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Chapter 3

Chapter 3. Nonlinear Motion. 1. MOTION IS RELATIVE. Example: Motion of a boat with respect to the ground and with respect to the river. Velocity of river. Velocity of boat with respect to river. Add the velocity of the river. Velocity of boat with respect to ground. Velocity of river.

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Chapter 3

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  1. Chapter 3 Nonlinear Motion

  2. 1. MOTION IS RELATIVE Example: Motion of a boat with respect to the ground and with respect to the river. Velocity of river Velocity of boat with respect to river Add the velocity of the river Velocity of boat with respect to ground

  3. Velocity of river Velocity of boat with respect to river Add the velocity of the river Velocity of boat with respect to ground

  4. Velocity of boat with respect to ground Velocity of river Velocity of boat with respect to river

  5. 2. VELOCITY - A VECTOR QUANTITY • Scalars are quantities that are specified by magnitude only. • Examples: distance, time, mass, density • Vectors are quantities that are specified by magnitude and direction. • Examples: displacement, velocity, acceleration, force, momentum, angular momentum

  6. The Displacement Vector What is the displacement for this trip? 5 miles 3 miles north 370 north of east 4 miles east

  7. 3. PROJECTILE MOTION • Projectile motion is a combination of vertical free-fall motion and horizontal motion at a constant speed.

  8. Parabola (approximately)

  9. Demo - Ball projector and dropper • Demo - Monkey in tree • Demo - Cart and ball launcher • Demo - Wall parabola

  10. The free-fall motion of a projectile near the surface of the earth is very nearly parabolic. A parabola is one of the of a conic sections. Ellipse Parabola Hyperbola Circle

  11. For a particular range less than the maximum and for a particular launch velocity, two different launch angles will give that range. The two angles add to give 900. 450 gives the maximum range. Simulation

  12. Free Fall Results • Horizontal motion is constant • Vertical Motion is accelerated • Rise time = Fall Time • Final speed = Initial speed

  13. Actual path and ideal path (free fall) are different.

  14. 4. FAST-MOVING PROJECTILES - SATELLITES • Lets throw stones horizontally with ever increasing velocity. • The Earth’s curvature is 16 ft for every 5 miles (4.9 m for 8 km).

  15. 5 miles 16 ft 16 ft Throw an object faster, faster, faster. Curvature of Earth We draw in each trajectory for 1 second

  16. Vescape = 7 mi/s = 11 km/s Vcircle = 5 mi/s = 8 km/s Ellipse Hyperbola Parabola Ellipse Ellipse - Circle Ellipse Ellipse

  17. 4. CIRCULAR MOTION Linear speed and rotational speed • Linear speed is a distance divided by time. • Rotational speed is an angle measurement divided by time.

  18. A A A A A B B B B B Two Flies on a Turntable Which fly has the greater rotational speed? Which fly has the greater linear speed? Same for both. B A B

  19. Chapter 3 Review Questions

  20. A rock is thrown upward at an angle. What happens to the horizontal component of its velocity as it rises? (Neglect air resistance.) (a) it decreases (b) it increases (c) it remains the same (c) it remains the same

  21. In the game of baseball which path would a home run most closely approximate? (Neglect air resistance.) (a) hyperbolic (b) parabolic (c) eccentric (b) parabolic

  22. A projectile is launched upward at an angle of 75o from the horizontal and strikes the ground a certain distance down range. What other angle of launch at the same launch speed would produce the same distance? (Neglect air resistance.) (a) 450 (b) 150 (c) 250 (b) 150

  23. A horizontally traveling car drives off of a cliff next to the ocean. At the same time that the car leaves the cliff a bystander drops his camera. Which hits the ocean first? (Neglect air resistance.) (a) car (b) camera (c) they both hit at the same time (c) they both hit at the same time

  24. Bug A is 3 inches from the center of a rotating 33.33 rpm record. Bug B is 5 inches from the center of the same record. Bug A has linear speed and rotational speed as bug B. (a) less, less (b) less, same (c) same, less (d) same, same (e) less, greater (b) less, same

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