Chapter 7 Circular Motion and Gravitation

1. Chapter 7Circular Motion and Gravitation

2. 7.1 Circular Motion Centripetal Acceleration • This car is traveling in circular motion • Any object that revolves about a single axis undergoes circular motion.

3. Tangential speed depends on distance • Tangential speed (vt) can be used to describe the speed of an object in circular motion. • The speed of a car on a Ferris wheel is the car’s speed along an imaginary line drawn tangent to the car’s circular path. • When the tangential speed is constant, the motion is described as uniform circular motion. • Tangential speed also depends on the object’s distance from the center.

4. Centripetal acceleration is due to a change in direction • As a car moves on a Ferris wheel, it can be moving at a constant speed. • However, even though its tangential speed is constant, it undergoes an acceleration. • Acceleration depends on a change in velocity. • Remember, velocity is both direction and magnitude. Centripetal Acceleration

5. Anything moving in a circular path, even at constant speed, is changing direction therefore accelerating. • This is known as centripetal acceleration. • This change in velocity can be shown here graphically. • Centripetal acceleration is always directed towards the center. • Also known as “center seeking”.

6. Practice ACentripetal Acceleration • A test car moves at a constant speed around a circular track. • If the car is 48.2 m from the track’s center and has a centripetal acceleration of 8.05 m/s2, what is the car’s tangential speed? r = 48.2 m ac = 8.05 m/s2  Answer 19.7 m/s

7. Tangential acceleration is due to a change in speed • We have learned that centripetal acceleration results from a change in direction. • In circular motion, an acceleration due to a change in speed is called tangential acceleration. • A car traveling a great rate of speed that slows down in a turn or sharp curve in the road, experiences a tangential component of acceleration.

8. Centripetal Force • A ball whirled in a horizontal circular path at a constant speed constantly changes direction. • As we know this is a centripetal acceleration directed towards the center of motion. • As the ball moves in its circular path it undergoes a force called centripetal force. • In this example, it is countering gravitational force pulling downward on the ball as well.

9. In chapter 4 we learned F = ma. • This has been applied to our new formula here. • Centripetal force is simply the name given to the net force on an object in uniform circular motion. Tires Gravity

10. Practice BCentripetal Force • A pilot is flying a small plane at 56.6 m/s in a circular path with a radius of 188.5 m. • The centripetal force needed to maintain the plane’s circular motion is 1.89 x 104 N. • What is the plane’s mass?  Answer 1110 kg

11. Centripetal force is necessary for circular motion • Centripetal force acts at right angles to an object’s circular motion, therefore, the force changes the direction of the object’s velocity. • If this force (like the string) breaks, the object stops moving in a circular path. • Example (b) shows parabolic path due to earth's gravity.

12. Describing a Rotating System • To understand the motion of a rotating system, consider a car turning sharply to the left. • A passenger sitting in this car will appear to slide to the right against the door. • The inside of the car, like the seatbelt and door, prevent the passenger from being thrown from the car.

13. Inertia is often misinterpreted as a force • Before a car enters a sharp curve, the passengers are traveling in a straight line. • Because of inertia, the passengers want to continue in a straight path. • Newton’s inertia law reminds us how all moving objects resist change in direction. • The passengers are directed in a circular or curved path due to the inward or center seeking force of the seatbelt or side door.

14. Questions1. Any object that revolves about a single axis undergoes _________ motion.2. When the tangential speed is constant, the motion is described as ________ circular motion.3. Anything moving in a circular path, even at constant speed, is changing ________ therefore accelerating.4. Centripetal _____ acts at right angles to an object’s circular motion, therefore, the force changes the direction of the object’s velocity. circular uniform direction force

15. 7.2 Newton’s Law of Universal Gravitation Gravitational Force • Earth and many other planets in our solar system travel in nearly circular orbits. • A centripetal force must keep them in orbit. • That force must be a gravitational force.

16. Orbiting objects are in free fall • Consider a canon sitting on a mountain top. • The path of each cannonball is a parabola, and the horizontal distance each cannon ball covers increases as its speed increases. • If the projectile is fired at just the right speed, it will fall around the earth. • In other words, it will orbit the earth like a satellite.

17. Gravitational force depends on the masses and the distance • Newton came up with the following to explain that all objects have gravity and therefore attract each other. • The letter “G” is called the constant of universal gravitation. Its value is 6.673 x 10-11 • When calculating the gravitational force between earth and the moon, you use their centers (radius).

18. Gravitational force acts between all masses • Gravitational force always attracts objects to one another.   • The force the moon exerts on the earth is equal and opposite to the force that the earth exerts on the moon. • As a result of these centripetal forces, the moon and earth orbit around a common center of mass. This axis is slightly within the earth. *Explain how a falling apple actually pulls up on the earth!

19. Practice CGravitational Force • Find the distance between a 0.300 kg billiard ball and a 0.400 kg billiard ball if the magnitude of gravitational force between them is 8.92 x 10-11 N. Note: G = 6.673 x 10-11  Answer 0.300 m

20. Black Holes in Space • Einstein’s special theory of relativity explains that gravity can bend light. • During a solar eclipse in 1922, we could see stars that the sun would normally block! • Black holes have such strong gravity, light can not escape them. • It is believed that super massive black holes are at the center of most galaxiesholding them together.

22. Applying the Law of Gravitation • Most coastlines see the oceans rise for six hours and then fall over the next six hours. • These continuous cyclesare known as the tides. • What is actually happening is the earth is rotating through two high water levels each day due the effects of the moon. • The side nearest the moon is closer, so it is pulled with more force than the center of the earth. • The water on the opposite side of the earth is pulled the least or sort of left behind.

23. Newton’s law of gravitation accounts for ocean tides • The size of ocean basins, coastline shape and water depth determine the tidal range and duration. • The sun also effects tides as well. • The sun’s gravity can enhance a tidal range or reduce it. • When the sun and moon pull together twice a month, this is called spring tide. • When they are perpendicular, neap tides.

24. Cavendish finds the value of G and Earth’s mass • In 1798, Henry Cavendish determined the value of the constant “G”. • By using the gravitational force of two large iron spheres, two smaller ones rotated just enough to cause a beam of light to slightly deflect. • Once this constant was know, we could calculate the mass of the earth.

25. Gravity is a field force • A gravitational force is an interaction between a mass and the gravitational field created by other masses. • According to field theory, the gravitational energy is stored in the gravitational field itself. • Gravitational field strength “g” is the magnitude of this force exerted on a mass.

26. Gravitational field strength equals free-fall acceleration • The value of “g” at any given point is equal to the acceleration due to gravity. • On the earth’s surface, g = 9.81 m/s2 • As one moves further away from the earth’s surface, this gravitational field strength rapidly decreases. • Every time you double your distance away, the force of gravity decreases by a factor of four. Gravitational Force

27. Weight changes with location • Newton’s law of universal gravitation shows that the value of g depends on mass and distance. • Based on our formula you can see… g = G • Thus, as your distance from the earth’s center increases, the value of g decreases due to the square of the radius. • This is also known as the inverse square law. mE ___ r2

28. Gravitational mass equals inertial mass • Gravitational field strength equals free-fall acceleration. • Free-fall acceleration does not depend on the falling object’s mass. • Gravity pulls on all the molecules of the mass equally and at the same time. • Another way of looking at free-fall, the greater the mass, the more it resists movement (inertia). However, the more force pulling on it.

29. Questions1. When calculating the gravitational force between objects, you use the radius or the _________ between centers.2. The force the moon exerts on the earth is equal and ________ to the force that the earth exerts on the moon.3. ______ result from the earth rotating through two high water levels each day due the effects of the moon.4. The value of “g” at any given point is equal to the acceleration due to _______.5. Every time you double your distance away from earth’s surface, the force of gravity decreases by a factor of _____. distance opposite Tides gravity four

30. 7.3 Motion in Space Weight and Weightlessness • When you step onto a bathroom scale, it does not actually measure your weight. • The scale measures the downward force exerted on it. • If someone pushed down at the same time, the reading would go up.

31. When an elevator is at rest (a) below, the magnitude of the normal force is equal to your weight. • When the elevator starts accelerating downward (b) the normal force will be smaller. • If the elevators acceleration were that of free-fall (c) you would be falling at the same rate as the elevator. • You would not feel the force of the floor at all, the scale would read zero. No normal force = apparent weightlessness.

32. Astronauts in orbit experience weightlessness • Astronauts floating in the International space station are experiencing apparent weightlessness. • In orbit, they feel the equivalent of free-fall because no normal force is acting on them. • This can lead to a few days of nausea (motion sickness) and dizziness. • After extended periods in space (months) weakened muscles and brittle bones occur. • For an astronaut to experience actual weightlessness, they must be in deep space away from stars and planets.

33. Once an astronaut were in deep space, they would travel at their current speed and in a straight line. • Here on earth, the only way to experience apparent weightlessness for about 20 seconds would be to free-fall in a passenger jet. • After the jet drops at the same speed as a falling object, it climbs back up to a high altitude and repeats the process.

34. Questions1. T / F When you are standing on a scale, the magnitude of the normal force is equal to your weight.2. Astronauts floating in a space shuttle are experiencing _________ weightlessness.3. For an astronaut to experience _______ weightlessness, they must be in deep space away from stars and planets. 4. After extended periods in space (months) weakened muscles and brittle _______ occur. true apparent actual bones

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