Horizontal and Vertical Circles

1 / 9

# 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

I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.

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

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript
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