Horizontal and vertical circles
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Horizontal and Vertical Circles PowerPoint PPT Presentation


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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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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

More complicated examples 1

  • Car on Track with Friction

    • Example 5-6

    • μ mg = mv2/r


More complicated examples 2

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


Horizontal vs vertical circle

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)


Vertical circle at the top

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


Vertical circle examples

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”)


Examples inside vertical circle

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?


Examples outside vertical circle

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


Example roto ride

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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