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Understanding Force and Motion II: Circular Motion and Drag Forces

Explore drag force and terminal speed, revisit uniform circular motion, and solve sample problems in this physics review session. Learn Newton's laws, centripetal forces, and why objects appear weightless in orbit.

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Understanding Force and Motion II: Circular Motion and Drag Forces

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  1. Class 14 - Force and Motion II Chapter 6 - Friday September 24th • Review drag force and terminal speed • Uniform circular motion revisited • Sample problems Reading: pages 99 thru 130 (chapter 6) in HRW Read and understand the sample problems Assigned problems from chapter 6: 8, 18, 20, 28, 30, 32, 40, 50, 52, 68, 84, 102 These will be due on Sunday October 3rd Note: chapter 5 homework deadline THIS SUNDAY! Exams available for pick-up now or in NPB1100.

  2. Drag force and terminal speed Mass • v is the velocity of the body. • ris the air density (mass unit per volume). • A is the effective cross sectional area of the body. • Cis the drag coefficient (typical values range from 0.4 to 1).

  3. Drag force and terminal speed Mass Newton's 2nd law: Terminal speed when a = 0.

  4. Terminal speeds in air

  5. The mysterious sliding stones - the remote Racetrack Playa in Death Valley, California 20 kg, mk = 0.80, A = 0.040 m2, C = 0.80, r = 1.21 kg/m3

  6. Review of uniform circular motion • Since v does not change, the acceleration must be perpendicular to the velocity. • Although v does not change, the direction of the motion does, i.e. the velocity (a vector) changes. • Thus, there is an acceleration associated with the motion. • We call this a centripetal acceleration.

  7. Newton's second law m

  8. Newton's second law m

  9. Newton's second law m

  10. Newton's second law m Centripetal force always directed towards the center of the motion

  11. More on Newton's laws • However, the magnitudes a, F, v and r are constants of the motion. • The frame in which the mass is moving is not inertial, i.e. it is accelerating. • Therefore, one cannot apply Newton's laws in the moving frame associated with the mass. • However, we can only apply Newton's laws from the stationary lab frame. • Examples of centripetal forces: gravity on an orbiting body; the tension in a string when you swirl a mass in around in a circle; friction between a car's tires and the racetrack as a racing car makes a tight turn....

  12. The normal forces between the roller coaster and tracks • The normal forces between you and the roller coaster

  13. So why do you appear weightless in orbit?

  14. So why do you appear weightless in orbit?

  15. So why do you appear weightless in orbit?

  16. So why do you appear weightless in orbit?

  17. So why do you appear weightless in orbit?

  18. So why do you appear weightless in orbit? • Gravity still exerts a centripetal force on your body! • However, this force acts upon each and every atom in your body, i.e. the centripetal force is distributed evenly over your entire body. • There is no normal force, as was the case in the roller coaster. There, the centripetal force was concentrated at the part of your body pushing against the roller coaster. • It is the normal force that gives us the sensation of weight. In orbit, we experience no normal force, so we feel weightless. • We are never massless!

  19. Looping the loop

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