Circular Motion Centripetal Force and Acceleration Tangential Velocity
![Circular Motion Centripetal Force and Acceleration Circular Motion Centripetal Force and Acceleration](https://slidetodoc.com/presentation_image/3c857d1efde722f2f3822ecf80cbd95a/image-1.jpg)
![Tangential Velocity • Tangential Velocity (Vt)- object’s speed along an imaginary line that is Tangential Velocity • Tangential Velocity (Vt)- object’s speed along an imaginary line that is](https://slidetodoc.com/presentation_image/3c857d1efde722f2f3822ecf80cbd95a/image-2.jpg)
![](https://slidetodoc.com/presentation_image/3c857d1efde722f2f3822ecf80cbd95a/image-3.jpg)
![Tangential Velocity Vt=2πr/T • r=radius of the circle • T=Period (amount of time to Tangential Velocity Vt=2πr/T • r=radius of the circle • T=Period (amount of time to](https://slidetodoc.com/presentation_image/3c857d1efde722f2f3822ecf80cbd95a/image-4.jpg)
![Example –A plane makes a complete circle with a radius of 3622 m in Example –A plane makes a complete circle with a radius of 3622 m in](https://slidetodoc.com/presentation_image/3c857d1efde722f2f3822ecf80cbd95a/image-5.jpg)
![Centripetal Acceleration • When an object is moving in a circular path, the direction Centripetal Acceleration • When an object is moving in a circular path, the direction](https://slidetodoc.com/presentation_image/3c857d1efde722f2f3822ecf80cbd95a/image-6.jpg)
![Centripetal Acceleration • Centripetal acceleration is always directed towards the center of the circle Centripetal Acceleration • Centripetal acceleration is always directed towards the center of the circle](https://slidetodoc.com/presentation_image/3c857d1efde722f2f3822ecf80cbd95a/image-7.jpg)
![Centripetal Acceleration Centripetal Acceleration](https://slidetodoc.com/presentation_image/3c857d1efde722f2f3822ecf80cbd95a/image-8.jpg)
![Tangential Accleration • Centripetal acceleration results from change in direction • When the speed Tangential Accleration • Centripetal acceleration results from change in direction • When the speed](https://slidetodoc.com/presentation_image/3c857d1efde722f2f3822ecf80cbd95a/image-9.jpg)
![Centripetal Force • Remember! • When an object is accelerating there is a net Centripetal Force • Remember! • When an object is accelerating there is a net](https://slidetodoc.com/presentation_image/3c857d1efde722f2f3822ecf80cbd95a/image-10.jpg)
![Examples • If a mass is twirled in a circle, at the end of Examples • If a mass is twirled in a circle, at the end of](https://slidetodoc.com/presentation_image/3c857d1efde722f2f3822ecf80cbd95a/image-11.jpg)
![Centripetal Force • • • Centripetal Force =mass x centripetal acceleration Fc=mac Substitute ac Centripetal Force • • • Centripetal Force =mass x centripetal acceleration Fc=mac Substitute ac](https://slidetodoc.com/presentation_image/3c857d1efde722f2f3822ecf80cbd95a/image-12.jpg)
![Example- Standard • A 0. 50 kg mass is whirled in a circle of Example- Standard • A 0. 50 kg mass is whirled in a circle of](https://slidetodoc.com/presentation_image/3c857d1efde722f2f3822ecf80cbd95a/image-13.jpg)
![Example-Honors • A 0. 50 kg mass sits on a frictionless table and is Example-Honors • A 0. 50 kg mass sits on a frictionless table and is](https://slidetodoc.com/presentation_image/3c857d1efde722f2f3822ecf80cbd95a/image-14.jpg)
![Example • A car traveling at 14 m/s goes around an unbanked curve in Example • A car traveling at 14 m/s goes around an unbanked curve in](https://slidetodoc.com/presentation_image/3c857d1efde722f2f3822ecf80cbd95a/image-15.jpg)
![Clicker Question • Calculate the centripetal force acting on a 925 kg car as Clicker Question • Calculate the centripetal force acting on a 925 kg car as](https://slidetodoc.com/presentation_image/3c857d1efde722f2f3822ecf80cbd95a/image-16.jpg)
![Clicker Question • An amusement park ride has a radius of 2. 8 m. Clicker Question • An amusement park ride has a radius of 2. 8 m.](https://slidetodoc.com/presentation_image/3c857d1efde722f2f3822ecf80cbd95a/image-17.jpg)
![Clicker Question • A 2. 7 x 103 kg satellite orbits the Earth at Clicker Question • A 2. 7 x 103 kg satellite orbits the Earth at](https://slidetodoc.com/presentation_image/3c857d1efde722f2f3822ecf80cbd95a/image-18.jpg)
![Clicker Question. An object moves in a circle at a constant speed. Which of Clicker Question. An object moves in a circle at a constant speed. Which of](https://slidetodoc.com/presentation_image/3c857d1efde722f2f3822ecf80cbd95a/image-19.jpg)
![Clicker Question A car traveling at 15 m/s on a flat surface turns in Clicker Question A car traveling at 15 m/s on a flat surface turns in](https://slidetodoc.com/presentation_image/3c857d1efde722f2f3822ecf80cbd95a/image-20.jpg)
![Centrifugal Force • When a driver takes a sharp left turn, the passenger slides Centrifugal Force • When a driver takes a sharp left turn, the passenger slides](https://slidetodoc.com/presentation_image/3c857d1efde722f2f3822ecf80cbd95a/image-21.jpg)
![Describing Motion • What happens when centripetal force disappears? Where does the object go? Describing Motion • What happens when centripetal force disappears? Where does the object go?](https://slidetodoc.com/presentation_image/3c857d1efde722f2f3822ecf80cbd95a/image-22.jpg)
![Vertical Versus Horizontal • Draw a free body diagram of a mass moving in Vertical Versus Horizontal • Draw a free body diagram of a mass moving in](https://slidetodoc.com/presentation_image/3c857d1efde722f2f3822ecf80cbd95a/image-23.jpg)
![Example • A 1. 7 kg object is swung from the end of a Example • A 1. 7 kg object is swung from the end of a](https://slidetodoc.com/presentation_image/3c857d1efde722f2f3822ecf80cbd95a/image-24.jpg)
![Constant Velocity • When you are trying to find the minimum speed of an Constant Velocity • When you are trying to find the minimum speed of an](https://slidetodoc.com/presentation_image/3c857d1efde722f2f3822ecf80cbd95a/image-25.jpg)
![Example • An object is swung in a vertical circle with a radius of Example • An object is swung in a vertical circle with a radius of](https://slidetodoc.com/presentation_image/3c857d1efde722f2f3822ecf80cbd95a/image-26.jpg)
![Circular Motion Gravitation Circular Motion Gravitation](https://slidetodoc.com/presentation_image/3c857d1efde722f2f3822ecf80cbd95a/image-27.jpg)
![What is Gravity? • The force that pulls us to the earth • It What is Gravity? • The force that pulls us to the earth • It](https://slidetodoc.com/presentation_image/3c857d1efde722f2f3822ecf80cbd95a/image-28.jpg)
![Gravity • The gravitational forces that two masses exert on each other are always Gravity • The gravitational forces that two masses exert on each other are always](https://slidetodoc.com/presentation_image/3c857d1efde722f2f3822ecf80cbd95a/image-29.jpg)
![Gravity • Is Proportional to the two masses • Is inversely proportional to the Gravity • Is Proportional to the two masses • Is inversely proportional to the](https://slidetodoc.com/presentation_image/3c857d1efde722f2f3822ecf80cbd95a/image-30.jpg)
![Example • Calculate the force of gravity between two 75 kg students if their Example • Calculate the force of gravity between two 75 kg students if their](https://slidetodoc.com/presentation_image/3c857d1efde722f2f3822ecf80cbd95a/image-31.jpg)
![Example 2 • A satellite weighs 9000 N on Earth’s surface. How much does Example 2 • A satellite weighs 9000 N on Earth’s surface. How much does](https://slidetodoc.com/presentation_image/3c857d1efde722f2f3822ecf80cbd95a/image-32.jpg)
![Clicker Question. Earth (m = 5. 97 1024 kg) orbits the sun (m = Clicker Question. Earth (m = 5. 97 1024 kg) orbits the sun (m =](https://slidetodoc.com/presentation_image/3c857d1efde722f2f3822ecf80cbd95a/image-33.jpg)
![Clicker Question • Gravitational force F exists between point objects A and B separated Clicker Question • Gravitational force F exists between point objects A and B separated](https://slidetodoc.com/presentation_image/3c857d1efde722f2f3822ecf80cbd95a/image-34.jpg)
![Common Misconception: Mass Versus Weight Mass • Amount of matter Weight • Gravitational attraction Common Misconception: Mass Versus Weight Mass • Amount of matter Weight • Gravitational attraction](https://slidetodoc.com/presentation_image/3c857d1efde722f2f3822ecf80cbd95a/image-35.jpg)
![Clicker Question Which of the following statements is correct? A. Mass and weight both Clicker Question Which of the following statements is correct? A. Mass and weight both](https://slidetodoc.com/presentation_image/3c857d1efde722f2f3822ecf80cbd95a/image-36.jpg)
![Satellites • Are constantly “falling” when in orbit • They are in freefall Satellites • Are constantly “falling” when in orbit • They are in freefall](https://slidetodoc.com/presentation_image/3c857d1efde722f2f3822ecf80cbd95a/image-37.jpg)
![Gravitational Field • Gravity is an example of a field force (ie not a Gravitational Field • Gravity is an example of a field force (ie not a](https://slidetodoc.com/presentation_image/3c857d1efde722f2f3822ecf80cbd95a/image-38.jpg)
![Gravitational Fields • Fields can be described as vectors or scalars, depends on what Gravitational Fields • Fields can be described as vectors or scalars, depends on what](https://slidetodoc.com/presentation_image/3c857d1efde722f2f3822ecf80cbd95a/image-39.jpg)
![Gravitational Field Strength • Gravitational field strength=acceleration due to gravity • Recall Fg=mg • Gravitational Field Strength • Gravitational field strength=acceleration due to gravity • Recall Fg=mg •](https://slidetodoc.com/presentation_image/3c857d1efde722f2f3822ecf80cbd95a/image-40.jpg)
![Example • What is the gravitational field strength on the Earth’s surface of the Example • What is the gravitational field strength on the Earth’s surface of the](https://slidetodoc.com/presentation_image/3c857d1efde722f2f3822ecf80cbd95a/image-41.jpg)
![Clicker Question. Which of the following is a correct interpretation of the expression? A. Clicker Question. Which of the following is a correct interpretation of the expression? A.](https://slidetodoc.com/presentation_image/3c857d1efde722f2f3822ecf80cbd95a/image-42.jpg)
![The Period of a Satellite • T=√(4π2 r 3) • Gm • m refers The Period of a Satellite • T=√(4π2 r 3) • Gm • m refers](https://slidetodoc.com/presentation_image/3c857d1efde722f2f3822ecf80cbd95a/image-43.jpg)
![Example • A satellite orbits the Earth at a radius of 2. 2 x Example • A satellite orbits the Earth at a radius of 2. 2 x](https://slidetodoc.com/presentation_image/3c857d1efde722f2f3822ecf80cbd95a/image-44.jpg)
- Slides: 44
![Circular Motion Centripetal Force and Acceleration Circular Motion Centripetal Force and Acceleration](https://slidetodoc.com/presentation_image/3c857d1efde722f2f3822ecf80cbd95a/image-1.jpg)
Circular Motion Centripetal Force and Acceleration
![Tangential Velocity Tangential Velocity Vt objects speed along an imaginary line that is Tangential Velocity • Tangential Velocity (Vt)- object’s speed along an imaginary line that is](https://slidetodoc.com/presentation_image/3c857d1efde722f2f3822ecf80cbd95a/image-2.jpg)
Tangential Velocity • Tangential Velocity (Vt)- object’s speed along an imaginary line that is drawn tangent to the circular path • Depends on distance from the object to the center of the circular path • When the tangential speed is constant then the motion is described as uniform circular motion
![](https://slidetodoc.com/presentation_image/3c857d1efde722f2f3822ecf80cbd95a/image-3.jpg)
![Tangential Velocity Vt2πrT rradius of the circle TPeriod amount of time to Tangential Velocity Vt=2πr/T • r=radius of the circle • T=Period (amount of time to](https://slidetodoc.com/presentation_image/3c857d1efde722f2f3822ecf80cbd95a/image-4.jpg)
Tangential Velocity Vt=2πr/T • r=radius of the circle • T=Period (amount of time to complete one circle) •
![Example A plane makes a complete circle with a radius of 3622 m in Example –A plane makes a complete circle with a radius of 3622 m in](https://slidetodoc.com/presentation_image/3c857d1efde722f2f3822ecf80cbd95a/image-5.jpg)
Example –A plane makes a complete circle with a radius of 3622 m in 2. 10 min. What is the speed of the plane?
![Centripetal Acceleration When an object is moving in a circular path the direction Centripetal Acceleration • When an object is moving in a circular path, the direction](https://slidetodoc.com/presentation_image/3c857d1efde722f2f3822ecf80cbd95a/image-6.jpg)
Centripetal Acceleration • When an object is moving in a circular path, the direction changes • If the object has a constant SPEED, Acceleration is due to the direction changing • This is called centripetal acceleration
![Centripetal Acceleration Centripetal acceleration is always directed towards the center of the circle Centripetal Acceleration • Centripetal acceleration is always directed towards the center of the circle](https://slidetodoc.com/presentation_image/3c857d1efde722f2f3822ecf80cbd95a/image-7.jpg)
Centripetal Acceleration • Centripetal acceleration is always directed towards the center of the circle • Centripetal=center seeking
![Centripetal Acceleration Centripetal Acceleration](https://slidetodoc.com/presentation_image/3c857d1efde722f2f3822ecf80cbd95a/image-8.jpg)
Centripetal Acceleration
![Tangential Accleration Centripetal acceleration results from change in direction When the speed Tangential Accleration • Centripetal acceleration results from change in direction • When the speed](https://slidetodoc.com/presentation_image/3c857d1efde722f2f3822ecf80cbd95a/image-9.jpg)
Tangential Accleration • Centripetal acceleration results from change in direction • When the speed changes in a circle it is called tangential acceleration • Consider a car moving in a circle
![Centripetal Force Remember When an object is accelerating there is a net Centripetal Force • Remember! • When an object is accelerating there is a net](https://slidetodoc.com/presentation_image/3c857d1efde722f2f3822ecf80cbd95a/image-10.jpg)
Centripetal Force • Remember! • When an object is accelerating there is a net force • If there is centripetal acceleration, there is a net force- Centripetal Force –This is not a new force –Net force that accelerates an object towards the center of a circle
![Examples If a mass is twirled in a circle at the end of Examples • If a mass is twirled in a circle, at the end of](https://slidetodoc.com/presentation_image/3c857d1efde722f2f3822ecf80cbd95a/image-11.jpg)
Examples • If a mass is twirled in a circle, at the end of a string, the centripetal force is provided by the tension • When a car rounds a corner on a highway, the centripetal force is provided by friction • When the moon orbits the Earth, the centripetal force is provided by gravity
![Centripetal Force Centripetal Force mass x centripetal acceleration Fcmac Substitute ac Centripetal Force • • • Centripetal Force =mass x centripetal acceleration Fc=mac Substitute ac](https://slidetodoc.com/presentation_image/3c857d1efde722f2f3822ecf80cbd95a/image-12.jpg)
Centripetal Force • • • Centripetal Force =mass x centripetal acceleration Fc=mac Substitute ac Fc=m V 2/r Substitute Vt Fc=m 4π2 r/T 2
![Example Standard A 0 50 kg mass is whirled in a circle of Example- Standard • A 0. 50 kg mass is whirled in a circle of](https://slidetodoc.com/presentation_image/3c857d1efde722f2f3822ecf80cbd95a/image-13.jpg)
Example- Standard • A 0. 50 kg mass is whirled in a circle of radius 0. 20 m at 2. 3 m/s. Calculate the centripetal force acting on the mass
![ExampleHonors A 0 50 kg mass sits on a frictionless table and is Example-Honors • A 0. 50 kg mass sits on a frictionless table and is](https://slidetodoc.com/presentation_image/3c857d1efde722f2f3822ecf80cbd95a/image-14.jpg)
Example-Honors • A 0. 50 kg mass sits on a frictionless table and is attached to hanging weight. The 0. 50 kg mass is whirled in a circle of radius 0. 20 m at 2. 3 m/s. Calculate the centripetal force acting on the mass. • Calculate the mass of the hanging weight
![Example A car traveling at 14 ms goes around an unbanked curve in Example • A car traveling at 14 m/s goes around an unbanked curve in](https://slidetodoc.com/presentation_image/3c857d1efde722f2f3822ecf80cbd95a/image-15.jpg)
Example • A car traveling at 14 m/s goes around an unbanked curve in the road that has a radius of 96 m. What is its centripetal acceleration? • What is the minimum coefficient of friction between the road and the car’s tires?
![Clicker Question Calculate the centripetal force acting on a 925 kg car as Clicker Question • Calculate the centripetal force acting on a 925 kg car as](https://slidetodoc.com/presentation_image/3c857d1efde722f2f3822ecf80cbd95a/image-16.jpg)
Clicker Question • Calculate the centripetal force acting on a 925 kg car as it rounds an unbanked curve with a radius of 75 m at a speed of 22 m/s.
![Clicker Question An amusement park ride has a radius of 2 8 m Clicker Question • An amusement park ride has a radius of 2. 8 m.](https://slidetodoc.com/presentation_image/3c857d1efde722f2f3822ecf80cbd95a/image-17.jpg)
Clicker Question • An amusement park ride has a radius of 2. 8 m. If the time of one revolution of a rider is 0. 98 s, what is the speed of the rider?
![Clicker Question A 2 7 x 103 kg satellite orbits the Earth at Clicker Question • A 2. 7 x 103 kg satellite orbits the Earth at](https://slidetodoc.com/presentation_image/3c857d1efde722f2f3822ecf80cbd95a/image-18.jpg)
Clicker Question • A 2. 7 x 103 kg satellite orbits the Earth at a distance of 1. 8 x 107 m from the Earth’s centre at a speed of 4. 7 x 103 m/s. What force does the Earth exert on the satellite?
![Clicker Question An object moves in a circle at a constant speed Which of Clicker Question. An object moves in a circle at a constant speed. Which of](https://slidetodoc.com/presentation_image/3c857d1efde722f2f3822ecf80cbd95a/image-19.jpg)
Clicker Question. An object moves in a circle at a constant speed. Which of the following is not true of the object? A. Its centripetal acceleration is constant. B. Its tangential speed is constant. C. Its velocity is constant. D. A centripetal force acts on the object.
![Clicker Question A car traveling at 15 ms on a flat surface turns in Clicker Question A car traveling at 15 m/s on a flat surface turns in](https://slidetodoc.com/presentation_image/3c857d1efde722f2f3822ecf80cbd95a/image-20.jpg)
Clicker Question A car traveling at 15 m/s on a flat surface turns in a circle with a radius of 25 m. 2. What is the centripetal acceleration of the car? A. 2. 4 10 -2 m/s 2 B. 0. 60 m/s 2 C. 9. 0 m/s 2 D. zero
![Centrifugal Force When a driver takes a sharp left turn the passenger slides Centrifugal Force • When a driver takes a sharp left turn, the passenger slides](https://slidetodoc.com/presentation_image/3c857d1efde722f2f3822ecf80cbd95a/image-21.jpg)
Centrifugal Force • When a driver takes a sharp left turn, the passenger slides to the right of the car and into the door, Why? • Centrifugal=center-fleeing • Apparent force that causes a revolving or rotating object to move in a straight line • However-Newton’s first law states- an object in motion will stay in motion until a force acts on it • Centrifugal force does not really exist!
![Describing Motion What happens when centripetal force disappears Where does the object go Describing Motion • What happens when centripetal force disappears? Where does the object go?](https://slidetodoc.com/presentation_image/3c857d1efde722f2f3822ecf80cbd95a/image-22.jpg)
Describing Motion • What happens when centripetal force disappears? Where does the object go? • A ball that is on the end of a string is whirled in a vertical circular path. – If the string breaks at the position shown in (a), the ball will move vertically upward in free fall. – If the string breaks at the top of the ball’s path, as in (b), the ball will move along a parabolic path.
![Vertical Versus Horizontal Draw a free body diagram of a mass moving in Vertical Versus Horizontal • Draw a free body diagram of a mass moving in](https://slidetodoc.com/presentation_image/3c857d1efde722f2f3822ecf80cbd95a/image-23.jpg)
Vertical Versus Horizontal • Draw a free body diagram of a mass moving in a vertical circle, when the object is at the top of the path and the bottom of the path • As with any object moving in a circle there is a net force acting on it towards the center of the circle • The net force is the centripetal force • At the top Fnet (Fc)=Ft +Fg • At the bottom Fnet (Fc)=Ft-Fg
![Example A 1 7 kg object is swung from the end of a Example • A 1. 7 kg object is swung from the end of a](https://slidetodoc.com/presentation_image/3c857d1efde722f2f3822ecf80cbd95a/image-24.jpg)
Example • A 1. 7 kg object is swung from the end of a 0. 60 m string in a vertical circle. If the time of one revolution is 1. 1 s, what is the tension in the string • A) at the top? • B) at the bottom?
![Constant Velocity When you are trying to find the minimum speed of an Constant Velocity • When you are trying to find the minimum speed of an](https://slidetodoc.com/presentation_image/3c857d1efde722f2f3822ecf80cbd95a/image-25.jpg)
Constant Velocity • When you are trying to find the minimum speed of an object at the top of its circular arc we can use the equation • Fc=Fg so • The centripetal acceleration equals the acceleration due to gravity (ac=9. 8 m/s/s) • So • g=Vt 2/r • V=√(gr)
![Example An object is swung in a vertical circle with a radius of Example • An object is swung in a vertical circle with a radius of](https://slidetodoc.com/presentation_image/3c857d1efde722f2f3822ecf80cbd95a/image-26.jpg)
Example • An object is swung in a vertical circle with a radius of 0. 75 m. What is the minimum speed of the object at the top of the motion for the object to remain in circular motion?
![Circular Motion Gravitation Circular Motion Gravitation](https://slidetodoc.com/presentation_image/3c857d1efde722f2f3822ecf80cbd95a/image-27.jpg)
Circular Motion Gravitation
![What is Gravity The force that pulls us to the earth It What is Gravity? • The force that pulls us to the earth • It](https://slidetodoc.com/presentation_image/3c857d1efde722f2f3822ecf80cbd95a/image-28.jpg)
What is Gravity? • The force that pulls us to the earth • It is much more than that • Gravity is the force that attracts two bodies that have mass and energy to each other • Newton discovered that gravity attracts any two objects depending on their masses and their distance apart
![Gravity The gravitational forces that two masses exert on each other are always Gravity • The gravitational forces that two masses exert on each other are always](https://slidetodoc.com/presentation_image/3c857d1efde722f2f3822ecf80cbd95a/image-29.jpg)
Gravity • The gravitational forces that two masses exert on each other are always equal in magnitude and are opposite in directions. • Newton’s Third Law
![Gravity Is Proportional to the two masses Is inversely proportional to the Gravity • Is Proportional to the two masses • Is inversely proportional to the](https://slidetodoc.com/presentation_image/3c857d1efde722f2f3822ecf80cbd95a/image-30.jpg)
Gravity • Is Proportional to the two masses • Is inversely proportional to the square of the distance between their center of mass • So if two objects are twice as far away from each what happens to the gravitational force by? • Fg=Gm 1 m 2 r 2 • G=6. 67 x 10 -11 N m 2/kg 2 • M 1= mass of the first object • M 2= mass of the second object • r= distance between the two centers of mass
![Example Calculate the force of gravity between two 75 kg students if their Example • Calculate the force of gravity between two 75 kg students if their](https://slidetodoc.com/presentation_image/3c857d1efde722f2f3822ecf80cbd95a/image-31.jpg)
Example • Calculate the force of gravity between two 75 kg students if their centers of mass are 0. 95 m apart
![Example 2 A satellite weighs 9000 N on Earths surface How much does Example 2 • A satellite weighs 9000 N on Earth’s surface. How much does](https://slidetodoc.com/presentation_image/3c857d1efde722f2f3822ecf80cbd95a/image-32.jpg)
Example 2 • A satellite weighs 9000 N on Earth’s surface. How much does it weigh if its mass is tripled and its orbital radius is doubled?
![Clicker Question Earth m 5 97 1024 kg orbits the sun m Clicker Question. Earth (m = 5. 97 1024 kg) orbits the sun (m =](https://slidetodoc.com/presentation_image/3c857d1efde722f2f3822ecf80cbd95a/image-33.jpg)
Clicker Question. Earth (m = 5. 97 1024 kg) orbits the sun (m = 1. 99 1030 kg) at a mean distance of 1. 50 1011 m. What is the gravitational force of the sun on Earth? (G = 6. 673 10 -11 N • m 2/kg 2) A. 5. 29 1032 N B. 3. 52 1022 N C. 5. 90 10– 2 N D. 1. 77 10– 8 N
![Clicker Question Gravitational force F exists between point objects A and B separated Clicker Question • Gravitational force F exists between point objects A and B separated](https://slidetodoc.com/presentation_image/3c857d1efde722f2f3822ecf80cbd95a/image-34.jpg)
Clicker Question • Gravitational force F exists between point objects A and B separated by distance R. If the mass of A is doubled and distance R is tripled, what is the new gravitational force between A and B? A) 9/2 F B) 2/3 F C) 2/9 F D) 3/2 F
![Common Misconception Mass Versus Weight Mass Amount of matter Weight Gravitational attraction Common Misconception: Mass Versus Weight Mass • Amount of matter Weight • Gravitational attraction](https://slidetodoc.com/presentation_image/3c857d1efde722f2f3822ecf80cbd95a/image-35.jpg)
Common Misconception: Mass Versus Weight Mass • Amount of matter Weight • Gravitational attraction (Fg) • Constant everywhere • Changes depending on location
![Clicker Question Which of the following statements is correct A Mass and weight both Clicker Question Which of the following statements is correct? A. Mass and weight both](https://slidetodoc.com/presentation_image/3c857d1efde722f2f3822ecf80cbd95a/image-36.jpg)
Clicker Question Which of the following statements is correct? A. Mass and weight both vary with location. B. Mass varies with location, but weight does not. C. Weight varies with location, but mass does not. D. Neither mass nor weight varies with location.
![Satellites Are constantly falling when in orbit They are in freefall Satellites • Are constantly “falling” when in orbit • They are in freefall](https://slidetodoc.com/presentation_image/3c857d1efde722f2f3822ecf80cbd95a/image-37.jpg)
Satellites • Are constantly “falling” when in orbit • They are in freefall
![Gravitational Field Gravity is an example of a field force ie not a Gravitational Field • Gravity is an example of a field force (ie not a](https://slidetodoc.com/presentation_image/3c857d1efde722f2f3822ecf80cbd95a/image-38.jpg)
Gravitational Field • Gravity is an example of a field force (ie not a contact force) • A force that is exerted which has no direct contact • A field- an area of influence • Think about a campfire • As you approach it • As you increase the size
![Gravitational Fields Fields can be described as vectors or scalars depends on what Gravitational Fields • Fields can be described as vectors or scalars, depends on what](https://slidetodoc.com/presentation_image/3c857d1efde722f2f3822ecf80cbd95a/image-39.jpg)
Gravitational Fields • Fields can be described as vectors or scalars, depends on what kind • Gravitational fields are field forces so. . • They are vectors • Gravitational fields are represented by arrows, magnitude is represented by how many arrows are present
![Gravitational Field Strength Gravitational field strengthacceleration due to gravity Recall Fgmg Gravitational Field Strength • Gravitational field strength=acceleration due to gravity • Recall Fg=mg •](https://slidetodoc.com/presentation_image/3c857d1efde722f2f3822ecf80cbd95a/image-40.jpg)
Gravitational Field Strength • Gravitational field strength=acceleration due to gravity • Recall Fg=mg • So… • g=Fg/m • g=acceleration due to gravity, gravitational field strength, 9. 80 m/s 2 near the Earth’s surface • g varies with distance • g=Gm 1 r 2 • Measured in N/kg, same as m/s 2
![Example What is the gravitational field strength on the Earths surface of the Example • What is the gravitational field strength on the Earth’s surface of the](https://slidetodoc.com/presentation_image/3c857d1efde722f2f3822ecf80cbd95a/image-41.jpg)
Example • What is the gravitational field strength on the Earth’s surface of the moon? The mass of the moon is 7. 35 x 1022 kg and the radius of the moon is 1. 74 x 106 m
![Clicker Question Which of the following is a correct interpretation of the expression A Clicker Question. Which of the following is a correct interpretation of the expression? A.](https://slidetodoc.com/presentation_image/3c857d1efde722f2f3822ecf80cbd95a/image-42.jpg)
Clicker Question. Which of the following is a correct interpretation of the expression? A. Gravitational field strength changes with an object’s distance from Earth. B. Free-fall acceleration changes with an object’s distance from Earth. C. Free-fall acceleration is independent of the falling object’s mass. D. All of the above are correct interpretation
![The Period of a Satellite T4π2 r 3 Gm m refers The Period of a Satellite • T=√(4π2 r 3) • Gm • m refers](https://slidetodoc.com/presentation_image/3c857d1efde722f2f3822ecf80cbd95a/image-43.jpg)
The Period of a Satellite • T=√(4π2 r 3) • Gm • m refers to the mass of the center of the orbit
![Example A satellite orbits the Earth at a radius of 2 2 x Example • A satellite orbits the Earth at a radius of 2. 2 x](https://slidetodoc.com/presentation_image/3c857d1efde722f2f3822ecf80cbd95a/image-44.jpg)
Example • A satellite orbits the Earth at a radius of 2. 2 x 107 m. What is its orbital period, when the mass of the earth is 5. 98 x 1024 kg. What is the speed of the satellite?
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