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Chapter 3: Measuring Motion

Chapter 3: Measuring Motion. Brent Royuk Phys-110 Concordia University. How Do Things Fall?.

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Chapter 3: Measuring Motion

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  1. Chapter 3: Measuring Motion Brent Royuk Phys-110 Concordia University

  2. How Do Things Fall? • Galileo, 1638: “鄭ristotle says that an iron ball of one hundred pounds falling from a height of one hundred cubits reaches the ground before a one-pound ball has fallen a single cubit. I say that they arrive at the same time.”

  3. Falling Things • Galileo and his famous experiment

  4. Falling Things • Falling objects accelerate at the same rate, g = 9.8 m/s2 • The acceleration is uniform • This is not obvious; Aristotle thought falling objects acquired some characteristic falling speed. • He was thinking of terminal velocity, perhaps? • Galileo: a rock falling 2 m drives a stake much more than a rock falling 10 cm. • g is altitude and latitude-dependent • Linear accelerations can be expressed in g’s (or any type of acceleration) fighter pilots, etc.

  5. Falling Things • ONLY IN VACUUM • Astronaut David Scott, 1971: hammer and feather • video • Painting by astronaut Alan Bean • g on the Moon

  6. Try This • If two objects are dropped one slightly after the other, what happens to the distance between them as they fall? Pretend there’s no air resistance. • It increases • It decreases • It stays the same

  7. Falling Problems • Equations of Motion For falling, what is a? • Examples • Make a table with columns for t,y,v,a. Fill in values for t = 0,1,2,3,4 • A boy throws a ball straight downward from a high bridge at a speed of 12 m/s. How far has it fallen after 3.0 s? How fast is it falling?

  8. The Drag Force • An object moving through a fluid experiences a drag force. • cannon ball sinking in water, car on highway, baseball, parachutist, dust, coffee filters • Fdragv2 • At terminal speed, Fdrag = mg • Equation: •  is density of fluid (1.2 kg/m3 for air), A is cross-sectional area, C is a shape coefficient, generally ranging from 0.5-1

  9. Some Approximate Terminal Speeds • Object Speed (m/s) • cannonball 250 • 16-lb shot 145 • high caliber bullet 100 • sky diver 60-100 • baseball 42 • tennis ball 31 • basketball 20 • mouse 13 • ping-pong ball 9 • penny 9 • raindrop 7 • parachutist 5 • snowflake 1 • sheet of paper (flat) 0.5 • fluffy feather 0.4 You can drop a mouse down a thousand-yard mine shaft and, on arriving at the bottom, it gets a slight shock and walks away. A rat is killed, a man is broken, a horse splashes. -J.B.S. Haldane, British geneticist, 1892-1964

  10. Projectile Motion • Horizontal Launch • What happens if you kick a ball off a cliff?

  11. Projectile Motion • Falling Comparison

  12. Projectile Motion • Horizontal Launch

  13. 100-ft Cliffdiving

  14. Projectile Motion

  15. Projectile Motion • Maximum Range • Estimate the range of a well-thrown baseball.

  16. Projectile Motion

  17. Projectile Motion

  18. Projectile Motion • Air Resistance • Data: 100 mph at 60o; vacuum = 581 ft., air = 323 ft. • How about the moon?

  19. ConcepTest • A battleship simultaneously fires two shells at enemy ships. If the shells follow the parabolic trajectories shown below, which ship gets hit first? • A • both at the same time • B • need more information

  20. Projectile Motion • a

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