April 19, Week 13 Today: Chapter 13, Gravity Homework Assignment - PowerPoint PPT Presentation

April 19, Week 13 Today: Chapter 13, Gravity Homework Assignment #10 - Due Today. Mastering Physics: 7 problems from chapter 9 Written Question: 10.86 From now on, Thursday office hours will be held in room 109 of Regener Hall Exam #4, Next Friday, April 26 Practice Exam on Website. Newton’s Gravity April 19, 2013 - p. 1/8

Newton’s Law of Gravitation Newton’s Law of Gravitation - Every object with mass exerts a gravitational force on every other object with mass. Newton’s Gravity April 19, 2013 - p. 2/8

Newton’s Law of Gravitation Newton’s Law of Gravitation - Every object with mass exerts a gravitational force on every other object with mass. The magnitude of this force is given by: Newton’s Gravity April 19, 2013 - p. 2/8

Newton’s Law of Gravitation Newton’s Law of Gravitation - Every object with mass exerts a gravitational force on every other object with mass. The magnitude of this force is given by: M 2 M 1 - Mass of first object M 2 - Mass of second object M 1 Newton’s Gravity April 19, 2013 - p. 2/8

Newton’s Law of Gravitation Newton’s Law of Gravitation - Every object with mass exerts a gravitational force on every other object with mass. The magnitude of this force is given by: M 2 M 1 - Mass of first object M 2 - Mass of second object M 1 M 1 M 2 F g = Newton’s Gravity April 19, 2013 - p. 2/8

Newton’s Law of Gravitation Newton’s Law of Gravitation - Every object with mass exerts a gravitational force on every other object with mass. The magnitude of this force is given by: M 2 M 1 - Mass of first object M 2 - Mass of second object r M 1 r - separation distance, center-to-center for spherical objects M 1 M 2 F g = Newton’s Gravity April 19, 2013 - p. 2/8

Newton’s Law of Gravitation Newton’s Law of Gravitation - Every object with mass exerts a gravitational force on every other object with mass. The magnitude of this force is given by: M 2 M 1 - Mass of first object M 2 - Mass of second object r M 1 r - separation distance, center-to-center for spherical objects M 1 M 2 F g = r 2 Newton’s Gravity April 19, 2013 - p. 2/8

Newton’s Law of Gravitation Newton’s Law of Gravitation - Every object with mass exerts a gravitational force on every other object with mass. The magnitude of this force is given by: M 2 M 1 - Mass of first object M 2 - Mass of second object r M 1 r - separation distance, center-to-center for spherical objects M 1 M 2 F g = r 2 Inverse square law Newton’s Gravity April 19, 2013 - p. 2/8

Newton’s Law of Gravitation Newton’s Law of Gravitation - Every object with mass exerts a gravitational force on every other object with mass. The magnitude of this force is given by: M 2 M 1 - Mass of first object M 2 - Mass of second object r M 1 r - separation distance, center-to-center for spherical objects F g = GM 1 M 2 r 2 Inverse square law Newton’s Gravity April 19, 2013 - p. 2/8

Newton’s Law of Gravitation Newton’s Law of Gravitation - Every object with mass exerts a gravitational force on every other object with mass. The magnitude of this force is given by: M 2 M 1 - Mass of first object M 2 - Mass of second object r M 1 r - separation distance, center-to-center for spherical objects F g = GM 1 M 2 Universal Gravitational Constant: r 2 G = 6 . 67 × 10 − 11 N · m 2 /kg 2 Inverse square law Newton’s Gravity April 19, 2013 - p. 2/8

Inverse Square Law Exercise When two masses are a distance r 1 apart from each other the gravitational force between them is 5 N . They are then moved to a new separation, r 2 , where the gravitational force between them is 10 N . What is the relation between r 1 and r 2 ? Newton’s Gravity April 19, 2013 - p. 3/8

Inverse Square Law Exercise When two masses are a distance r 1 apart from each other the gravitational force between them is 5 N . They are then moved to a new separation, r 2 , where the gravitational force between them is 10 N . What is the relation between r 1 and r 2 ? (a) r 2 = r 1 Newton’s Gravity April 19, 2013 - p. 3/8

Inverse Square Law Exercise When two masses are a distance r 1 apart from each other the gravitational force between them is 5 N . They are then moved to a new separation, r 2 , where the gravitational force between them is 10 N . What is the relation between r 1 and r 2 ? (a) r 2 = r 1 (b) r 2 = 2 r 1 Newton’s Gravity April 19, 2013 - p. 3/8

Inverse Square Law Exercise When two masses are a distance r 1 apart from each other the gravitational force between them is 5 N . They are then moved to a new separation, r 2 , where the gravitational force between them is 10 N . What is the relation between r 1 and r 2 ? (a) r 2 = r 1 (b) r 2 = 2 r 1 � √ � (c) r 2 = 2 r 1 = (1 . 4) r 1 Newton’s Gravity April 19, 2013 - p. 3/8

Inverse Square Law Exercise When two masses are a distance r 1 apart from each other the gravitational force between them is 5 N . They are then moved to a new separation, r 2 , where the gravitational force between them is 10 N . What is the relation between r 1 and r 2 ? (a) r 2 = r 1 (b) r 2 = 2 r 1 � 1 � � √ � (c) r 2 = 2 r 1 = (1 . 4) r 1 (d) r 2 = r 1 2 Newton’s Gravity April 19, 2013 - p. 3/8

Inverse Square Law Exercise When two masses are a distance r 1 apart from each other the gravitational force between them is 5 N . They are then moved to a new separation, r 2 , where the gravitational force between them is 10 N . What is the relation between r 1 and r 2 ? (a) r 2 = r 1 (b) r 2 = 2 r 1 � 1 � � √ � (c) r 2 = 2 r 1 = (1 . 4) r 1 (d) r 2 = r 1 2 � 1 � (e) r 2 = r 1 = (0 . 707) r 1 √ 2 Newton’s Gravity April 19, 2013 - p. 3/8

Inverse Square Law Exercise When two masses are a distance r 1 apart from each other the gravitational force between them is 5 N . They are then moved to a new separation, r 2 , where the gravitational force between them is 10 N . What is the relation between r 1 and r 2 ? (a) r 2 = r 1 (b) r 2 = 2 r 1 � 1 � � √ � (c) r 2 = 2 r 1 = (1 . 4) r 1 (d) r 2 = r 1 2 � 1 � (e) r 2 = r 1 = (0 . 707) r 1 √ 2 Newton’s Gravity April 19, 2013 - p. 3/8

Inverse Square Law Exercise When two masses are a distance r 1 apart from each other the gravitational force between them is 5 N . They are then moved to a new separation, r 2 , where the gravitational force between them is 10 N . What is the relation between r 1 and r 2 ? (a) r 2 = r 1 (b) r 2 = 2 r 1 � 1 � � √ � (c) r 2 = 2 r 1 = (1 . 4) r 1 (d) r 2 = r 1 2 � 1 � (e) r 2 = r 1 = (0 . 707) r 1 √ 2 F 2 = GM 1 M 2 = GM 1 M 2 � 2 = GM 1 M 2 = GM 1 M 2 × 2 = 2 F 1 √ r 2 r 2 r 2 1 / 2 � r 1 / 2 2 1 Newton’s Gravity April 19, 2013 - p. 3/8

Direction The gravitational force is an “attractive" force ⇒ each object feels a force towards the other. Newton’s Gravity April 19, 2013 - p. 4/8

Direction The gravitational force is an “attractive" force ⇒ each object feels a force towards the other. M 2 M 1 Newton’s Gravity April 19, 2013 - p. 4/8

Direction The gravitational force is an “attractive" force ⇒ each object feels a force towards the other. M 2 M 1 Newton’s Gravity April 19, 2013 - p. 4/8

Direction The gravitational force is an “attractive" force ⇒ each object feels a force towards the other. − → 1 - Force on 1 due to 2 F M 2 → − F 1 M 1 Newton’s Gravity April 19, 2013 - p. 4/8

Direction The gravitational force is an “attractive" force ⇒ each object feels a force towards the other. − → 1 - Force on 1 due to 2 F → − M 2 2 - Force on 2 due to 1 F → − F 1 M 1 Newton’s Gravity April 19, 2013 - p. 4/8

Direction The gravitational force is an “attractive" force ⇒ each object feels a force towards the other. − → 1 - Force on 1 due to 2 F → − M 2 2 - Force on 2 due to 1 F → − F 2 → − F 1 M 1 Newton’s Gravity April 19, 2013 - p. 4/8

Direction The gravitational force is an “attractive" force ⇒ each object feels a force towards the other. → − 1 - Force on 1 due to 2 F → − M 2 2 - Force on 2 due to 1 F → − F 2 Geometry determines direction → − F 1 M 1 Newton’s Gravity April 19, 2013 - p. 4/8

Direction The gravitational force is an “attractive" force ⇒ each object feels a force towards the other. − → 1 - Force on 1 due to 2 F → − M 2 2 - Force on 2 due to 1 F → − F 2 Geometry determines direction → − F 1 M 1 φ Newton’s Gravity April 19, 2013 - p. 4/8

Direction The gravitational force is an “attractive" force ⇒ each object feels a force towards the other. − → 1 - Force on 1 due to 2 F → − M 2 2 - Force on 2 due to 1 F → − F 2 Geometry determines direction → − F 1 M 1 φ f. b. d. for M 1 Newton’s Gravity April 19, 2013 - p. 4/8

Direction The gravitational force is an “attractive" force ⇒ each object feels a force towards the other. − → 1 - Force on 1 due to 2 F → − M 2 2 - Force on 2 due to 1 F → − F 2 Geometry determines direction → − F 1 M 1 φ f. b. d. for M 1 → − F 1 Newton’s Gravity April 19, 2013 - p. 4/8