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Physics of Technology PHYS 1800

Physics of Technology PHYS 1800. Lecture 11 Circular Motion and Gravitational Force. PHYSICS OF TECHNOLOGY Spring 2009 Assignment Sheet. *Homework Handout. Physics of Technology PHYS 1800. Lecture 11 Circular Motion and Gravitational Force. Introduction and Review.

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Physics of Technology PHYS 1800

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  1. Physics of TechnologyPHYS 1800 Lecture 11 Circular Motion and Gravitational Force

  2. PHYSICS OF TECHNOLOGYSpring 2009 Assignment Sheet *Homework Handout

  3. Physics of TechnologyPHYS 1800 Lecture 11 Circular Motion and Gravitational Force Introduction and Review

  4. Describing Motion and Interactions Position—where you are in space (L or meter) Velocity—how fast position is changing with time (LT-1 or m/s) Acceleration—how fast velocity is changing with time (LT-2 or m/s2) Force— what is required to change to motion of a body (MLT-2 or kg-m/s2) We will focus on a special kind of force, termed a central forces [e.g., gravity, Coulombic (charge) or centripetal forces]. Important: Velocity, acceleration and force are VECTORS!!!

  5. The Math Approach • We are going to explore a different kind of force that is no longer constant, but is proportional to 1/r.  k/r

  6. Newton’s Laws in Review • 1st Law—a special case of the 2nd Law for statics, with a=0 or Fnet=0 • An objects velocity remains unchanged, unless a force acts on the object. • 2nd Law(and 1st Law)—How motion of a object is effected by a force. • The acceleration of an object is directly proportional to the magnitude of the imposed force and inversely proportional to the mass of the object. The acceleration is the same direction as that of the imposed force. • 3rd Law—Forces come from interactions with other objects. • For every action(force),there is an equal but opposite reaction(force).

  7. Net Forces • It is the total force or net force that determines an object’s acceleration. • If there is more than one vector acting on an object, the forces are added together as vectors, taking into account their directions.

  8. Free Body Diagrams • Fancy Science: Vector analysis of complex force problems is facilitated by use of a free body diagram. • Common Sense: A picture is worth a 100 words. (A scale picture is worth an A!) • Key is to: • Isolate a single body and draw all the forces acting on it. • Add up all the arrows (vectors). • What’s left is the net force. • Net force (and masses)  a. • A plus initial conditions motion!

  9. Does the circular motion of the moon around the Earth ... ... have anything in common with circular motion on Earth?

  10. A ball is whirled on the end of a string with constant speed when the string breaks. Which path will the ball take? • Path 1 • Path 2 • Path 3 • Path 4 • Path 3, in the direction of the tangent to point A. Neglecting gravity, the body would move in the direction it was moving when the force disappeared, in accordance with the first law.

  11. If the string breaks, the ball flies off in a straight-line path in the direction it was traveling at the instant the string broke. • If the string is no longer applying a force to the ball, Newton’s First Law tells us that the ball will continue to move in a straight line. • Circular motion is called centripetal motion, with the string providing a centripetal force.

  12. Centripetal Acceleration • Centripetal accelerationis the rate of change in velocity of an object that is associated with the change in direction of the velocity. • Centripetal acceleration is always perpendicular to the velocity. • Centripetal acceleration always points toward the center of the curve (It’s a central force!). F~1/r A central force!

  13. Centripetal Acceleration • Centripetal accelerationis the rate of change in velocity of an object that is associated with the change in direction of the velocity. • Centripetal acceleration is always perpendicular to the velocity. • Centripetal acceleration always points toward the center of the curve. • The centripetal force refers to any force or combination of forces that produces a centripetal acceleration.

  14. A Simple Demonstration of Centripetal Force(with commentary by Newton) • The horizontal component of T produces the centripetal acceleration. • The vertical component of T is equal to the weight of the ball. • At higher speeds, the string is closer to horizontal because a large horizontal component of T is needed to provide the required centripetal force.

  15. Centripetal Forces—Negotiating a Flat Curve • The centripetal force is the total force that produces a centripetal acceleration. • The centripetal force may be due to one or more individual forces, such as a normal force and/or a force due to friction. • TheStatic force of friction is the frictional force acting when there is no motion along the surfaces. • No skidding or sliding • TheKinetic force of friction is the frictional force acting when there is motion along the surfaces.

  16. Centripetal Forces—Leaning Into a Curve • The friction between the tires and road produces the centripetal acceleration on a level curve. • On a banked curve, the horizontal component of the normal force also contributes to the centripetal acceleration.

  17. What forces are involved in riding a Ferris wheel? Depending on the position: • Weight of the rider • Normal force from seat • Gravity

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