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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:
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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.
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).
Drag force and terminal speed Mass Newton's 2nd law: Terminal speed when a = 0.
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
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.
Newton's second law m Centripetal force always directed towards the center of the motion
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....
The normal forces between the roller coaster and tracks • The normal forces between you and the roller coaster
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!