THE VIPER THE VIPER (Six Flags Over Magic Mountain) 188 feet high 70 mph One of the largest looping roller coasters in the world 3.3 Carousels and Roller Coasters

Top Thrill Dragster (Cedar Point) 420 feet tall 120 mph 0 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 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… F Feeling of acceleration

What about at the end of a race? F Feeling of acceleration

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

Force But the cables pull you inward!

F Feeling of acceleration 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 circle Uniform circular motion – constant speed Tennis ball on string

Centripetal acceleration Centripetal force Always points to center of circle As you move to the edge of the carousel:  is constant, force increases, speed increases

So far: Feeling of acceleration always opposite to acceleration: FOA = -ma Uniform circular motion involves force toward center of circle

The 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 changes in these support forces as a change in weight!

The Feeling of Acceleration and Apparent Weight AW = W + FOA

 Feeling of acceleration  Feeling is caused by your support forces acting on your body  It points in the direction opposite the acceleration  It has a strength proportional to the acceleration  “Apparent weight” is felt due to the combined effects of gravitational acceleration and the feeling of acceleration Acceleration and Weight

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? ABCDE Clicker Question Feeling of acceleration Apparent weight

Clicker Question What has to be true about the acceleration a of the vomit comet (if the apparent weight of the passengers is zero)? A. a points upward B. a points downward C. a points towards the center of their circular trajectory

Roller 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! Loop

At top of loop:  acceleration is large and downward  so feeling of acceleration is large and upward  apparent weight is therefore much less than equilibrium weight: can feel weightless or even feel force upward. Roller Coaster Loops

 Just over the top of hill (think about descent),  acceleration is mostly downward  so feeling of acceleration is mostly upward  apparent weight is therefore less than equilibrium weight, and into the track.  Just past the bottom of hill (think about ascent),  acceleration is mostly upward  So feeling of acceleration is mostly downward  apparent weight is therefore more than equilibrium weight, and into the track. Roller Coasters Hills

Why we want the last seat on the roller coaster The weight of the first cars combined accelerates the last cars over the hill

See you next class! For next class: Read Section 4.1