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Centripetal Motion

Things that go round and round…. Centripetal Motion. What you already know…. When on snowboarding and you want to turn to the right, what do you do? Why does that work? What if your board can’t cut into the snow?. F f. Turns. When turning, are you accelerating?

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Centripetal Motion

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  1. Things that go round and round… Centripetal Motion

  2. What you already know… • When on snowboarding and you want to turn to the right, what do you do? • Why does that work? • What if your board can’t cut into the snow? Ff

  3. Turns • When turning, are you accelerating? • Turning = Change in direction = Accelerating • Proof? • Δv = vf - vi • So… vf = Δv + vi vf vi Δv vi vf

  4. Centripetal Acceleration (ac) • Since the Dv is towards the center, the direction of the acceleration is to the center of a circle. • ac = v2/r • Also, since v = Dx/T then v = 2pr/T • ac = v2/r = 4p2r/T2 • This is more useful at times as you can easily measure time and distance.

  5. Centripetal Force (Fc) • In what direction does the net force act when making a turn? • ALWAYS to the center of the circle. • Fnet = Fc and both are the sum of forces… not a true force (so you never draw it on an FBD).

  6. Centripetal Lab • Think back to the lab you just completed. • Draw a FBD of the stopper. • Draw a FBD of the hanging mass. • What force/s caused the centripetal force? • Evidence?

  7. Running Practice • What is the acceleration on a runner sprinting at 9.0m/s around the turn on a track with a radius of 27m? • 3.0 m/s2 • Why can a runner go faster on the straights?

  8. Making the Turn • What is the centripetal force on a 1200kg car going around a 45m radius turn at 12m/s? • 3840 N • What is the friction on you to not slide on the seat?

  9. Tubing behind a boat… • You find that it is more difficult to hold on to the tube and make the turn as the speed of the boat increases. Why is this? Be sure to discuss centripetal force in your reason. • Write down your reasoning… pictures/diagrams may help you explain yourself.

  10. Heliocentric Model • Our 5.97 x 1024kg Earth circles the sun. Assume (incorrectly but do so any how) that our orbit is a perfect circle with a radius of 1.50 x 108km. • What is the Earth’s acceleration? • 5.95x10-3m/s2 • What is the centripetal force on the Earth? • 3.55x1022N

  11. Kids Today… • Mary has a mass of 56kg and sits 30.cm from the center of the merry-go-round. If she makes 5 revolutions in 3 seconds: • How much centripetal force must exist if she is to stay on the merry-go-round? • 1842 N • Would it be easier, the same, or more difficult if she sits 60.cm from the center of the merry-go-round? Prove it mathematically. • 3685 N • Explain the findings so that a junior could understand it. (Hint: consider your acceleration) GENIOUS

  12. Going Vertical • Unlike horizontal circular motion, vertical motion changes both in speed and direction. • Where does the object travel the fastest? • And the slowest?

  13. Special Situations • Spinning a brick on a rope: • Top • Draw the FBD • Bottom • Draw the FBD

  14. Top of the Circle • Both FT and Fg are straight down and toward the center of the circle. • Which way does Fnet point? • Which way does Fc point? • If the brick has the minimum velocity necessary to make the turn, how does the tension in the rope compare to the force of gravity?

  15. Minimum Velocity • Who does cares about minimum velocity? • What minimum velocity must the 1.00-kg brick achieve in order to continue through the top of the circle made by the 1.00-m rope? • 3.13m/s • What is the tension in the rope at the top of the path? • ZERO! • How would the minimum velocity change if we were on the moon (a=1.64m/s2)? • Decreases • Prove it. • 1.28m/s

  16. Bottom of the Circle • How does the tension force compare to the gravitational force? Why must this be true? • If the brick experiences a velocity of 7.00m/s at the bottom, then what tension will be in the rope as the brick passes through the lowest point in its path? • 58.8N

  17. Not Top or Bottom of Circle? • Let’s not go here today…

  18. Hills • While driving to school you pass over a "crest" in the road that has a radius of 30 meters. • Do you feel lighter, the same, or heavier? Why? • How fast would you need to be traveling to experience apparent "weightlessness" while passing over the crest? • 17.2m/s

  19. Pendulum • Spiderman has a mass of 78.0-kg. To save a child 12.2-m below him from death, he shoots out webbing and swings down. Spiderman reaches the kid at the bottom of his swing at what velocity if the tension in the web is 2301N? • 15.5m/s 12.2 m FT = 2301N V = ? Fg Fg

  20. Ferris Wheel(Using constant acceleration) • While at the top of the 25-m radius Ferris Wheel you (65-kg) are stopped while others get off of it. Then the brakes go out and it is allowed to rotate freely. YIKES!!! • What will happen to your apparent weight as you fall? • What is your maximum apparent weight? • 3200N

  21. Swings • Two guys share a double harness, totaling a mass of 165kg. The harness is attached to a 53m “special” rope swing. The guys then lean backwards off of a bridge. • When (consider the path they will take) will the net force on the guys be at its greatest? Explain. • They experience a maximum centripetal force of 3238N, how fast are they traveling at this point? • What is the centripetal force on the guys at the top of the swing’s path? Explain. • Do you dare?

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