertialobserver

  11. Motion in the Presence of resistive Forces. R = - b v consider object dropping in air or a liquid Total vertical force = b v - mg d v Newtons 2 nd law Þ m = b v - mg dt d v b v Þ = - g º Differential Equation dt m which has the solution ( ) mg ( ) - bt v t = 1 - e m b

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