Newton’s Laws of Motion

1. Newton’s Laws of Motion I. Law of Inertia II. F=ma III. Action-Reaction

2. Background Sir Isaac Newton (1643-1727) an English scientist and mathematician famous for his discovery of the law of gravity also discovered the three laws of motion. He published them in his book Philosophiae Naturalis Principia Mathematica (mathematic principles of natural philosophy) in 1687. Today these laws are known as Newton’s Laws of Motion and describe the motion of all objects on the scale we experience in our everyday lives.

3. Newton’s Laws of Motion • 1st Law – An object at rest will stay at rest, and an object in motion will stay in motion at constant velocity, unless acted upon by an unbalanced force. • 2nd Law – Force equals mass times acceleration. • 3rd Law – For every action there is an equal and opposite reaction.

4. 1st Law of Motion (Law of Inertia) An object at rest will stay at rest, and an object in motion will stay in motion at constant velocity, unless acted upon by an unbalanced force.

5. What is motion? If an object moves from one location to another location – it is said to be in motion.

6. What is a force? A force is a push or a pull.

7. Newton’s First Law is also called the Law of Inertia Inertia: the tendency of an object to resist changes in its state of motion The First Law states that all objects have inertia. The more mass an object has, the more inertia it has (and the harder it is to change its motion).

8. What does this mean? Basically, an object will “keep doing what it was doing” unless acted on by an unbalanced force. If the object was sitting still, it will remain stationary. If it was moving at a constant velocity, it will keep moving. It takes force to change the motion of an object.

9. What is meant by unbalanced force? If the forces on an object are equal and opposite, they are said to be balanced, and the object experiences no change in motion. If they are not equal and opposite, then the forces are unbalanced and the motion of the object changes.

10. 1st Law • Once airborne, unless acted on by an unbalanced force (gravity and air – fluid friction), it would never stop!

11. 1st Law • Unless acted upon by an unbalanced force, this golf ball would sit on the tee forever.

12. Some Examples from Real Life A soccer ball is sitting at rest. It takes an unbalanced force of a kick to change its motion. Two teams are playing tug of war. They are both exerting equal force on the rope in opposite directions. This balanced force results in no change of motion.

13. More Examples from Real Life A powerful locomotive begins to pull a long line of boxcars that were sitting at rest. Since the boxcars are so massive, they have a great deal of inertia and it takes a large force to change their motion. Once they are moving, it takes a large force to stop them. On your way to school, a bug flies into your windshield. Since the bug is so small, it has very little inertia and exerts a very small force on your car (so small that you don’t even feel it).

14. If objects in motion tend to stay in motion, why don’t moving objects keep moving forever? Things don’t keep moving forever because there’s almost always an unbalanced force acting upon it. A book sliding across a table slows down and stops because of the force of friction. If you throw a ball upwards it will eventually slow down and fall because of the force of gravity.

15. Objects on earth, unlike the frictionless space the moon travels through, are under the influence of friction.

16. In outer space, away from gravity and any sources of friction, a rocket ship launched with a certain speed and direction would keep going in that same direction and at that same speed forever.

17. Why then, do we observe every day objects in motion slowing down and becoming motionless seemingly without an outside force? It’s a force we sometimes cannot see – friction.

18. What is this unbalanced force that acts on an object in motion? Friction! • There are four main types of friction: • Sliding friction: ice skating • Rolling friction: bowling • Fluid friction (air or liquid): air or water resistance • Static friction: initial friction when moving an object

19. Slide a book across a table and watch it slide to a rest position. The book comes to a rest because of the presence of a force - that force being the force of friction - which brings the book to a rest position.

20. In the absence of a force of friction, the book would continue in motion with the same speed and direction - forever! (Or at least to the end of the table top.)

21. Newtons’s 1st Law and You Don’t let this be you. Wear seat belts. Because of inertia, objects (including you) resist changes in their motion. When the car going 80 km/hour is stopped by the brick wall, your body keeps moving at 80 km/hour.

22. 2nd Law F = m x a

23. 2nd Law The net force of an object is equal to the product of its mass and acceleration, or F=ma.

24. 2nd Law • When mass is in kilograms and acceleration is in m/s/s, the unit of force is in newtons (N). • One newton is equal to the force required to accelerate one kilogram of mass at one meter/second/second.

25. 2nd Law (F = m x a) • How much force is needed to accelerate a 1400 kilogram car 2 meters per second/per second? • Write the formula • F = m x a • Fill in given numbers and units • F = 1400 kg x 2 meters per second/second • Solve for the unknown • 2800 kg-meters/second/second or2800 N

26. What is acceleration? Acceleration is a change in the speed of an object – either faster or slower Acceleration can also be a change in direction of motion

27. What does F = ma mean? Force is directly proportional to mass and acceleration. Imagine a ball of a certain mass moving at a certain acceleration. This ball has a certain force. Now imagine we make the ball twice as big (double the mass) but keep the acceleration constant. F = ma says that this new ball has twice the force of the old ball. Now imagine the original ball moving at twice the original acceleration. F = ma says that the ball will again have twice the force of the ball at the original acceleration.

28. More about F = ma If you double the mass, you double the force. If you double the acceleration, you double the force. What if you double the mass and the acceleration? (2m)(2a) = 4F Doubling the mass and the acceleration quadruples the force. So . . . what if you decrease the mass by half? How much force would the object have now?

29. What does F = ma say? F = ma basically means that the force of an object comes from its mass and its acceleration. Something very massive (high mass) that’s changing speed very slowly (low acceleration), like a glacier, can still have great force. Something very small (low mass) that’s changing speed very quickly (high acceleration), like a bullet, can still have a great force. Something very small changing speed very slowly will have a very weak force.

30. Newton’s 2nd Lawproves that different masses accelerate to the earth at the same rate, but with different forces. • We know that objects with different masses accelerate to the ground at the same rate. • However, because of the 2nd Law we know that they don’t hit the ground with the same force. F = ma 98 N = 10 kg x 9.8 m/s/s F = ma 9.8 N = 1 kg x 9.8 m/s/s

32. Check Your Understanding • 1. What acceleration will result when a 12 N net force is applied to a 3 kg object? A 6 kg object? • 2. A net force of 16 N causes a mass to accelerate at a rate of 5 m/s2. Determine the mass. • 3. How much force is needed to accelerate a 66 kg skier 1 m/sec/sec? • 4. What is the force on a 1000 kg elevator that is falling freely at 9.8 m/sec/sec?

33. Check Your Understanding • 1. What acceleration will result when a 12 N net force is applied to a 3 kg object? 12 N = 3 kg x 4 m/s/s • 2. A net force of 16 N causes a mass to accelerate at a rate of 5 m/s2. Determine the mass. 16 N = 3.2 kg x 5 m/s/s • 3. How much force is needed to accelerate a 66 kg skier 1 m/sec/sec? 66 kg-m/sec/sec or 66 N • 4. What is the force on a 1000 kg elevator that is falling freely at 9.8 m/sec/sec? • 9800 kg-m/sec/sec or 9800 N

35. 3rd Law • For every action, there is an equal and opposite reaction.

36. 3rd Law According to Newton, whenever objects A and B interact with each other, they exert forces upon each other. When you sit in your chair, your body exerts a downward force on the chair and the chair exerts an upward force on your body.

37. 3rd Law There are two forces resulting from this interaction - a force on the chair and a force on your body. These two forces are called action and reaction forces.

38. What does this mean? For every force acting on an object, there is an equal force acting in the opposite direction. Right now, gravity is pulling you down in your seat, but Newton’s Third Law says your seat is pushing up against you with equal force. This is why you are not moving. There is a balanced force acting on you– gravity pulling down, your seat pushing up.

39. Think about it . . . What happens if you are standing on a skateboard or a slippery floor and push against a wall? You slide in the opposite direction (away from the wall), because you pushed on the wall but the wall pushed back on you with equal and opposite force. Why does it hurt so much when you stub your toe? When your toe exerts a force on a rock, the rock exerts an equal force back on your toe. The harder you hit your toe against it, the more force the rock exerts back on your toe (and the more your toe hurts).

40. Newton’s 3rd Law in Nature • Consider the propulsion of a fish through the water. A fish uses its fins to push water backwards. In turn, the water reacts by pushing the fish forwards, propelling the fish through the water. • The size of the force on the water equals the size of the force on the fish; the direction of the force on the water (backwards) is opposite the direction of the force on the fish (forwards).

41. 3rd Law Flying gracefully through the air, birds depend on Newton’s third law of motion. As the birds push down on the air with their wings, the air pushes their wings up and gives them lift.

42. Consider the flying motion of birds. A bird flies by use of its wings. The wings of a bird push air downwards. In turn, the air reacts by pushing the bird upwards. • The size of the force on the air equals the size of the force on the bird; the direction of the force on the air (downwards) is opposite the direction of the force on the bird (upwards). • Action-reaction force pairs make it possible for birds to fly.

44. Other examples of Newton’s Third Law • The baseball forces the bat to the left (an action); the bat forces the ball to the right (the reaction).

45. 3rd Law • Consider the motion of a car on the way to school. A car is equipped with wheels which spin backwards. As the wheels spin backwards, they grip the road and push the road backwards.

46. 3rd Law The reaction of a rocket is an application of the third law of motion. Various fuels are burned in the engine, producing hot gases. The hot gases push against the inside tube of the rocket and escape out the bottom of the tube. As the gases move downward, the rocket moves in the opposite direction.

47. Vocabulary Inertia: the tendency of an object to resist changes in its state of motion Acceleration: •a change in velocity •a measurement of how quickly an object is changing speed, direction or both Velocity: The rate of change of a position along a straight line with respect to time Force: strength or energy