Forces and Motion

1. Forces and Motion Chapter 6

2. Gravity and Motion Section 1

3. Gravity and Falling Objects • Galileo Galilei questioned Aristotle’s idea about falling objects • He argued that the mass of an object does not affect the time the object takes to fall to the ground • Dropped two cannonballs with different masses from the top of the Leaning Tower of Pisa in Italy

4. Gravity and Acceleration • Objects fall to the ground at the same rate because the acceleration due to gravity is the same for all objects • Acceleration depends on both force and mass; a heavier object experiences a greater gravitational force but ifs also harder to accelerate because it has more mass • The extra mass of the heavy object balances the additional gravitational force

6. Acceleration Due to Gravity • Acceleration: the rate at which velocity changes over time • So, the acceleration of an object is the object’s change in velocity divided by the amount of time during which the change occurs

7. Acceleration Due to Gravity • All objects accelerate towards Earth at a rate of 9.8 m/s2 • So, for every second that an object falls, the object’s downward velocity increases by 9.8 m/s

8. Velocity of Falling Objects • Change in velocity equation: ∆v = g x t g = acceleration due to gravity on Earth t = time ∆v = difference between Vfinaland Vinitial

9. Example • A stone at rest is dropped from a cliff, and the stone hits the ground after a time of 3 s. What is the stone’s velocity when it hits the ground?

10. Air Resistance and Falling Objects • Air resistance: the force that opposes the motion of objects through air • The amount of air resistance on an object depends on the size, shape, and speed of the object

12. Acceleration Stops at the Terminal Velocity • As the speed of a falling object increases, air resistance increases • The upward force of air resistance continues to increase until it is equal to the downward force of gravity • At this point, the net force is O N and the object stops accelerating

13. Acceleration Stops at the Terminal Velocity • Terminal velocity: the constant velocity of a falling object when the force of air resistance is equal in magnitude and opposite in direction to the force of gravity

14. Free Fall Occurs When There is No Air Resistance • Free fall: the motion of a body when only the force of gravity is acting on the body • Because air resistance is a force, free fall can occur only where there is no air • Space • vacuum

15. Orbiting Objects are in Free Fall • It is impossible for any object to be weightless anywhere in the universe • The gravitational force acting on you would be very small, but you still have mass, so gravity is still attracting you to other objects, which means you still have weight

16. Two Motions Combine to Cause Orbiting • An object is orbiting when it is traveling around another object in space • Ex: when a spacecraft is orbiting earth, it is moving forward, but the spacecraft is also in free fall towards Earth • Astronauts don’t hit their head because they are also in free fall towards the Earth

18. Orbiting and Centripetal Force • Many other objects in the universe are in orbit • Moon orbits the Earth • Earth and the other planets orbit the sun • Satellites orbit the Earth • Stars orbit large masses in the center of galaxies

19. Orbiting and Centripetal Force • Any object in circular motion is constantly changing direction • Because an unbalanced force is necessary to change the motion of any object, there must be an unbalanced force working on any object in circular motion • The unbalanced force that causes objects to move in a circular path is called a centripetal force

20. Projectile Motion and Gravity • Projectile motion: the curved path an object follows when it is thrown or propelled near the surface of the Earth • Has two components: • Horizontal motion • Vertical motion • These components are independent of one another; they have no effect on one another

21. Projectile Motion and Gravity • When the two motions are combined, they form a curved path • Examples of projectile motion: • A frog leaping • Water sprayed by a sprinkler • A swimmer diving into water • Balls being juggled • An arrow shot by an archer

22. Horizontal Motion • When you throw a ball, your hand exerts a force on the ball that makes the ball move forward • This is horizontal motion, which is motion parallel to the ground • After you release the ball, no horizontal forces are acting on the ball • Horizontal velocity is constant after the ball leaves the pitcher’s hand

23. Horizontal Motion

24. Vertical Motion • Gravity pulls everything on Earth downward toward the center of Earth • A ball in your hand is prevented from falling by your hand • After you throw the ball, gravity pulls it downward and gives the ball vertical motion • Vertical motion is motion that is perpendicular to the ground

25. Vertical Motion • Gravity pulls objects in projectile motion down at an acceleration of 9.8 m/s2 • Same for all falling objects • Because objects in projectile motion accelerate downward, you always have to aim above a target if you want to hit it with a thrown or propelled object

26. Vertical Motion

27. Newton’s Laws of Motion Section 2

28. Newton’s First Law of Motion • An object at rest remains at rest, and an object in motion remains in motion at a constant speed and in a straight line unless acted on by an unbalanced force • Describes the motion of an object that has a net force of 0N acting on it

29. Newton’s First Law of Motion • Part 1: Objects at Rest • An object that is not moving is said to be at rest • Object will not start moving unless they are acted on by an unbalanced force • A push or a pull

30. Newton’s First Law of Motion • Part 2: Objects in Motion • Objects will continue to move forever with the same velocity unless an unbalanced force acts on them • Ex: bumper cars

31. Newton’s First Law of Motion • Friction and Newton’s First Law • An object in motion will stay in motion forever unless it is acted on by an unbalanced force • Why do things stop moving if you push them? • Friction! • Friction is an unbalanced force that works against the motion of the moving object • Why a desk stops sliding or a ball stops rolling

32. Newton’s First Law of Motion • Inertia and Newton’s First Law • Sometimes called the law of inertia • Inertia: the tendency of all objects to resist any change in motion • Because of inertia, an object at rest will remain at rest until a force makes it move • Because of inertia, a moving object will stay in motion with the same velocity unless a force changes its speed or direction

33. Newton’s First Law of Motion • Mass and Inertia • Mass is a measure of inertia • An object that has a small mass has less inertia than an object that has a large mass • So, changing the motion of an object that has a small mass is easier than changing the motion of an object that has a large mass

34. Newton’s Second Law of Motion • The acceleration of an object depends on the mass of the object and the amount of force applied • Describes the motion of an object when an unbalanced force acts on the object

35. Newton’s Second Law of Motion • Part 1: Acceleration Depends on Mass • Only a small force has to be exerted on an object with a small mass • That same amount of force will not accelerate an object with a large mass as much

36. Newton’s Second Law of Motion • Part 2: Acceleration Depends on Force • An object’s acceleration increases as the force on the object increases • An objects acceleration decreases as the force on the object decreases • The acceleration of an object is always in the same direction as the force applied

38. Newton’s Second Law of Motion • Expressing the Second Law Mathematically a = F/m or F = m x a a = acceleration F = force M = mass • Explains why objects fall to Earth with the same acceleration

39. Example What is the acceleration of a 3 kg mass if a force of 14.4 N is used to move the mass? (Note: 1 N is equal to 1 kg x m/s2)

40. Newton’s Third Law of Motion • Whenever one object exerts a force on a second object, the second object exerts and equal and opposite force on the first. • Simplified: • All forces act in pairs. If a force is exerted, another force occurs that is equal in size and opposite in direction.

41. Newton’s Third Law of Motion • Action and reaction force pairs are present even when there is no motion • Force pairs Do Not Act on the Same Object • Force is always exerted by one object on another object • Action and reaction forces in a pair do not act on the same object • If they did, the net force would always be 0N and nothing will move!

42. Newton’s Third Law of Motion • All Forces Act in Pairs—Action and Reaction • When a force is exerted, there is always a reaction force • A force never acts by itself

44. Newton’s Third Law of Motion • The Effect of a Reaction Can Be Difficult to See • Gravity is a force of attraction between objects that is due their masses • It’s easy to see the effect of the action force—ball falls to Earth • Why don’t you notice the effect of the reaction force—Earth being pulled upward? • Acceleration of Earth is much smaller than the acceleration of the ball

45. Momentum Section 3

46. Momentum, Mass, and Velocity • Momentum: depends on the object’s mass and velocity • The more momentum an object has, the harder it is to stop the object or change its direction

47. Momentum, Mass, and Velocity • Calculating Momentum p = m x v p = momentum (in kg x m/s) m = mass (in kg) v = velocity (in m/s)

48. Momentum, Mass, and Velocity • Calculating Momentum • Momentum has a direction • Its direction is always the same as the direction of the object’s velocity

49. Example • What is the momentum of an ostrich with a mass of 120 kg that runs with a velocity of 16 m/s north?

50. The Law of Conservation of Momentum • When a moving object hits another object, some or all of the momentum of the first object is transferred to the object that is hit • If only some of the momentum is transferred, the rest of the momentum stays with the first object