THE VIPERTHE VIPER(Six Flags Over Magic Mountain)

188 feet high70 mph

One of the largest looping roller coasters in the world

3.3 Carousels3.3 Carousels and Roller and Roller CoastersCoasters

Top Thrill DragsterTop Thrill Dragster(Cedar Point)

420 feet tall120 mph0 to 120 mph in 4 sec

“ …free-falls back to Earth, reaching a speed of 120 mph for the second time…”

$ 25 million

Amusement park rides are fun when they make us accelerate around loops, twists, turns, etc.

WHY?

New ideas for todayNew ideas for today•Feeling of acceleration•Circular motion•Roller coaster physics!

•Which direction is the force on the driver?•Which way is the feeling of acceleration?

At the start of a NASCAR race…At the start of a NASCAR race…

F

Feeling of accelerationFeeling of acceleration

What about at the end of a race?What about at the end of a race?

F

Feeling of acceleration

Which way do you feel the Which way do you feel the acceleration for circular motion?acceleration for circular motion?

Feeling of acceleration

Force

But the cables pull you inward!

FFeeling of accelerationFeeling of acceleration

Circular motion:Circular motion: force is toward center of circle

Note: the kid in the middle feels no acceleration!

v

a t

Try this at home – acceleration always points toward the middle of the circleUniform circular motion – constant speed

Tennis ball on stringTennis ball on string

22

c

va r

r Centripetal Centripetal

accelerationacceleration2

2

c c

vF ma m

rm r

Centripetal Centripetal forceforce

•Always points to center of circle•As you move to the edge of the

carousel: is constant, force increases, speed increases

So far:So far:•Feeling of acceleration always opposite to acceleration:

FOA = -ma•Uniform circular motion involves force toward center of circle

The experience of weightThe experience of weight

The force of your weight causes a series of support forces between parts of your body

Force from accelerating elevator

Your body senses Your body senses changes in these changes in these support forces as support forces as a change in a change in weight!weight!

The Feeling of The Feeling of AccelerationAcceleration and and Apparent WeightApparent Weight

AW = W + FOA

Feeling of accelerationFeeling of acceleration

Feeling is caused by your support forces Feeling is caused by your support forces acting on your bodyacting on your body

It points in the direction opposite the It points in the direction opposite the accelerationacceleration

It has a strength proportional to the It has a strength proportional to the accelerationacceleration

““Apparent weight” is felt due to the combined effects of gravitational Apparent weight” is felt due to the combined effects of gravitational acceleration and the feeling of accelerationacceleration and the feeling of acceleration

Acceleration and Acceleration and WeightWeight

A woman is riding one of those “barrel of fun” rides at the amusement park. Which one of the diagrams best shows the forces acting on the woman?

A B C D E

Clicker QuestionClicker Question

Feeling ofacceleration

Apparent weight

Clicker QuestionClicker QuestionWhat has to be true about the acceleration a of the vomit comet (if the apparent weight of the passengers is zero)?

A. a points upwardB. a points downwardC. a points towards the

center of their circular trajectory

Roller coastersRoller coasters

You better believe in conservation of energy if you want to live!

“Most people find this sudden reduction in apparent weight terrifying.”

Note: this is not uniform circular motion!Note: this is not uniform circular motion!

LoopLoop

At top of loop:At top of loop:

acceleration is large and downwardacceleration is large and downward so feeling of acceleration is large and so feeling of acceleration is large and

upwardupward apparent weight is therefore much less apparent weight is therefore much less

than equilibrium weight: than equilibrium weight: can feel weightless or even feel force can feel weightless or even feel force upward.upward.

Roller Coaster LoopsRoller Coaster Loops

Just over the top of hill Just over the top of hill (think about descent),(think about descent), acceleration is mostly downwardacceleration is mostly downward so feeling of acceleration is mostly upwardso feeling of acceleration is mostly upward apparent weight is therefore less than equilibrium weight, and into apparent weight is therefore less than equilibrium weight, and into

the track.the track. Just past the bottom of hill Just past the bottom of hill

(think about ascent),(think about ascent), acceleration is mostly upwardacceleration is mostly upward So feeling of acceleration is mostly downwardSo feeling of acceleration is mostly downward apparent weight is therefore more than equilibrium weight, and into apparent weight is therefore more than equilibrium weight, and into

the track.the track.

Roller Coasters HillsRoller Coasters Hills

Why we want theWhy we want thelast seat on the last seat on the roller coasterroller coasterThe weight of the first cars

combined accelerates the last cars over the hill

See you next class!

For next class: Read Section 4.1