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Physics 201

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.

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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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