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Chapter 3: Measuring Motion

This chapter explores the principles of motion, particularly the behavior of falling objects as demonstrated by Galileo in 1638. It discusses the against Aristotle's belief that heavier objects fall faster, presenting the uniform acceleration of objects under gravity, g = 9.8 m/s². The chapter examines conditions like vacuum effects on falling objects, terminal velocity, and provides relatable examples including a hammer and feather demonstration on the Moon. Additionally, it delves into projectile motion, drag force, and various factors influencing the rate of 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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