BEFORE THE BELL RINGS Please copy your homework into your assignment book

1. BEFORE THE BELL RINGS • Please copy your homework into your assignment book

2. Warm Up A space station revolves around the Earth as a satellite, 100 km above the earth’s surface. What is the net force on an astronaut at rest inside the space station? A- equal to their weight on earth B- A little less than half their weight on earth C- Less than half their weight on earth D- Zero( They are weightless) E- Somewhat larger than their weight on earth

3. Monday, December 19, 2016 • Warm-up • Introduction to Circular Motion and Gravitation • Practice • Lab Introduction • Homework: Due Wednesday: Pg. 130: 1-13, odds

4. Chapter 5 Circular Motion; Gravitation

5. https://www.youtube.com/watch?v=L6-kn2tB-9E

6. Units of Chapter 5 • Kinematics of Uniform Circular Motion • Dynamics of Uniform Circular Motion • Highway Curves, Banked and Unbanked • Nonuniform Circular Motion • Centrifugation • Newton’s Law of Universal Gravitation

7. Units of Chapter 5 • Gravity Near the Earth’s Surface; Geophysical Applications • Satellites and “Weightlessness” • Kepler’s Laws and Newton’s Synthesis • Types of Forces in Nature

8. 5-1 Kinematics of Uniform Circular Motion Uniform circular motion: motion in a circle of constant radius at constant speed Instantaneous velocity is always tangent to circle.

9. 5-1 Kinematics of Uniform Circular Motion Looking at the change in velocity in the limit that the time interval becomes infinitesimally small, we see that (5-1)

10. Summarizing An object moving in a circle of radius r at a constant speed V has an acceleration whose direction is toward the center of the circle and whose radius is ar=v2/r

11. 5-1 Kinematics of Uniform Circular Motion This acceleration is called the centripetal(Center pointing), or radial(directed along the radius), acceleration, and it points towards the center of the circle.

12. Frequency What is frequency? Frequency (f) is the number of revolutions per second Period(T) of an object is the time required for for one complete revolution Period = 1/ Frequency or T=1/f

13. Acceleration of a Revolving Ball • A 150-g ball at the end of a string is revolving uniformly in a horizontal circle of a radius 0.600 m. The ball makes 2.00 revolutions in one second. What is the centripetal acceleration?

14. Moon’s Centripetal Acceleration • The Moon’s nearly circular orbit about the Earth has a radius of about 384,000 km and a period T of 23.7 days. Determine the acceleration of the Moon toward Earth.

15. Do Now! • Sometimes people say that water is removed from clothes in a spin dryer by centrifugal force throwing the water outward. What is wrong with this statement? • Will the acceleration of a car be the same when the car travels around a sharp curve at a constant as when it travels around a gentle curve at the same speed? Explain.

16. 5-2 Dynamics of Uniform Circular Motion For an object to be in uniform circular motion, there must be a net force acting on it. We already know the acceleration, so can immediately write the force: (5-1)

17. 5-2 Dynamics of Uniform Circular Motion We can see that the force must be inward by thinking about a ball on a string:

18. 5-2 Dynamics of Uniform Circular Motion There is no centrifugal force pointing outward; what happens is that the natural tendency of the object to move in a straight line must be overcome. If the centripetal force vanishes, the object flies off tangent to the circle.

19. Force on Revolving Ball • Estimate the force a person must exert on a string attached to a 0.150-kg ball to make the ball revolve in a horizontal circle of radius 0.600m. The ball make 2.00 revolutions per second.

20. Revolving Ball (Vertical Circle) A 0.150-kg ball on the end of a 1.10m long cord (negligible mass) is swung in a vertical circle. Determine the speed the must have at the top of its arc so that the ball continues to move in a circle. Calculate the tension in the cord at the bottom of the arc, assuming the ball is moving at two times the original speed.

21. Tetherball The game of tetherball is played with a ball tied to a pole with a string. After the ball is struck, it revolves around the pole as shown. In what direction is the acceleration of the ball, and what force causes the acceleration?

22. Do Now: Force on a revolving ball (horizontal) • Estimate the force a person must exert on a string attached to a 150- kg ball to make the ball revolve in a horizontal circle of radius 0.600m. The ball makes 2.00 revolutions per second (T=0.5s)

23. 5-3 Highway Curves, Banked and Unbanked When a car goes around a curve, there must be a net force towards the center of the circle of which the curve is an arc. If the road is flat, that force is supplied by friction.

24. 5-3 Highway Curves, Banked and Unbanked If the frictional force is insufficient, the car will tend to move more nearly in a straight line, as the skid marks show.

25. 5-3 Highway Curves, Banked and Unbanked • As long as the tires do not slip, the friction is static. If the tires do start to slip, the friction is kinetic, which is bad in two ways: • The kinetic frictional force is smaller than the static. • The static frictional force can point towards the center of the circle, but the kinetic frictional force opposes the direction of motion, making it very difficult to regain control of the car and continue around the curve.

26. 5-3 Highway Curves, Banked and Unbanked Banking the curve can help keep cars from skidding. In fact, for every banked curve, there is one speed where the entire centripetal force is supplied by the horizontal component of the normal force, and no friction is required. This occurs when:

27. 5-4 Nonuniform Circular Motion If an object is moving in a circular path but at varying speeds, it must have a tangential component to its acceleration as well as the radial one.

28. 5-4 Nonuniform Circular Motion This concept can be used for an object moving along any curved path, as a small segment of the path will be approximately circular.

29. 5-5 Centrifugation A centrifuge works by spinning very fast. This means there must be a very large centripetal force. The object at A would go in a straight line but for this force; as it is, it winds up at B.

30. Think ‘bout it! Welcome back;) • Why do bicycle riders lean inward when rounding a curve at high speed?

31. 5-6 Newton’s Law of Universal Gravitation If the force of gravity is being exerted on objects on Earth, what is the origin of that force? Newton’s realization was that the force must come from the Earth. He further realized that this force must be what keeps the Moon in its orbit.

32. 5-6 Newton’s Law of Universal Gravitation The gravitational force on you is one-half of a Third Law pair: the Earth exerts a downward force on you, and you exert an upward force on the Earth. When there is such a disparity in masses, the reaction force is undetectable, but for bodies more equal in mass it can be significant.

33. 5-6 Newton’s Law of Universal Gravitation Therefore, the gravitational force must be proportional to both masses. By observing planetary orbits, Newton also concluded that the gravitational force must decrease as the inverse of the square of the distance between the masses. In its final form, the Law of Universal Gravitation reads: where (5-4)

34. Can you attract another person… gravitationally? • A 50-kg person and a 75-kg person are sitting on a bench. Estimate the gravitational force each exerts on the other.

35. 5-6 Newton’s Law of Universal Gravitation The magnitude of the gravitational constant G can be measured in the laboratory. This is the Cavendish experiment.

36. Spacecraft at 2rE • What is the force of gravity on a 2000-kg spacecraft when it orbits two earth radii from the Earth’s center (that is a distance of rE = 6380 km above the Earth’s surface) The mass of the Earth is ME = 5.98 x 1024kg

37. Do Now. • Determine the force of gravitational attraction between the earth (m = 5.98 x 1024 kg) and a 70-kg physics student if the student is standing at sea level, a distance of 6.38 x 106 m from earth's center. • Determine the force of gravitational attraction between the earth (m = 5.98 x 1024 kg) and a 70-kg physics student if the student is in an airplane at 40000 feet above earth's surface. This would place the student a distance of 6.39 x 106 m from earth's center.

38. Force on the Moon Find the net force on the moon (mm = 7.35 x 1022 kg) due to the gravitational attraction of both the Earth (mE = 5.98x1024 kg) and the sun (ms = 1.99 x 1030 kg) assuming that they are at right angles of each other.

39. Will an object weigh more at the equator or at the poles? What two effects are at work? Do they oppose each other? • Is the centripetal acceleration of Mars in its orbit around the Sun larger or smaller than the centripetal acceleration of the Earth?

40. 5-7 Gravity Near the Earth’s Surface; Geophysical Applications Now we can relate the gravitational constant to the local acceleration of gravity. We know that, on the surface of the Earth: Solving for g gives: Now, knowing g and the radius of the Earth, the mass of the Earth can be calculated: (5-5)

41. 5-7 Gravity Near the Earth’s Surface; Geophysical Applications The acceleration due to gravity varies over the Earth’s surface due to altitude, local geology, and the shape of the Earth, which is not quite spherical.

42. Gravity on Everest • Estimate the effective value of g on the top of Mt. Everest, 8850 m (29,035 ft) above sea level. That is, what is the acceleration due to gravity of objects allowed to fall freely at this altitude?

43. Do Now • At what distance from Earth will a spacecraft traveling directly from the Earth to the Moon experience zero net force because the Earth and the Moon pull with equal and opposite forces?

44. 5-8 Satellites and “Weightlessness” Satellites are routinely put into orbit around the Earth. The tangential speed must be high enough so that the satellite does not return to Earth, but not so high that it escapes Earth’s gravity altogether.

45. 5-8 Satellites and “Weightlessness” The satellite is kept in orbit by its speed – it is continually falling, but the Earth curves from underneath it.

46. 5-8 Satellites and “Weightlessness” Objects in orbit are said to experience weightlessness. They do have a gravitational force acting on them, though! The satellite and all its contents are in free fall, so there is no normal force. This is what leads to the experience of weightlessness.

47. 5-8 Satellites and “Weightlessness” More properly, this effect is called apparent weightlessness, because the gravitational force still exists. It can be experienced on Earth as well, but only briefly:

48. Geosynchronous Satellite A geosynchronous satellite is one that stays above the same point on the Earth, which is only possible if it is above a point on the equator. Such satellites are used for TV and radio transmission, for weather forecasting, and communication relays. Determine the height above the Earth’s surface the satellite must orbit, and such a satellite’s speed. Compare to the speed of a satellite orbiting 200 km above the Earth’s surface.

49. 5-9 Kepler’s Laws and Newton's Synthesis Kepler’s laws describe planetary motion. • The orbit of each planet is an ellipse, with the Sun at one focus.

50. 5-9 Kepler’s Laws and Newton's Synthesis 2. An imaginary line drawn from each planet to the Sun sweeps out equal areas in equal times.