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# Horizontal and Vertical Circles - PowerPoint PPT Presentation

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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## PowerPoint Slideshow about ' Horizontal and Vertical Circles ' - arch

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Presentation Transcript

• Car on Curve

• Car on banked Curve

• Horizontal vs. Vertical Circle

• Vertical circle at top

• Examples

• Car on Track with Friction

• Example 5-6

• μ mg = mv2/r

• 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 - 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)

• 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

• 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

• 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

• 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