April 22, Week 14 Today: Chapter 13, Gravity Exam #4, Next Friday, - PowerPoint PPT Presentation

April 22, Week 14 Today: Chapter 13, Gravity Exam #4, Next Friday, April 26 Practice Exam on Website. Review Sessions: Thursday, April 25, 5:15PM, 114 Regener Hall Newton’s Gravity April 22, 2013 - p. 1/11

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 22, 2013 - p. 2/11

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 22, 2013 - p. 2/11

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 22, 2013 - p. 2/11

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 22, 2013 - p. 2/11

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 22, 2013 - p. 2/11

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 22, 2013 - p. 2/11

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 22, 2013 - p. 2/11

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 22, 2013 - p. 2/11

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 22, 2013 - p. 2/11

The Negative Sign For distances larger than a planet’s radius: M 2 U g = − GM 1 M 2 r r M 1 Newton’s Gravity April 22, 2013 - p. 3/11

The Negative Sign For distances larger than a planet’s radius: M 2 U g = − GM 1 M 2 r This equation comes with a built in zero. r M 1 Newton’s Gravity April 22, 2013 - p. 3/11

The Negative Sign For distances larger than a planet’s radius: M 2 U g = − GM 1 M 2 r This equation comes with a built in zero. r As r → ∞ , U g = 0 M 1 Newton’s Gravity April 22, 2013 - p. 3/11

The Negative Sign For distances larger than a planet’s radius: M 2 U g = − GM 1 M 2 r This equation comes with a built in zero. r As r → ∞ , U g = 0 When M 1 and M 2 are infinitely far apart M 1 U g = 0 . When objects move in the direc- tion of the force acting on them their poten- tial energy decreases ⇒ as M 2 gets closer to M 1 , its potential energy decreases from zero ⇒ a negative amount. Newton’s Gravity April 22, 2013 - p. 3/11

The Negative Sign For distances larger than a planet’s radius: M 2 U g = − GM 1 M 2 r → − F g This equation comes with a built in zero. r As r → ∞ , U g = 0 When M 1 and M 2 are infinitely far apart M 1 U g = 0 . When objects move in the direc- tion of the force acting on them their poten- tial energy decreases ⇒ as M 2 gets closer to M 1 , its potential energy decreases from zero ⇒ a negative amount. Newton’s Gravity April 22, 2013 - p. 3/11

Escape Speed When gravity is the only force doing work on a rocket with mass M near a planet, M P : 1 1 − GM P M = 1 2 − GM P M 2 Mv 2 2 Mv 2 r 1 r 2 Newton’s Gravity April 22, 2013 - p. 4/11

Escape Speed When gravity is the only force doing work on a rocket with mass M near a planet, M P : 1 1 − GM P M = 1 2 − GM P M 2 Mv 2 2 Mv 2 r 1 r 2 Escape speed - The initial speed needed by a rocket in order to barely escape from a planet’s gravity. Newton’s Gravity April 22, 2013 - p. 4/11

Escape Speed When gravity is the only force doing work on a rocket with mass M near a planet, M P : 1 1 − GM P M = 1 2 − GM P M 2 Mv 2 2 Mv 2 r 1 r 2 Escape speed - The initial speed needed by a rocket in order to barely escape from a planet’s gravity. To escape a planet’s gravity ⇒ U g = 0 Newton’s Gravity April 22, 2013 - p. 4/11

Escape Speed When gravity is the only force doing work on a rocket with mass M near a planet, M P : 1 1 − GM P M = 1 2 − GM P M 2 Mv 2 2 Mv 2 r 1 r 2 Escape speed - The initial speed needed by a rocket in order to barely escape from a planet’s gravity. To escape a planet’s gravity ⇒ U g = 0 ⇒ r 2 → ∞ Newton’s Gravity April 22, 2013 - p. 4/11

Escape Speed When gravity is the only force doing work on a rocket with mass M near a planet, M P : 1 1 − GM P M = 1 2 − GM P M 2 Mv 2 2 Mv 2 r 1 r 2 Escape speed - The initial speed needed by a rocket in order to barely escape from a planet’s gravity. To escape a planet’s gravity ⇒ U g = 0 ⇒ r 2 → ∞ v 1 = v es =? r 1 v 2 = r 2 Newton’s Gravity April 22, 2013 - p. 4/11

Escape Speed When gravity is the only force doing work on a rocket with mass M near a planet, M P : 1 1 − GM P M = 1 2 − GM P M 2 Mv 2 2 Mv 2 r 1 r 2 Escape speed - The initial speed needed by a rocket in order to barely escape from a planet’s gravity. To escape a planet’s gravity ⇒ U g = 0 ⇒ r 2 → ∞ v 1 = v es =? r 1 = R (planet’s radius) v 2 = r 2 Newton’s Gravity April 22, 2013 - p. 4/11

Escape Speed When gravity is the only force doing work on a rocket with mass M near a planet, M P : 1 1 − GM P M = 1 2 − GM P M 2 Mv 2 2 Mv 2 r 1 r 2 Escape speed - The initial speed needed by a rocket in order to barely escape from a planet’s gravity. To escape a planet’s gravity ⇒ U g = 0 ⇒ r 2 → ∞ v 1 = v es =? r 1 = R (planet’s radius) v 2 = 0 (barely makes it) r 2 Newton’s Gravity April 22, 2013 - p. 4/11

Escape Speed When gravity is the only force doing work on a rocket with mass M near a planet, M P : 1 1 − GM P M = 1 2 − GM P M 2 Mv 2 2 Mv 2 r 1 r 2 Escape speed - The initial speed needed by a rocket in order to barely escape from a planet’s gravity. To escape a planet’s gravity ⇒ U g = 0 ⇒ r 2 → ∞ v 1 = v es =? r 1 = R (planet’s radius) v 2 = 0 (barely makes it) r 2 → ∞ Newton’s Gravity April 22, 2013 - p. 4/11

Escape Speed When gravity is the only force doing work on a rocket with mass M near a planet, M P : 1 1 − GM P M = 1 2 − GM P M 2 Mv 2 2 Mv 2 r 1 r 2 Escape speed - The initial speed needed by a rocket in order to barely escape from a planet’s gravity. To escape a planet’s gravity ⇒ U g = 0 ⇒ r 2 → ∞ v 1 = v es =? r 1 = R (planet’s radius) v 2 = 0 (barely makes it) r 2 → ∞ � 2 GM P v es = R Newton’s Gravity April 22, 2013 - p. 4/11

Review Question! A projectile is fired horizontally on earth. (At a small height.) How far does it fall during 1 s . For simplicity use g = 10 m/s 2 . Newton’s Gravity April 22, 2013 - p. 5/11

Review Question! A projectile is fired horizontally on earth. (At a small height.) How far does it fall during 1 s . For simplicity use g = 10 m/s 2 . (a) ∆ y = 0 Newton’s Gravity April 22, 2013 - p. 5/11

Review Question! A projectile is fired horizontally on earth. (At a small height.) How far does it fall during 1 s . For simplicity use g = 10 m/s 2 . (a) ∆ y = 0 (b) ∆ y = − 1 m Newton’s Gravity April 22, 2013 - p. 5/11

Review Question! A projectile is fired horizontally on earth. (At a small height.) How far does it fall during 1 s . For simplicity use g = 10 m/s 2 . (a) ∆ y = 0 (b) ∆ y = − 1 m (c) ∆ y = − 2 . 5 m Newton’s Gravity April 22, 2013 - p. 5/11

Review Question! A projectile is fired horizontally on earth. (At a small height.) How far does it fall during 1 s . For simplicity use g = 10 m/s 2 . (a) ∆ y = 0 (b) ∆ y = − 1 m (c) ∆ y = − 2 . 5 m (d) ∆ y = − 5 m Newton’s Gravity April 22, 2013 - p. 5/11