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Upcoming Classes. Thursday, Sept. 13 th 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. 18 th Dance at the Nexus

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    1. 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

    2. 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)

    3. Oral Presentations The following persons will give oral presentations on Thursday, September 27th : • Batres, Adan • Boyd, Heidi • Chen, Emily • Kwiatkowski, Dajon • Lebedeff, Christopher • Lipton, Christopher For everyone else, your first term paper is due on that date.

    4. 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

    5. 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

    6. 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.

    7. 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?

    8. Motion & Dance (I) Balance and Motion without Turns

    9. Dance Dance is artistic motion of the human body. Athletics Ballet Break Dancing Acrobats (Cirque du Soleil) Tommie Smith & John Carlos Mexico City 1968 Olympics

    10. Newton’s Laws of Motion Physical motion is governed by Newton’s three laws of motion: • Principle of Inertia • Force = Mass x Acceleration • Action & Reaction We’ll see how these laws apply to dance. Sir Isaac Newton (1643 – 1727)

    11. Newton’s First Law of Motion An object moves with constant, uniform motion until acted on by a force. No force FORCE

    12. 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.

    13. Demo: Tablecloth Pull Flower Vase Yank quickly Tablecloth Due to the vase’s inertia it remains at rest since almost no force acts on the vase if one pulls quickly & straight.

    14. 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.

    15. 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.

    16. Net Force When several forces act on an object, the forces add together. Sum of forces called net force or total force 3 Newtons 8 Newtons BRICK 5 Newtons same as The Newton is metric unit of force (about 1/5 pound).

    17. Equilibrium Rule If an object is at rest then the net force must be zero. Similarly if in uniform motion. Zero Newtons (No Force) 3 Newtons 3 Newtons BRICK same as When this happens we say that forces “balance.”

    18. Support Force Solid surfaces exert a force, called a support force, on objects pressed against them. Downward force (weight) balanced by upward force (support). 100 Newton Gold Brick 100 Newton Support force How much is the net force on the brick?

    19. Friction Force Origin 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.

    20. 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)

    21. 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. Center of Gravity

    22. Stability & Balance Object is stable if CG is above the base. STABLE CG CG UNSTABLE Weight Weight Support Support Axis BASE BASE Axis

    23. Demo: Find your Center Your CG is roughly in the center of your body. Varies with orientation. CG CG UNSTABLE STABLE

    24. 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. Demo: Balanced Bird Where is the bird’s center of gravity?

    25. Balance & Dance 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. Center of Gravity located above the dancer’s toe

    26. Base of Support with a Partner 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? x Center of Gravity x

    27. Ballet Barre The ballet barre also extends the base of support, with the hand acting as a “third foot.” Hand Base of Support Toe Foot

    28. Motion & Center of Gravity Arbitrary 4 1 5 3 3 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. 2 6 5 General tumbling motion (e.g., throw a chair) is very complicated! 7 1 7 Note: If axe is about 10” long then 4 frames between keys.

    29. Movie: Grand Jeté

    30. Jumps & Center of Gravity 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. If the dancer jumps a lesser height then the time in the air decreases 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

    31. Shifting the Center of Gravity By raising their arms and legs, dancers can raise the location of their center of gravity (CG). Lower torso CG CG Near hips

    32. Grand Jeté Floating Illusion 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

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

    34. 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. (Net Force) (Acceleration) = (Mass)

    35. Newton’s Second Law (Part 1) The greater the force on acting on an object, the greater the acceleration of that object.

    36. Newton’s Second Law (Part 2) The greater the mass of an object, the less it accelerates when acted on by the same force.

    37. Spool moves? Spool moves? Demo: Spool Pull on string wrapped around a spool. Force is to the right. In what direction does the spool move? Pull Pull

    38. Bike moves? Bike moves? Demo: Tricycle Pull on tricycle pedal with a string. Which direction does the tricycle move? Pedal in bottom position Pedal in top position Pull Pull

    39. 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)

    40. 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.

    41. 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. B has more mass than Mr. A Mr. B Mr. A

    42. 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? Mr. B Mr. A Action Reaction Mr. B has more mass than Mr. A Mr. A goes faster (greater acceleration) since his mass is less.

    43. 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? Mr. B Reaction Mr. A Action Action Reaction Twice the force so twice the acceleration (by 2nd Law)

    44. 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. Mr. B Mr. A Action Reaction Standing on skateboards

    45. IMPORTANT!!! Action force & reaction force NEVER balance each other because they act on different objects! Repeat this to yourself over and over again

    46. Walking, Running & Jumping What forces accelerate us into motion when we walk, run, or jump?

    47. 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.

    48. 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 X (CG) If there were no friction then dancer would fall straight down and could not walk forward Reaction Action

    49. 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.

    50. 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.