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Horizontal and Vertical Circles

Horizontal and Vertical Circles . Car on Curve Car on banked Curve Horizontal vs. Vertical Circle Vertical circle at top Examples . More complicated examples 1. Car on Track with Friction Example 5-6 μ mg = mv 2 /r. More complicated examples 2. Car on Banked Track Example 5-7

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Horizontal and Vertical Circles

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  1. Horizontal and Vertical Circles • Car on Curve • Car on banked Curve • Horizontal vs. Vertical Circle • Vertical circle at top • Examples

  2. More complicated examples 1 • Car on Track with Friction • Example 5-6 • μ mg = mv2/r

  3. More complicated examples 2 • Car on Banked Track • Example 5-7 • Don’t use tilted axes • FNcosθ = mg, • FN sinθ = mv2/r • tanθ = v2/rg

  4. Horizontal vs.Vertical Circle • Horizontal - circular perp. (┴) to gravity • Vertical – circular inline with gravity • Situations • Ball on a cord (tension only pulls in) • Car going over hump (normal pushes up)

  5. Vertical circle at the top • Inside Problem • Tension force (ball on string) - v starts high, slowing down mg + FT = mv2/r • Outside Problem • - Normal force - (car on hump) v starts low, speeding up mg - FN = mv2/r FT mg FT adds to mg for high RHS. As RHS gets smaller, mg takes over and FT not needed Required ma starts high, gets smaller as v decreases FN mg Required ma starts low, gets larger as v increases FN balances mg for low RHS. As RHS gets larger more mg required and FN not needed

  6. Vertical Circle Examples • Situations • Ball on a cord (tension only pulls in) • Car going over hump (normal pushes up) • Example 5-4 (ball on vertical string) • (“inside problem”) • Problem 14 (sports car on hump) • (“outside problem”) • Problem 15 (ferris wheel) • (“outside problem”) • Problem 16 (bucket with water) • (“inside problem”)

  7. Examples - “Inside” Vertical Circle • Example 5-4 (ball on vertical string) • 0.15 kg ball on 1.1 m cord • What speed does string go slack at top? • What is tension for v = 5 m/s? • Problem 16 (bucket with water) • 2 kg bucket on 1.1 m cord • Tension at bottom 25 N, what is speed at bottom? • What speed does string go slack at top?

  8. Examples - “Outside” Vertical Circle • Problem 14 (sports car on hump) • 950 kg car, 95 m radius hump • Goes over top at 22 m/s • What is normal force of road? • What is normal force on 72 kg driver? • What speed does driver feel weightless? • Problem 15 (ferris wheel) • 7.5 m radius ferris wheel • weightless at top

  9. Example – Roto-Ride • 4.6 m drum radius • 0.5 rev/sec frequency (14.45 m/s) • Radial • Vertical • Dividing vertical by Radial

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