Law of Universal Gravitation

1. Law of Universal Gravitation Holt Physics Pages 263 - 265

2. Unlike object moving in horizontal circles, an object moving in a vertical circle is effected by weight. In vertical circles, the speed is not constant and neither is the tension in the string. Vertical vs horizontal circles

3. At the top of the circular path, the speed and the tension in the string are at a minimum. At the bottom of the circle, the speed and tension in the string are at a maximum. Vertical vs horizontal circles

4. forces acting in a vertical circle

5. forces acting in a vertical circle At the top and bottom of the circle, FC = ?FV. Therefore, at the top of the circle TS = Tension in string(N) m = mass (kg) g = 9.8 m/s2, down v = speed at that point (m/s) r = radius of circle (m)

6. forces acting in a vertical circle At the top and bottom of the circle, FC = ?FV. Therefore, at the bottom of the circle TS = Tension in string (N) m = mass (kg) g = 9.8 m/s2, down v = speed at that point (m/s) r = radius of circle (m)

7. The formulas you learned that apply to horizontal circles can also be used to apply to vertical circles at certain points.

8. formulas

9. T = period or time for one revolution (sec) f = frequency or revolutions per second (Hz or sec-1) formulas

10. ac = centripetal acceleration (m/s2) r = radius of circle (m) v = speed (m/s) formulas

11. ac = centripetal acceleration (m/s2) r = radius of circle (m) T = period or time for one revolution (sec) formulas

12. Fc = centripetal force (N) m = mass (kg) ac = centripetal acceleration (m/s2) formulas

13. Fc = centripetal force (N) m = mass (kg) v = speed (m/s) r = radius of circle (m) formulas

14. Fc = centripetal force (N) m = mass (kg) r = radius of circle (m) T = period or time for one revolution (sec) formulas

15. A stuntman swings from the end of a 4 m long rope along the arc of a circle. At the bottom of his path his speed is 9 m/s. (a) What is the centripetal acceleration at this point? (b) If his mass is 70 kg, find the tension in the rope at this point. Sample Problem

16. The critical velocity is the minimum velocity an object can have and remain in a vertical circle of constant radius. If an object does not maintain the critical velocity, the radius of the orbit begins to decay (get smaller). critical velocity

17. vcrit = critical velocity (m/s) r = radius (m) g = acceleration due to gravity (m/s2) Critical velocity

18. A carnival clown rides a motorcycle down a ramp and around a �loop-the-loop.� If the loop has a radius of 18 m, what is the slowest speed the rider can have at the top of the loop to avoid falling? Sample Problem

19. A 75-kg pilot flies a plane in a loop near the earth�s surface. At the top of the loop, where the plane is completely upside-down for an instant, the pilot hangs freely in the seat and does not push against the seat belt. The airspeed indicator reads 120 m/s. What is the radius of the plane�s loop? Sample Problem

21. Law of Universal Gravitation - there is a force of attraction between any two objects with mass. Newton�s Law of Universal Gravitation

22. F = Force of attraction (N) G = 6.67 * 10-11 Nm2/kg2 m1 = mass of object one (kg) m2 = mass of object two (kg) d = distance between the centers of the two objects (m) Newton�s Law of Universal Gravitation

23. me = mass of the Earth (5.98 *1024 kg) re = radius of the Earth (6.37 * 106 m) Accepted Values

24. Satellites actually move in elliptical orbits but we will treat them as though they are circular orbits. The weight of the satellite is actually the gravitational attraction between the satellite and the Earth. Satellites

25. When the weight of the satellite (msg) is set equal to the gravitational attraction between the earth and the satellite (Gmsme/d2), the mass of the satellite will cancel out telling us that the acceleration due to gravity at any point can be calculated using the following equation. Acceleration due to Gravity

26. G = 6.67 * 10-11 Nm2/kg2 m2 = mass of the celestial body at the center of rotation (kg) d = distance between the centers of the two objects (m) Acceleration due to Gravity

27. A force field is a region of space in which a suitable detector experiences a force. A suitable detector for a gravitational field is an object with a very small mass. The units for gravitational field strength are N/kg or m/s2 Keeping track of the acceleration due to gravity is a good way to look at gravitational field strength Field Concept

28. Gravity Near the Earth�s Surface;

29. 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. Satellites and �Weightlessness�

30. The satellite is kept in orbit by its speed � it is continually falling, but the Earth curves from underneath it. Satellites and �Weightlessness

31. True weightlessness does not exist. In order to be truly weightless you would have to be infinitely far from all other objects with mass, since this is not possible, all objects have weight. Weightlessness

32. Astronauts are said to be weightless but in actuality they are in freefall toward the Earth just as their spaceship is. Hence they are both accelerating at the same rate so you have the appearance of weightlessness. The misnomer (wrong name) came about due to the fact that if you attempted to weigh them the scale would register a value of zero since both are in free fall Therefore, the astronauts would weigh zero but would not have a weight of zero. Weightlessness

33. 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.

34. 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:

35. The period of a satellite can be calculated using Period of a Satellite

36. The critical speed of a satellite can be calculated using Satellite Speed

37. Therefore, the astronauts would weigh zero but would not have a weight of zero.