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Horizontal and Vertical Circles PowerPoint Presentation

Horizontal and Vertical Circles

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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

- Tension force (ball on string) - v starts high, slowing down
- Outside Problem
- - Normal force - (car on hump) v starts low, speeding up
mg - FN = mv2/r

- - Normal force - (car on hump) v starts low, speeding up

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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