Before and after the collision, there is a rightward force pushing you into the door.

1. You are a passenger in a car and not wearing your seat belt. Without changing its speed, the car makes a sharp left turn, and you find yourself colliding with the right-hand door. Which is the correct analysis of the situation? • Before and after the collision, there is a rightward force pushing you into the door. • Starting at the time of the collision, the door exerts a leftward force on you. • Both of the above • Neither of the above

2. Your little brother wants a ride on his sled. On flat ground, should you push or pull him if you want to use the least force ? • Pull • Push • Not enough information

3. In the 17th century, Otto von Guericke, a physicist in Magdeburg, fitted two hollow bronze hemispheres together and removed the air from the resulting sphere with a pump he invented. Two eight horse teams could not pull the halves apart, even though the hemispheres fell apart when air was admitted. Suppose he had tied both teams of horses to one side and bolted the other side to a heavy tree trunk. In this case, the tension on the hemispheres would be (…) what it was before. • twice • exactly the same • half • Not enough information

4. Consider a frictionless Atwood’s machine. Can we assume that the magnitudes of the accelerations of the elevator car and the counterweight are the same? • Yes • No • Not enough information

5. Identifying Forces • Divide the problem into “system” and “environment”. The system is just the object whose motion we wish to study. • Draw a picture of the situation, showing the object and everything in the environment that touches the object. Ropes, springs, surfaces, etc. are all parts of the environment. • Draw a closed curve around the system, with the object inside the curve and everything else outside. • Locate every point on the boundary of this curve where the environment touches or contacts the system. These are the points where the environment exerts contact forces on the object. Don’t leave any out! • Identify by name the contact forces at each point of contact (there may be more than one!), then give each an appropriate symbol. • Identify any long-range forces (for us: gravity) acting on the object and write its symbol beside your picture.

6. Analyze the following two situations: a) a mass of 10 kg hangs vertically from a pulley attached to a spring scale which is attached to the wall. b) the wall is replaced by another mass hanging from a second pulley. Which is correct? • The scale shows a larger force in a) • The scale shows a larger force in b) • The scale shows the same force in a) & b)

7. Key question: How are things happening? Major Works: Harmonices Mundi (1619) Rudolphian Tables (1612) Astronomia Nova Dioptrice Johannes Kepler–The Phenomenologist Johannes Kepler (1571–1630)

8. Kepler’s First Law The orbits of the planets are ellipses, with the Sun at one focus

9. Ellipses a = “semimajor axis”; e = “eccentricity”

10. Kepler’s Second Law An imaginary line connecting the Sun to any planet sweeps out equal areas of the ellipse in equal times

11. Why is it warmer in the summer than in the winter in the USA? • Because the Earth is closer to the Sun • Because the Sun rises higher in the sky in the summer • None of the above

12. Kepler’s Third Law The square of a planet’s orbital period is proportional to the cube of its orbital semi-major axis: P 2 a3 a P Planet Orbital Semi-Major AxisOrbital Period Eccentricity P2/a3 Mercury 0.3870.241 0.206 1.002 Venus 0.723 0.615 0.007 1.001 Earth 1.000 1.000 0.017 1.000 Mars 1.524 1.881 0.093 1.000 Jupiter 5.203 11.86 0.048 0.999 Saturn 9.539 29.46 0.056 1.000 Uranus 19.19 84.01 0.046 0.999 Neptune 30.06 164.8 0.010 1.000 Pluto 39.53 248.6 0.248 1.001 (A.U.) (Earth years)

13. “Strange” motion of the Planets Planets usually move from W to E relative to the stars, but sometimes strangely turn around in a loop, the so called retrograde motion.

14. The heliocentric Explanation of retrograde planetary motion

15. The Planets from Otterbein Venus Mars

16. The Planets from Otterbein Jupiter

17. The Planets from Otterbein Saturn

18. The Planets from Otterbein Uranus Neptune

19. The Planets from Otterbein The Moon

20. Isaac Newton – The Theorist • Key question: Why are things happening? • Invented calculus and physics while on vacation from college • His three Laws of Motion, together with the Law of Universal Gravitation, explain all of Kepler’s Laws (and more!) Isaac Newton (1642–1727)

21. Isaac Newton (1642–1727) Major Works: • Principia (1687) [Full title: Philosophiae naturalis principia mathematica] • Opticks[sic!](1704) • Major findings: • Three axioms of motion • Universal gravity

22. Mman MEarth R Law of Universal Gravitation Force = G Mearth Mman/ R2

23. Which of the following depends on the inertial mass of an object (as opposed to its gravitational mass)? • The time it takes on object to fall from a certain height • The weight of an object on a bathroom-type spring scale • The acceleration given to the object by a compressed spring • The weight of the object on an ordinary balance

24. Orbital Motion

25. Cannon “Thought Experiment” • http://www.phys.virginia.edu/classes/109N/more_stuff/Applets/newt/newtmtn.html

26. Suppose Earth had no atmosphere, and a ball were fired from the top of Mt. Everest in a direction tangent to the ground. If the initial speed were high enough to cause the ball to travel in a circular trajectory around Earth, the ball’s acceleration would be… • Much less than g (b/c the ball doesn’t fall to the ground) • Be approximately g • Depend on the ball’s speed • None of the above

27. Two satellites A and B of the same mass are going around Earth in concentric orbits. The distance of satellite B from Earth’s center is twice that of satellite A. What is the ratio of centripetal force acting on B to that acting on A? • 1/8 • ¼ • ½ • 1

28. You lift up a stone to a new height. In the energy-money analogy this is like … • Receiving a check from the stone • Writing a check to the stone • Putting money in your bank account • Taking out cash from an ATM

29. Two marbles, one twice as heavy as the other, are dropped to the ground from the top of a building. Just before hitting the ground, the heavier marble has… • …as much kinetic energy as the lighter one. • …twice as much kinetic energy as the lighter one. • …half as much kinetic energy as the lighter one. • …four times as much kinetic energy as the lighter one.

30. A car is connected to a hanging weight by a string on a pulley. What happens to the kinetic energy of the car as it is released? • increases • decreases • stays the same • Impossible to tell

31. A car is connected to a hanging weight by a string on a pulley. What is the change in kinetic energy? • ∆K = 0 • ∆K > 0 • ∆K < 0 • Impossible to tell

32. A car is connected to a hanging weight by a string on a pulley. The car is accelerated due to the tension. What work does tension do on the car? • None • Positive work • Negative work • Impossible to tell

33. A car is connected to a hanging weight by a string on a pulley. The car is accelerated due to the tension. Is the net work done on the car …? • Zero • Positive • Negative • Impossible to tell

34. A car is connected to a hanging weight by a string on a pulley. The car is now pushed to the left, lifting the mass. What happens to the kinetic energy of the car before it stops and turns around? • increases • decreases • Stays the same • Impossible to tell

35. A car is connected to a hanging weight by a string on a pulley. The car is now pushed to the left, lifting the mass. What is the change in kinetic energy of the car before it stops and turns around? • ∆K = 0 • ∆K > 0 • ∆K < 0 • Impossible to tell

36. A car is connected to a hanging weight by a string on a pulley. The car is now pushed to the left, lifting the mass. What work does tension do on the car before it stops and turns around? • None • Positive work • Negative work • Impossible to tell

37. A car is connected to a hanging weight by a string on a pulley. The car is now pushed to the left, lifting the mass. What is the net work done on the car before it stops and turns around? • Wnet = 0 • Wnet > 0 • Wnet < 0 • Impossible to tell

38. A car is connected to a hanging weight by a string on a pulley. The car is now pushed to the left, lifting the mass. What is correct analysis of the situation before the car stops and turns around? • Change in K and net work done are negative • Change in K is pos., net work done negative • Change in K is neg., net work done positive • Change in K and net work done are positive

39. Potential Energy • Work done around any closed path is zero for conservative forces • For conservative forces a function exists that describes the amount of energy stored in a certain configuration involving these forces • We can calculate how much work it took to configure the configuration • Analogy: building a building costs money because it takes work to build it.

40. Gravitational potential energy • Lifting up a stone we do work against gravity: W=Fd=mgh • This is energy transferred into the system and stored int the configuration “stone sits at height h above the Earth”

41. Potential energy of a spring • Compressing a spring we do work against the elastic forces in the wire: W=1/2 k x2 • This is energy transferred into the system and stored int the configuration “spring is compressed by a distance x”

42. Potential energy & work-energy theorem • Change in potential energy will be equal to the work done ON the system ΔU=U2-U1 =Wsystem,external = Wext • System defined by ITS forces, define potential energy as work AGAINST the forces of the system ΔU=-Wexternal, system = -Wsystem

43. A ball is pushed up an incline. What work does gravity do on the ball? • Positive • Zero • Negative • Depends on angle

44. A ball is pushed up an steeper incline. What work does gravity do on the ball compared to the shallower incline? • Same • More negative • Less negative • More positive

45. Energy Problem Solving • Draw a picture • Determine the system: objects and forces on them • What is the unknown? • Choose initial and final positions • Choose convenient reference frame for potential energy • Draw an energy bar chart • If mech. Energy is conserved: K+U=K+U • Solve for the unknown

46. Dissipative Forces • Non-conservative forces at work means mechanical energy is not conserved, but energy still is K1+U1= K2+U2+ Wnon-conservative • Example: Friction has Wnon-conservative = Ffriction d

47. Group Work • A 60kg skateboarder starts up a 20 degree slope at 5m/s, then falls and slides up the hill on his kneepads. The coefficient of friction is 0.30. How far does he slide before stopping?