1. Physics 218 Lecture 4 Ice shell floating on a saltwater ocean on Europa Galileo mission, NASA 1989-2003

2. A “police car” problem x=0 x1x1 x2x2 V 3 =20m/s a=0 a p =kt x 2 – x 1 = 3.5 km V 1 =30m/sV 2 =40m/s

3. Aristotle said that a heavy body falls faster than a light body. A feather, for example, clearly falls more slowly than a gold coin. But Galileo considered the following paradox. Suppose that one drops two gold coins. They fall at the same rate, according to Aristotle, because they are equally heavy. But now suppose that the coins are connected with a very light thread. This, according to Aristotle, should make them fall faster, because they are now one object that is twice as heavy. But why? How do they know that the thread is there? Since the coins are falling at the same rate when unconnected, neither can pull on the other through the thread to make it fall faster. Galileo carefully analyzed this paradox and concluded that Aristotle must be wrong. In the absence of air resistance (which slows the feather more than the coin) all bodies must fall the same, whether they are heavy or light. Free Fall

6. A legend says that Galileo dropped cannonballs of unequal weights from the Leaning Tower of Pisa to show that both objects reach ground at the same time. This story is probably not true. In fact, Galileo experimented with balls rolling down a ramp. Galileo experimentally proved that objects fall with the same acceleration independently on their masses. He found a correct mathematical formula describing this motion: the distance traveled by a falling body increases as the square of the time that has passed.

8. Free fall www.glenbrook.k12.il.us

9. Falling with air resistance

10. Gravity is a strange force. It has a unique property: M m R All bodies in the same point in space experience the same acceleration! Galileo, about 1600

11. Universality of g means that in the freely-falling elevator cabin you don’t feel any effects of gravity! You and all objects around you experience the same acceleration. Vice versa: in outer space you can imitate the effect of gravity by acceleration.

12. In 1907, Einstein was preparing a review of special relativity when he suddenly wondered how Newtonian gravitation would have to be modified to fit in with special relativity. At this point there occurred to Einstein, described by him as the happiest thought of my life, namely that an observer who is falling from the roof of a house experiences no gravitational field. He proposed the Equivalence Principle as a consequence:-... we shall therefore assume the complete physical equivalence of a gravitational field and the corresponding acceleration of the reference frame. This assumption extends the principle of relativity to the case of uniformly accelerated motion of the reference frame. Equivalence Principle

14. Gravity Assist