Galileo s inertia Descartes Huygens on motion and impact of bodies

1. Galileo�s inertia � Descartes & Huygens on motion and impact of bodies

2. Rolling a ball down a double ramp

3. Second Ramp Horizontal

4. A new model of motion Aristotle: �natural state of rest.� Elements have natural resting places. Once they reach it, they stay there. Objects move only when pushed away from their place of rest (violent motion)  Galileo: �natural state of inertia.� Objects have no natural resting places. Moving objects continue to move forever�  Later developments: motion in straight path

5. Galileo � Law of �Horizontal Inertia� Movement continues indefinitely in a given direction parallel to the earth�s surface - ie globally

6. Recall: If the Earth rotates in 24 hours, someone on the equator would travel�? Can you see how this solves the �problem� of a spinning Earth?

7. Parabolic Motion

8. Parabolic Motion

9. Dropping Ball

10. A modern experiment (using strobe photography) Two balls are released at exactly the same time One is just dropped; the other is forced (violently?) to the right Photos were taken at even time intervals � what do they show?

11. Descartes and Mechanics Two important points: (1) directed attention to problem of transfer of motion from one object to another emphasis that helped set Newton on the right path (2) construction of the conservation law in a complicated situation in which things are constantly changing, a conservation law is an assertion and that some simple quantity remains the same

12. Theory of Motion and idea of inertia Galileo - motion of bodies on Earth where acted on by force that pulls them to the center Descartes - physical theory that explains all phenomena of motion Descartes� idea of inertia implied forces acting on a body would produce not motion but change of motion�not velocity but acceleration (like modern ideas)

13. Theory of Motion and idea of inertia 1st Law of Nature: �That each thing remains in the state it is in, so long as nothing changes it� 2nd Law of Nature: �That every moving body tends to continue in its motion in a straight line� Extension of Galileo�s work ? later known as Newton�s 1st Law An object will have a constant velocity [Galileo] unless acted upon by an unbalanced force [Descartes]

14. Descartes and Conservation of Motion 3rd Law of Nature and set of seven rules: description of change of motion produced as a result of collisions between two bodies interactions between two bodies ? motion lost by one body gained by the other - overall amount of motion in the system the same For Descartes a scalar quantity (only magnitude) now defined as vector quantity (having magnitude and direction)

15. �Some� problems with rules of impact Discontinuities ~ Behavior different almost vs. exactly equal in mass Rule # 1 - C and B equal: C ? ? B - C & B collide: ? C B ? [same speed] Rule # 2 - B �slightly larger: C ? ? B - C & B collide: ? C ? B [same speed]

16. Head-on collision moving & stationary bodies (A) Bodies of equal mass ~ moving body�s motion? - rebound with � of original speed ~ stationary body�s motion? - moves forward with remaining � of the motion

17. Head-on collision moving & stationary bodies (B) Moving body heavier ~ two bodies move together ~ same direction as heavier body ~ slower speed

18. Head-on collision moving & stationary bodies (C) Moving body less heavy ~ heavier stationary object�s motion? - no motion ~ less heavy moving body�s motion? - rebound backwards with same speed as before

19. �Some� problems with rules of impact Rule vs. observation ~ which to ignore and for what reasons � bad intuition (not Galileo) - Rule # 4 smaller object can never move larger object at rest Frame of reference ~ objections of Huygens - �conservation of momentum� m1v1 = m2v2

20. Huygens revision of Descartes revised Descartes� rules of motion to produce outcomes based on considerations of symmetry collisions between bodies of equal mass accepted Descartes if bodies approach each other with equal velocities rebound with equal velocities generalized principle to all other collisions between equal-mass bodies When moving body strikes stationary body of the same mass should come to a stop as a result of the collision stationary body moves at same velocity as moving body before collision consistent with current understanding [Newton�s laws of motion]

21. Huygens � conservation of momentum collisions between bodies of different masses should be same �quantity of motion� before and after a collision If two bodies moving in opposite directions total quantity of motion determined by subtracting momentum of one body from momentum of the other body. If two bodies moving in the same direction Momentums added together to calculate total quantity of motion When the colliding bodies have unequal masses Momentum conserved when: m1v1 = m2v2

22. Huygens �Thus, if someone conveyed on a boat that is moving with a uniform motion were to cause equal balls to strike one another at equal speeds with respect to himself and the parts of the boat, we say that both should rebound also at equal speeds with respect to the same passenger, just as would clearly happen if he were to cause the same balls to collide at equal speeds in a boat at rest or while standing on the ground.�

23. Descartes (frame of reference)

24. Descartes (frame of reference) What is seen depends on observer location Observer on the boat (case # 1) Both objects moving at each other at 4 mph rebound opposite directions at same speed (4 mph)

25. Descartes (frame of reference) Observer on the boat (case # 2) Both objects moving at each other at 4 mph � BUT boat moving to the right at 4 mph Appearance: two bodies equal mass with moving body (8 mph) striking a stationary body Moving body reflects back with speed of 6 mph stationary body moves forward with remaining speed (2 mph)

26. Christiaan Huygens Argued any collision should look the same regardless of whether frame of reference is stationary or moving at a constant velocity Collision of bodies of equal mass ~ Equal velocity ? rebound with equal velocities ~ Moving body (X) hitting stationary body (Y) ? (X) stops (Y) moves same incoming velocity of (X)

27. Newton�s Cradle