Physics of Amusement Park Rides
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Physics of Amusement Park Rides. The Carousel Ferris Wheel Loop-the-Loop The Rotor. The Carousel: An Example of Uniform Circular Motion. Turning about axis O w/ Constant Angular Speed . Axis O. . Draw the Forces on the Rider. What is the nature of the net force on

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Physics of Amusement Park Rides

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Physics of amusement park rides

Physics of Amusement Park Rides

  • The Carousel

  • Ferris Wheel

  • Loop-the-Loop

  • The Rotor


Physics of amusement park rides

The Carousel: An Example of Uniform Circular Motion

Turning about axis O

w/ Constant Angular Speed 

Axis O


Physics of amusement park rides

Draw the Forces on the Rider

What is the nature of the net force on

the rider ? Where is this pointing ?

Central force pointing to O

What provides the net force on him ?

The normal support force

of the back of the seat

What kind of net force along the y-axis ?

Is there motion along y ?

y: stationary uniform motion

What is the sensation he feels ?

Pressed against the chair

(or alternatively, chair pressing against his back)

How can this be enhanced ?

Increase 

O

y

N’ = mg

N = mv2/R

x

mg


Physics of amusement park rides

The Ferris Wheel

“Weightless” Feeling

at the top

‘Heavy’ feeling at

the bottom


Physics of amusement park rides

Draw the Forces on the Rider

constant 

2

N

What is the nature of the net force on

the rider ? Where is this pointing ?

a central force

mg

At 2: mg - N = mv2/R

or N = mg - mv2/R

‘feels lighter’

1

At 1: N - mg = mv2/R

or N = mg + mv2/R

‘feels heavier’

3

N

What is the sensation he feels

At locations 2 and 4 ?

4

mg

What happens if the rotational speed is increased beyond (gR)1/2?

He flies off upon reaching position 2


Physics of amusement park rides

The Roller Coaster

SLOW

FAST

Weightless Sensation

Heavy Sensation


Physics of amusement park rides

How is Energy conserved in the roller coasterride ?

Potential Energy = mgh

Kinetic Energy= 0

A.

C

Vo = 0

h

R

B. KE = (1/2) mv2

PE = 0

To clear the top of the loop, h  2R.

In fact, ignoring friction, minimum h = 2.5 R


Physics of amusement park rides

Draw the Forces on the Rider

constant 

What is the nature of the net force on

the rider ? Where is this pointing ?

A central force towards O

2

v

Radius R

At 2: N + mg = mv2/R

or N = mv2/R - mg

N

mg

1

O

At 1:N - mg = mv2/R

or N = mg + mv2/R

N

3

What is the sensation he feels

at locations 2 and 4 ?

Heavier at 4, lighter at 2

4

mg

What happens if the speed v is decreased below (gR)1/2?

Rider falls out of car at 2, if not wearing harness.


Physics of amusement park rides

The Rotor

Radius R

  • A large cylinder spins.

  • You are thrown and pinned against the wall.

  • The floor then slides out.

  • Yet you do not fall.


Physics of amusement park rides

Draw the forces on the rider

‘pinned’ to the rotor’s wall:

Friction

f = N

N= Fc = mv2/R

rotor wall

Floor pulled out

mg

The central force Fc is provided by the normal or

support force N from the rotor’s walls.

For a minimum rotor speed, the normal force is large enough

that the friction f is enough to overcome the weight mg, keeping

the man pinned to the wall.

The critical minimum speed is solved from mg = N =mv2/R

or v = (gR/)1/2


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