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

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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 = mv2/r

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 - 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

- 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

- 4.6 m drum radius
- 0.5 rev/sec frequency (14.45 m/s)
- Radial
- Vertical
- Dividing vertical by Radial

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