Slide 1 / 57 Slide 2 / 57 Algebra Based Physics Newton's Law of Universal Gravitation 2015-11-30 www.njctl.org Slide 3 / 57 Slide 4 / 57 Newton's Law of Universal Gravitation Click on the topic to go to that section · Gravitational Force · Gravitational Field · Surface Gravity · Gravitational Field in Space Gravitational Force · Orbital Motion · Kepler's Third Law of Motion Return to Table of https://www.njctl.org/video/?v=IP_u0xQvP04 Contents Slide 5 / 57 Slide 6 / 57 Newton’s Law of Universal Gravitation Newton’s Law of Universal Gravitation Newton connected the idea that objects, like apples, fall towards the center of Earth with the idea that the moon It has been well orbits around Earth...it's known since ancient also falling towards the times that Earth is a center of Earth. sphere and objects that are near the The moon just stays in surface tend fall circular motion since it has down. a velocity perpendicular to its acceleration. https://www.njctl.org/video/?v=uhS8K4gFu4s Slide 7 / 57 Slide 8 / 57 Newton’s Law of Universal Gravitation Gravitational Constant Newton concluded that all objects attract one another with a G = 6.67 x 10-11 N-m2 /kg2 "gravitational force". The magnitude of the gravitational force decreases as the centers of the masses increases in distance. In 1798, Henry Cavendish MORE Gravitational attraction measured G using a torsion beam M1 M2 balance. He did not initially set out to measure G, he was instead trying r to measure the density of the Earth. M1 LESS Gravitational attraction M2 r https://www.njctl.org/video/?v=2PdiUoKa9Nw Slide 9 / 57 Slide 10 / 57 Newton’s Law of Universal Gravitation Newton’s Law of Universal Gravitation Mathematically, the magnitude of the gravitational force decreases with the inverse of the square of the distance The direction of the force is along the line connecting the between the centers of the masses and in proportion to the centers of the two masses. Each mass feels a force of product of the masses. attraction towards the other mass...along that line. r Slide 11 / 57 Slide 12 / 57 Newton’s Law of Universal Gravitation 1 What is the magnitude of the gravitational force between two 1 kg objects which are located 1.0 m apart? Newton's third law tells us that the force on each mass is A 3.3 x 10-11 N equal. B 1.7 x 10-11 N That means that if I drop a pen, the force of Earth pulling the C 2.7 x 10-10 N pen down is equal to the force of the pen pulling Earth up. D 6.7 x 10-11 N However, since the mass of Earth is so much larger, that force causes the pen to accelerate down, while the movement of Earth up is completely unmeasurable. https://www.njctl.org/video/?v=IP_u0xQvP04 Slide 12 (Answer) / 57 Slide 13 / 57 1 What is the magnitude of the gravitational 2 What is the magnitude of the gravitational force between two 1 kg objects which are force acting on a 4.0 kg object which is 1.0 m located 1.0 m apart? from a 1.0 kg object? -11 A 3.3 x 10-11 N A 3.3 x 10 N B 1.7 x 10-11 N B 1.7 x 10-11 N C 2.7 x 10-10 N C 2.7 x 10-10 N D 6.7 x 10-11 N D 6.7 x 10-11 N Answer D [This object is a pull tab] https://www.njctl.org/video/?v=IP_u0xQvP04 https://www.njctl.org/video/?v=dPFsPm5UYhg Slide 13 (Answer) / 57 Slide 14 / 57 2 What is the magnitude of the gravitational 3 What is the magnitude of the gravitational force acting on a 4.0 kg object which is 1.0 m force acting on a 1.0 kg object which is 1.0 m from a 1.0 kg object? from a 4.0 kg object? A 3.3 x 10-11 N A 3.3 x 10-11 N B 1.7 x 10-11 N B 1.7 x 10-11 N -10 C 2.7 x 10-10 N C 2.7 x 10 N D 6.7 x 10-11 N D 6.7 x 10-11 N Answer C [This object is a pull tab] https://www.njctl.org/video/?v=iOovJt1I8lc https://www.njctl.org/video/?v=dPFsPm5UYhg Slide 14 (Answer) / 57 Slide 15 / 57 3 What is the magnitude of the gravitational 4 What is the magnitude of the gravitational force acting on a 1.0 kg object which is 1.0 m force acting on a 1.0 kg object which is 2.0 m from a 4.0 kg object? from a 4.0 kg object? A 3.3 x 10-11 N A 3.3 x 10-11 N B 1.7 x 10-11 N B 1.7 x 10-11 N C 2.7 x 10-10 N C 2.7 x 10-10 N D 6.7 x 10-11 N D 6.7 x 10-11 N Answer C [This object is a pull tab] https://www.njctl.org/video/?v=tjkf5sqwLT0 https://www.njctl.org/video/?v=iOovJt1I8lc Slide 15 (Answer) / 57 Slide 16 / 57 4 What is the magnitude of the gravitational 5 What is the magnitude of the gravitational force force acting on a 1.0 kg object which is 2.0 m between Earth and its moon? from a 4.0 kg object? r = 3.8 x 108m 24 mEarth = 6.0 x 10 kg -11 22 A 3.3 x 10 N mmoon = 7.3 x 10 kg B 1.7 x 10-11 N A 2.0 x 10 18 N C 2.7 x 10-10 N 19 D 6.7 x 10-11 N B 2.0 x 10 N C 2.0 x 1020 N Answer D D 2.0 x 1021 N [This object is a pull tab] https://www.njctl.org/video/?v=tjkf5sqwLT0 https://www.njctl.org/video/?v=4MieN1BT4Yc Slide 16 (Answer) / 57 Slide 17 / 57 5 What is the magnitude of the gravitational force 6 What is the magnitude of the gravitational between Earth and its moon? force between Earth and its sun? 11 r = 3.8 x 108m r = 1.5 x 10 m 24 24 mEarth = 6.0 x 10 kg mEarth = 6.0 x 10 kg 30 22 msun = 2.0 x 10 kg mmoon = 7.3 x 10 kg -18 A 2.0 x 10 18 N A 3.6 x 10 N B 3.6 x 1019 N B 2.0 x 1019 N C 3.6 x 1021 N 20 Answer C C 2.0 x 10 N D 3.6 x 1022 N D 2.0 x 1021 N [This object is a pull tab] https://www.njctl.org/video/?v=mAC5GoXjJGE https://www.njctl.org/video/?v=4MieN1BT4Yc Slide 17 (Answer) / 57 Slide 18 / 57 6 What is the magnitude of the gravitational force between Earth and its sun? r = 1.5 x 1011 m 24 mEarth = 6.0 x 10 kg 30 msun = 2.0 x 10 kg A 3.6 x 10-18 N B 3.6 x 1019 N C 3.6 x 1021 N * 22 D 3.6 x 10 N Answer D Gravitational Field [This object is a pull tab] Return to Table of https://www.njctl.org/video/?v=mAC5GoXjJGE https://www.njctl.org/video/?v=p_OteaRhSsk Contents Slide 19 / 57 Slide 20 / 57 *Gravitational Field *Gravitational Field While the force between two objects can always be computed The magnitude of the gravitational field created by an object varies from location to location in space; it depends on the distance from by using the formula for FG ; it's sometimes convenient to consider one mass as creating a gravitational field and the the object and the object's mass. other mass responding to that field. Gravitational field, g, is a vector. It's direction is always towards the object creating the field. That's the direction of the force that a test mass would experience if placed at that location. In fact, g is the acceleration that a mass would experience if placed at that location in space. Slide 21 / 57 Slide 21 (Answer) / 57 *Gravitational Field *Gravitational Field 7 Where is the gravitational field the strongest? 7 Where is the gravitational field the strongest? E E B B D D A A A Answer C C [This object is a pull tab] Slide 22 / 57 Slide 22 (Answer) / 57 8* What happens to the gravitational field if the 8* What happens to the gravitational field if the distance from the center of an object doubles? distance from the center of an object doubles? A It doubles A It doubles B It quadruples B It quadruples C It is cut to one half C It is cut to one half Answer D D It is cut to one fourth D It is cut to one fourth [This object is a pull tab] Slide 23 / 57 Slide 23 (Answer) / 57 9* What happens to the gravitational field if the 9* What happens to the gravitational field if the mass of an object doubles? mass of an object doubles? A It doubles A It doubles B It quadruples B It quadruples C It is cut to one half C It is cut to one half D It is cut to one fourth D It is cut to one fourth Answer A [This object is a pull tab] https://www.njctl.org/video/?v=E1KR_75YClA https://www.njctl.org/video/?v=E1KR_75YClA Slide 24 / 57 Slide 25 / 57 * Surface Gravity Planets, stars, moons, all have a gravitational field...since they all have mass.