Upcoming Classes

Thursday, Sept. 13th

Motion and Dance, Part 2

Assignment due:

* Read “Motions without Turns”, Physics and the Art of Dance, K. Laws, Pages 36-51

* First draft of first oral presentation or written paper

Tuesday, Sept. 18th

Dance at the Nexus Assignment due:

* Read “The Mechanics of Movement”, The New Way Things Work, D. Macaulay, Pages 8-27

Upcoming Deadlines

Thursday, September 13th

First draft of your first term paper or your

oral presentation

Thursday, September 27th

First Set of Oral Presentations

First term paper (if not giving presentation)

Oral Presentations

The following persons will give oral presentations on Thursday, September 27th :

• Batres, Adan• Boyd, Heidi• Chen, Emily• Kwiatkowski, Dajon• Lebedeff, Christopher• Lipton, ChristopherFor everyone else, your first term paper is due on

that date.

Extra Credit: SF Museum of Art

Visit San Francisco Museum of Modern Art and see Abstract Expressionist paintings.

Turn in your ticket receipt ($7 for students). Worth one homework assignment; deadline is Oct. 16th

Guardians of the Secret, Jackson Pollock, 1943

Extra Credit: San Jose Ballet

See a performance of San Jose Ballet in San Jose Center for Performing Arts (Nov. 15th – 18th ).

Turn in your ticket receipt. Worth one homework assignment or three quiz/participation credits.

Ramon Moreno in CARMINA BURANA

Extra Credit: Cypress Quartet

SJSU Celebrates 150th with Cypress String Quartet Event Fusing Precision Playing with World-Class Technology

SJSU Music Concert Hall, 7 p.m. Thur., Sept. 20th.I will hand out tickets at the door from 6:30 to 6:50pm; don’t be late to the performance! Worth two quiz/participation extra credits.

Quiz

Put your name on a sheet of paper and answer the following questions from today’s reading assignment:

What is a Grand Jeté?

What is the Grand Jeté “Floating” Illusion?

Motion & Dance (I)

Balance and

Motion without Turns

Dance

Dance is artistic motion of the human body.

Ballet

Acrobats(Cirque du Soleil)

BreakDancing

Athletics

Tommie Smith & John CarlosMexico City 1968 Olympics

Newton’s Laws of Motion

Physical motion is governed by Newton’s three laws of motion:

1.Principle of Inertia

2.Force = Mass x Acceleration

3.Action & Reaction

We’ll see how these laws apply to dance.

Sir Isaac Newton(1643 – 1727)

Newton’s First Law of Motion

An object moves with constant, uniform motion until acted on by a force.

FO

RC

E

No force

First Law (Full Version)

An object at rest remains at rest &an object in motion remains

in uniform motion*,unless a force acts on the object.

*Moving in a straight line with constant speed.

First Law is also known as principle of inertia.

Demo: Tablecloth Pull

Tablecloth

FlowerVase

Yank quickly

Due to the vase’s inertia it remains at rest since almost no force acts on the vase if one pulls quickly & straight.

Demo: Riding Light Rail

When a moving train stops, you continue moving forward.

When the stopped train starts moving again, you remain stationary and are thrown backwards.

In both cases, it’s due to your inertia.

Follow-through & Inertia

Follow-through is a good example of the principle of inertia.

An object won’t move until a force acts on it so long hair trails behind as head turns.

Hair then remains in motion even after the head stops turning.

Net Force

same as

The Newton is metric unit of force (about 1/5 pound).

When several forces act on an object, the forces add together.

Sum of forces called net force or total force

BRICK

3 Newtons5 Newtons

8 Newtons

Equilibrium Rule

same as

If an object is at rest then the net force must be zero. Similarly if in uniform motion.

BRICK3 Newtons 3 Newtons

Zero Newtons(No Force)

When this happens we say that forces “balance.”

Support Force

Solid surfaces exert a force, called a support force, on objects pressed against them.

100 NewtonGold Brick

100 NewtonSupport force

Downward force (weight) balanced by upward force (support).

How much is the net force on the brick?

Friction ForceOrigin of friction is molecular interaction between

solid surfaces.

Friction is complicated.

Friction depends on support force and on properties of the surface.

Basic properties of friction first established by Leonardo da Vinci.

Forces on a Dancer

Newton’s First Law of Motion states that a stationary object (not moving) remains stationary if the net force on it is zero.

For a dancer, the three main forces are:

• Gravity (Downward)

• Support of the floor (Upward)

• Frictional force of the floor (Horizontal)

Center of Gravity

Average position of an object’s weight distribution is called the center of gravity (CG).

Force of gravity acts on an object as if pulling straight down at the CG.

Centerof

Gravity

Stability & Balance

Object is stable if CG is above the base.

CG CG

Wei

ght

Wei

ght

BASEAxis

AxisBASE

STABLE

UNSTABLE

Sup

port

Sup

port

Demo: Find your Center

Your CG is

roughly in the

center of your

body.

Varies with

orientation.

CG CG

STABLE UNSTABLE

Demo: Balanced Bird

Where is the bird’s center of gravity?

Point of support is the tip of the beak. Center of gravity must be directly above or below that point. Wings are weighted so CG is below the beak.

Balance & Dance

On one foot

Feet flat on the floor

Balance is

OK anywhere

in here

Center of Gravitylocated above thedancer’s toe

The force of gravity and the support force of the floor can balance only when a dancer’s center of gravity is located above the base of support.

Base of Support with a Partner

x

x

Center ofGravity

Two dancers, together, can form a larger base of support.

The center of gravity is roughly located in between the two dancers, as shown.

What happens if he shifts his front foot back?

What if he shifts his back foot forward?

Ballet Barre

The ballet barre also extends the base of support, with the hand acting as a “third foot.”

Base ofSupport

Foot

Toe

Hand

Motion & Center of Gravity

2

3

4

5

7

3

1 5

1

6

7

A spinning object turns about its center of gravity as it flies through the air.

The center of gravity follows a parabolic trajectory which is the same for all objects.

Note: If axe is about 10” long then 4 frames between keys.

General tumbling motion (e.g., throw a chair) is very complicated!

Arbitrary

Movie: Grand Jeté

2 ft

7.1 ft

While a dancer is in the air (not in contact with the floor) the only force on the dancer is gravity and the trajectory of the center of gravity is a parabolic arc.

During a two foot vertical jump a dancer is in the air for slightly less than ¾ of a second.

If the dancer’s horizontal speed is 10 feet per second then the CG travels about 7.1 feet during the jump.

CG

CG

Jumps & Center of Gravity

If the dancer jumps a lesser height then the time in the air decreases

Shifting the Center of Gravity

By raising their arms and legs, dancers can raise the location of their center of gravity (CG).

CG CG

Near hips

Lower torso

Grand Jeté Floating Illusion

2 ft

1.3 ft

Shifting the CG upward, the distance the dancer’s head rises is reduced, giving illusion of floating longer.

Time in the air is 25% longer than a similar leap where the CG rises only 1.3 feet

Half the time in the jump is spentbetween these two points

Top of the dancer’s headspends half the time of the

jump between these two points

Grand Jeté Floating IllusionIllusion of floating is enhance by the fact that during the peak of the jump the vertical motion is the slowest.

Newton’s Second Law of Motion

Acceleration occurs when an object’s velocity changes, such as speeding up or slowing down.

Acceleration depends on Force and Mass.

Acceleration is always in the direction of the net Force acting on an object.

(Acceleration) = (Net Force)

(Mass)

Newton’s Second Law (Part 1)

The greater the force on acting on an object, the greater the acceleration of that object.

The greater the mass of an object, the less it accelerates when acted on by the same force.

Newton’s Second Law (Part 2)

Demo: Spool

Pull on string wrapped around a spool. Force is to the right. In what direction does the spool move?

Spool moves? Spool moves?

Pull Pull

Demo: Tricycle

Pull on tricycle pedal with a string.

Which direction does the tricycle move?

Bike moves? Bike moves?

PullPull

Pedal in top position Pedal in bottom position

Newton’s Third Law of Motion

Whenever an object exerts a force on a second object, the second object exerts a force of equal magnitude in the opposite direction on the first object.

First Object(Hammer)

Second Object(Nail)

Action and Reaction

Common expression of 3rd Law is,

To every action there’s an equal and opposite reaction.

What’s an “action”? A force exerted by one object on second object.

How can reaction be “equal” and “opposite”?Equal in magnitude but opposite in direction.

Demo: Mutual Attraction

What happens when:

• Mr. A pulls, Mr. B holds.

• Mr. A holds, Mr. B pulls.

• Mr. A & Mr. B both pull.

Mr. BMr. A

Mr. B has more mass than Mr. A

Demo: Mutual Attraction (cont.)

If only Mr. A pulls on Mr. B then Mr. B accelerates.

Reaction force of equal magnitude so Mr. A also moves.

Who moves faster? Mr. A, Mr. B, or the same?

ActionReactionMr. A Mr. B

Mr. A goes faster (greater acceleration) since his mass is less.

Mr. B has more mass than Mr. A

Demo: Mutual Attraction (cont.)

When both guys pull then there are two action forces and two reaction forces.

If both pull with same force, how much greater is the acceleration than when only one pulls?

ActionReactionMr. A Mr. B

Twice the force so twice the acceleration (by 2nd Law)

ReactionAction

Demo: Mutual Repulsion

Similar demonstration is to have Mr. A and Mr. B push away instead of pull together.

Same results; if Mr. A pushes and Mr. B holds then both move apart.

Standing on skateboards

ActionReaction

Mr. AMr. B

IMPORTANT!!!

Action force & reaction force NEVER balance each other because they act on different objects!

Repeat this to yourself over and over again

Walking, Running & Jumping

What forces accelerate us into motion when we walk, run, or jump?

Forces on a Dancer

For a dancer, the three main forces are:

• Gravity (Downward)

• Support of the floor (Upward)

• Frictional force of the floor (Horizontal)

Only these forces can accelerate the dancer.

Gravity is constant but the force exerted by the floor can increase in reaction to the dancer exerting a force on the floor.

ReactionAction

Walking Forward

When weight is on back foot it acts by pushing back on the floor. Reaction is the friction of the floor, which pushes your body forward

If there were no friction then dancer would fall straight down and could not walk forward

X (CG)

Jumping

Jumping is done by pushing downward on the ground (action) so the ground pushes upward on you (reaction).

How high you jump depends on the force and on the distance over which you apply that force.

Can only push while in contact with the ground so squatting helps by increasing distance.

Swinging Arms and Jumping

You swing your arms upward as you jump to increase the force pushing down on the ground.

Try jumping and swinging your arms upward after you leave the ground; you won’t jump as high.

Work & Force

The work done on an object is defined as

(Work done) = (Net Force) x (Distance)

The greater the work done, the greater the change in the object’s velocity.

Pushing Off on a Jump

Notice the orientation of the foot on the ground, which is pushing off on a jump

Push-Off with Turnout

The angle of flex is small so the distance over which the foot exerts a force is small.

Jump will not be very high.

Distance

Push-Off without Turnout

The angle of flex is larger so the distance over which the foot exerts a force is larger.

Jump will be higher.

Distance

Next Lecture Motion & Dance (II)

Remember:Assignment due: First draft or outline

of term paper or oral presentation