1. Homework (due Monday) Section 7 Problems # 60, 63 A block of mass m is projected with an initial speed v 0 along the horizontal plane with coefficient of kinetic friction μ k and of static friction μ s. How far will the block go until it stops?

2. Newton's Laws of Gravity

3. Planets’ motions: Brahe and Kepler I.All planets move in elliptical orbits, with the sun at one focus. II.A line that connects a planet to the sun sweeps out equal areas in equal times III. T 2 is proportional to R 3 Kepler’s Laws

4. Free fall: constant acceleration Galileo: Unequal weights fall with the same acceleration + Newton's laws mg There is a constant force that attracts the apple to the Earth This force is proportional to mass And this force reaches to the top of the tallest apple tree and the tallest tower

5. Newton’s insight The moon is falling!!! v F

6. m1m1 m2m2 R F ~ m1m1 m2m2 R2R2 Newton’s Law of Universal gravitation Philosophiae Naturalis Principia Mathematica - 1687

7. Cavendish experiment G = 6.67 x 10 -11 Nm 2 /kg 2 F = G m1m1 m2m2 R2R2

8. M earth m R earth 2 ≈9.8m/s 2 Gravitational acceleration R1R1 R2R2 R 2 < R 1 g 1 > g 2 G = 6.67 x 10 -11 Nm 2 /kg 2 M earth = 5.97x 10 24 kg R earth = 6370 km

10. Pendulum Suspended from Spring Scale A bob is hung by a string, attached to a spring scale which is suspended from a stand. First note the reading on the spring scale when the bob is not moving. The bob and string will then be pulled back so that the string makes an angle theta with the vertical. The bob will then be released and allowed to swing. Predict what will happen to the reading on the spring scale at the bottom of the swing (more, less or same as when the object is at rest).

11. A small wheel and a large wheel are connected by a belt. The small wheel is turned at a constant angular velocity  s. How does the magnitude of the angular velocity of the large wheel  L compare to that of the small wheel? There is a bug S on the rim of the small wheel and another bug L on the rim of the large wheel. How do their speeds compare? A:  s =  L B:  s >  L C:  s <  L A: V S = V L B: V S > V L C: V S < V L

12. Quiz A car passes over a hill in the road that has a circular cross-section with a radius of 30m. The speed of the car at the top of the hill is 10 m/s. What is the force exerted by the seat of the car on a 60kg passenger when the car is at the top pf the hill? V