Newton’s Laws of Motion

1. Newton’s Laws of Motion • The Laws of Motion are governed by three principles developed by one man…Sir Isaac Newton (1643-1727)

2. Law of Inertia • Every object in motion stays in motion and any object at rest stays at rest until acted upon by an outside force. • Inertia: is the term for the property of matter that resists change in its state of motion. • Why aren’t you falling out of your seats? • Why is it so hard to push a car out of the mud? • Why is it even harder to push a cruise ship off the dock? • Objects at rest want to stay that way!

3. Motion • Motion is a change in position relative to a frame of reference • Speed is the distance traveled in a given amount of time • Speed=distance time

4. Objects in motion want to stay that way! Why is it harder to stop an 18-wheeler moving at 60 mph than a compact car moving at the same speed? A: 18 wheeler has more mass!!! • If no breaks were applied, would the two vehicles move forever? NO!!!!!!!!! • But I thoughtobjects in motion wanted to stay that way??? • Friction is a force opposing motion, caused by the contact of two surfaces.

5. Drawing Net forces

6. 1 • The law of inertia is most commonly experienced when riding in cars and trucks. • Consider the unfortunate collision of a car with a wall. • Upon contact with the wall, an unbalanced force acts upon the car to abruptly decelerate it to rest. • Any passengers in the car will also be decelerated to rest if they are strapped to the car by seat belts. • Being strapped tightly to the car, the passengers share the same state of motion as the car. • As the car accelerates, the passengers accelerate • As the car decelerates, the passengers decelerate As the car maintains a constant speed, the passengers maintain a constant speed.

7. But what would happen if the passengers were not wearing the seat belt? What motion would the passengers undergo if they failed to use their seat belts and the car were brought to a sudden and abrupt halt by a collision with a wall? 1

8. 1 • If the car were to abruptly stop and the seat belts were not being worn, then the passengers in motion would continue in motion. • Assuming a negligible amount of friction between the passengers and the seats, the passengers would likely be propelled from the car and be hurled into the air. • Once they leave the car, the passengers become projectiles and continue in projectile-like motion. 1) From: The Car and The Wall http://www.geocities.com/Athens/Academy/9208/cci.html

9. Velocity • Speed in a given direction • Velocities in the same direction combine by adding • Velocities in different directions combine by subtracting

10. Acceleration • The change in velocity • Acceleration is measured in m/sec/sec or m/sec2 • Formula is: • (final velocity - original velocity)/time • A decrease in velocity is deceleration or negative acceleration • A distance-time graph for acceleration is always a curve • Acceleration directed toward the center of circular path Deceleration vs. Acceleration Centripetal Acceleration

11. Law of Inertia An object’s orientation can change it’s inertia by altering its center of gravity! Center of Gravity: the average location of the weight of an object.

12. While all objects exhibit the property of inertia, all objects do not have the same inertia! Think about it… is it easier to kick an empty can or a full can? Inertia is affected by mass. Mass: is the quantity of matter in an object. **Mass is not weight!** Weight: is a measure of an object’s gravitational attraction to earth. Weight can change. Mass does not! Why is it easier to kick an empty can than a full can? The full can had more mass and therefore, more inertia. In other words, the more mass an object has, the more it will resist change in its state of motion.

13. Newton’s 2nd Law (a.k.a.) F = m x a • The acceleration produced by a net force on an object is directly proportional to the magnitude of the net force, is in the same direction as the net force, and is inversely proportional to the mass of the object. • So what does this mean??? The amount of force applied to an object is equal to the mass of the object multiplied by its acceleration due to that force: F = m x a • What is acceleration? How fast something speeds up.

14. Gravity • Gravity is a force of attraction between two bodies with mass. • Since all object have mass, all objects exert gravity on all other objects. Even you have your own gravity. • So why don’t we observe our own gravity? Because compared to the earth, our mass is very, very small…so small that our own gravity is too small to observe. • More mass = More Gravity

15. Gravity • Gravity is a force applied to all objects by the earth. No matter what the object, the acceleration due to gravity is 9.8 m/s2.

16. Example: A textbook has a mass of 1 kg and a piece of paper has a mass of 0.0001kg. What is the force of gravity on each of these falling objects? F = ma F= ma Ftextbook = 1kg x 9.8 m/s2 Fpaper = 0.0001kg x 9.8m/s2 Ftextbook = 9.8 N Fpaper = 0.00098 N A Newton, N, is equal to a kg m/s2 Was the force of gravity on the textbook and the paper the same? Does this mean that they should fall at the same time or not? What was the real reason that they did not fall at the same time? Air resistance works against the force of gravity. Air Resistance: Friction due to air. Because the piece of paper has more air resistance, its acceleration due to gravity is slowed. Other forces are resisted by friction.

17. Free Fall: falling free of air resistance or other constraints. • On earth, we do not have the luxury of experiencing free fall, but we can experience something similar… • Terminal Velocity: The point in movement where the force propelling the object forward is equal to the forces resisting the forward motion (i.e. air resistance/friction = gravity) causing the speed of the object to be constant.

18. Suppose that air resistance could be eliminated so neither the elephant nor the feather would experience any air drag during the course of their fall. • Which object - the elephant or the feather - will hit the ground first? • Many people are surprised by the fact that in the absence of air resistance, the elephant and the feather strike the ground at the same time. 3) From: Elephant and Feather-Air Resistance http://www.geocities.com/Athens/Academy/9208/efff.html

19. In the absence of air resistance, both the elephant and the feather are in a state of free-fall. That is to say, the only force acting upon the two objects is gravity. • This force of gravity is what causes both the elephant and the feather to accelerate downwards. The force of gravity experienced by an object is dependent upon the mass of that object.

20. Why then does it hit the ground at the same time as the feather?3 • When figuring the acceleration of object, there are two factors to consider - force and mass. • The elephant experiences a much greater force (which tends to produce large accelerations. Yet, the mass of an object resists acceleration. • The greater mass of the elephant (which tends to produce small accelerations) offsets the influence of the greater force It is the force/mass ratio which determines the acceleration..

21. The greater mass of the elephant requires the greater force just to maintain the same acceleration as the feather. • We say that mass and acceleration are inversely proportional. A large mass will accelerate slowly, while a small mass will accelerate quickly with the same force.

22. Other forces are affected by the area the force is applied to. How does a snow shoe work? • Because your mass and the acceleration due to gravity do not change, the force you apply to the ground is the same with each step. • So why then can you walk across deep snow without sinking in a snow shoe and not in a regular boot? • The snow shoe allows the force of your step to be applied over a large surface area. • The force per unit area is a called pressure.

23. Inertia, Gravity and Satellites4 • Satellites require great speeds to avoid crashing! • Altitude determines it speed • a satellite in low orbit (about 800km/497mi) from the Earth is exposed to an immense amount of gravity • has to move at considerable speed to keep from crashing • Gravity is important to keep the satellite from moving off into space. 4) From: Satellite Orbits http://www.eduspace.esa.int/subtopic/default.asp?document=297

24. As the satellites are in orbit outside the atmosphere there is no air resistance, and therefore, the speed of the satellite is constant. • If orbiting inside the atmosphere, the satellite must overcome air resistance (must be able to speed up when it slows down because of air resistance)4. • Satellites are both natural (the moon) and man made.

25. Newton’s 3rd Law • Whenever one object exerts a force on a second object, the second object exerts an equal but opposite force on the first object. • Newton’s Third Law says that for every action there is an equal but opposite reaction.

26. There is a pair of forces acting on the two interacting objects. • The size of the forces on the first object equals the size of the force on the second object. • The direction of the force on the first object is opposite to the direction of the force on the second object. • Forces always come in pairs - equal and opposite action-reaction force pairs.

27. Rifle has Ma Bullet is Shot Out by force from gun powder Bullet has mA • Have you ever shot a rifle and felt the kickback? Where does that come from and how does this help us explain how a rifle works? • The rifle shoots the bullet with a force and the bullet pushes the rifle back with the same force. Because the rifle has a much larger mass than the bullet, it will accelerate much less than the bullet.

28. What about two forces in opposite directions? Me You • I hit a football and you hit a football in the opposite direction. • The two opposite forces “cancel” each other out and the ball goes nowhere. • The football will give us both a reaction force though.

29. Work & Energy

30. WORK WORK:It is used by physicists to measure something that is accomplished. So it results in the equation: Work = Force x displacement The symbol for work is the variable = W W=(F)(d) You must move something (d) with a force (F) to accomplish work. Is work being done? Pushing a car. Attempting to lift 2,000,000 N. Swimming in a rip current.

31. WORK SO WHAT IF I PUSH ON A WALL THAT DOES NOT MOVE? HAVE I DONE WORK?… NO! HAVE I USED ENERGY?... YES! WHAT IS ENERGY? UH OH… another definition coming…

32. Energy… • …is the ability to make things move

33. The seven types of energy… • Chemical - gasoline, • Light – flash light, • Heat – burner on a stove, • Nuclear - sun, • Mechanical - car, • Sound – music on the radio, • Electrical - lightning

34. POTENTIAL ENERGY How do you “store up energy?... There are two kinds we study… GPE - GRAVITY POTENTIAL ENERGY: If you put an object up in the air… gravity will pull it down and make it move some distance… WORK will be done… an object is moved some displacement… GPE = mgh… mg=force gravity, h=height… the heavier the object is, the more force on it, the higher it is, the further down it moves… GPE = mgh EPE- ELASTIC POTENTIAL ENERGY: This is stored in a spring or rubber band. The stronger the spring, or the further you stretch it, the more work it can do. So, the EPE=(1/2)(k)(x2) … k = how strong the spring is, and x= how far you stretch it… EPE=(1/2)(k)(x2)‏

35. KINETIC ENERGY KINETIC ENERGY = KE: This is moving energy. Something that is moving will collide and crash into another object, and move it a distance,… SO, the energy that it has, will be equal to how BIG it is, m (mass), and how FAST, v (velocity), it is moving…. KE = (1/2)(m)(v2)‏

36. Definitions • Kinetic Energy: the energy of motion • KE = ½ mv2 • Potential Energy: stored energy • PE = mgh

37. A Roller Coaster A roller coaster speeds along its track. It has kinetic energy because it is moving.

39. A Roller Coaster As it slows to a stop at the top of a hill, it has potential energy because of where it is. It has the potential to move because it is above the ground and has somewhere to go.

41. Substances like wood, coal, oil, and gasoline have storedenergy because of their chemistry – they can burn • Stored energy is potential energy

42. NEW FORMULAS W=(F)(d)GPE=(m)(g)(h)‏ EPE=(1/2)(k)(x2)KE=(1/2)(m)(v2)‏ ENERGY is what you “can do”……… WORK is what you “do do”……… and isn’t work doo-doo?

43. Calculating Work F d A mass is being pulled to the right by a force, F , it is moving to the right so that the displacement is d… BUT is ALL of the force, F , doing work?.... NO…. because some of the force is lifting up in the positive +y direction This means that the part of F that is pulling to the right in the +x direction is doing work, because that is the way the box is moving… m

44. Calculating Work F d What about the other forces on the box like weight, mg, pulling down, or the F-normal, of the ground pushing up…. NO… they do NO WORK, because the box is not moving up or down…. m

45. Calculating Work F d • What about F-friction, is it doing work?... YES…BUT WAIT… THE FRICTION FORCE IS NOT IN THE SAME DIRECTION THE BOX IS MOVING!! IT IS TO THE LEFT!! • This force is fighting the work being done by F. It is doing what we call negativework because it is being done in the OPPOSITE DIRECTION THAT THE OBJECT IS MOVING… m

46. Calculating Work F d • FINALLY, we can find the TOTAL WORK, Wt, done on the box…. It is the positive work done by F plus the negative work done by friction Ff… Wt = W - Wf m

47. QUICK OVERVIEW ON WORK…. • Work equals Force x displacement… W = (F)(d)‏ • Work is measured in Nm called Joules, or J • Work is positive if the force, F, is in the same direction as the displacement • Any force that pushes on the object, but does not move the object in the direction it is pushing… does NO work • Any force that pushes in the opposite direction that the object is moving, (especially friction), does negative work

48. Potential Energy can be changed into Kinetic Energy • Also Kinetic Energy can be changed into Potential Energy KE and PE are conserved! KEfinal + PEfinal = KEinitial + PEinitial

49. Momentum and Impulse

50. Momentum and Impulse • Momentum describes the motion of an object before and after a collision • Common sense tells us that when you collide with another object or person… HOW MUCH you feel that collision, or how much it hurts!... Depends on two things: • 1) How big the object was that hit you • 2) How fast it was going when it hit you • But this is PHYSICS: 1) MASS (in kilograms) is a measure of the object’s size, and 2) VELOCITY (in m/s) is a measure of the object’s speed • Formula for momentum is P = mv (YES… the variable P is momentum)