Chapter 4

1. Chapter 4 Newton’s Laws of Motion

2. Goals for Chapter 4 • To understand the meaning of forcein physics • To view force as a vector and learn how to combine forces • To understand the behavior of a body on which the forces “balance”: • Newton’s First Law of Motion: if there is no NET force on an object it will remain in the same state of motion

3. Goals for Chapter 4 To learn the relationship between mass, acceleration, and force: Newton’s Second Law of Motion: F = maa = F/m To relate mass(quantity of matter) and weight (force on that matter from gravity)

4. Goals for Chapter 4 To see the effect of action-reaction pairs: Newton’s Third Law of Motion Forceonobjectafromobjectb is EQUAL in magnitude (and opposite in direction) to Forceonobjectbfromobjecta

5. What are some properties of a force? • A force is a push or a pull • A force is an interaction between two objects, or between an object and its environment • A force is a VECTOR quantity, with magnitude and direction.

6. There are fourcommon types of forces • #1: The normalforce: When an object pushes on a surface, the surface pushes back on the object perpendicular to the surface. • This is a contact force.

7. There are four common types of forces #2: Friction force:This force occurs when a surface resists sliding of an object and is parallel to the surface. Friction is a contact force.

8. There are four common types of forces II • #3: Tension force:A pulling force exerted on an object by a rope or cord. • This is a contact force.

9. There are four common types of forces II #4: Weight: The pull of gravity on an object. This is a long-range force, not a contact force, and is also a “field” force.

10. What are the magnitudes of common forces?

11. Drawing force vectors • Use a vector arrow to indicate the magnitude and direction of the force.

12. Superposition of forces • Several forces acting at a point on an object have the same effect as their vector sum acting at the same point.

13. Decomposing a force into its component vectors • Choose coordinate system with perpendicular x and y axes. • Fx and Fyare components of force along axes. • Use trigonometry to find force components.

14. Notation for the vector sum • Vector sum of all forces on an object is resultantof forces • The netforce.

15. Superposition of forces • Force vectors are added using components: Rx = F1x + F2x + F3x + … Ry = F1y + F2y + F3y + …

16. Newton’s First Law “An object at rest tends to stay at rest, an object in motion tends to stay in uniform motion.”

17. Newton’s First Law Mathematically, “A body acted on by zero net force moves with constant velocity and zero acceleration.”

18. Newton’s First Law II • In part (a) net force acts, causing acceleration. • In part (b) netforce= 0 resulting in no acceleration.

19. When is Newton’s first law valid? • You are on roller skates in a stopped BART car… • The car starts to accelerate forwards. • What happens to you? • If no net force acts on you, you maintain a constant velocity (0!)

20. When is Newton’s first law valid? • You are on roller skates in a moving BART car… • The car starts to slow - accelerate backwards. • What happens to you? • If no net force acts on you, you maintain a constant velocity

21. When is Newton’s first law valid? • If no net force acts on you, you maintains a constant velocity (a vector!) • But as seen in the non-inertial frame of the accelerating vehicle, it appears that you are being pushed to the outside! • Newton’s first law is valid only in non-accelerating inertial frames.

22. Newton’s Second Law • If the net force on an object is zero, the object will not accelerate.

23. Newton’s Second Law • If the net force on an object is not zero, it causes the object to accelerate.

24. Newton’s Second Law • If the net force on an object is not zero, it causes the object to accelerate.

25. An object undergoing uniform circular motion • An object in uniform circular motion is accelerated toward the center of the circle. • So net force on object must point toward the center of the circle.

26. Force and acceleration • Magnitude of acceleration of an object is directly proportional to the net force  on the object. • | | = F/m

27. Mass and acceleration • Magnitude of acceleration of an object is inversely proportional to object’s mass if net force remains fixed. • | | = F/m

28. Newton’s second law of motion • The acceleration of an object is directly proportional to the net force acting on it, and inversely proportional to the mass of the object. • The SI unit for force is the newton (N). 1 N = 1 kg·m/s2

29. Using Newton’s Second Law Ex. 4.4 • Worker pushes box of mass 40 kg, with constant force of 20N. What is acceleration?

30. Using Newton’s Second Law Ex. 4.4

31. Using Newton’s Second Law II—Example 4.5 • Shove bottle of mass 0.45 kg at initial speed of 2.8 m/s a distance of 1 m before it stops. What is the magnitude and direction of force on bottle?

32. Using Newton’s Second Law II—Example 4.5 • Shove bottle of mass 0.45 kg at initial speed of 2.8 m/s a distance of 1 m before it stops. What is the magnitude and direction of force on bottle?

33. Using Newton’s Second Law II—Example 4.5 • We know: • Displacement in x = +1.0 m • Initial x velocity = +2.8 m/s • Final x velocity = 0 m/s • THREE THINGS!

34. Using Newton’s Second Law II—Example 4.5 • vf2 = vi2 + 2aDx • So… • a = (vf2 - vi2)/2Dx • a = - 3.9 m/s2 • NOTE apoints in the direction of f ! +x

35. Systems of units (Table 4.2) • In MKS (SI) system • force is measured in Newtons, distance in meters, mass in kilograms.

36. Systems of units (Table 4.2) • In British system, force is measured in pounds, distance in feet, mass in slugs. • In cgs system, force in dynes, distance in centimeters, and mass is in grams.

37. Mass and weight • The weightof an object (on Earth) is gravitational force that Earth exerts on it. • The weight W of an object of mass m is W = mg • The value of g depends on altitude. • On other planets, g will have an entirely different value than on the earth.

38. A euro in free fall

39. A bit coin in free fall?

40. Don’t confuse mass and weight! • Keep in mind that the Newton is a unit of force, not mass. • A 2.49 x 104 N Rolls-Royce Phantom traveling in +x direction makes an emergency stop; the x component of the net force acting on its -1.83 x 104 N. What is its acceleration?

41. Newton’s Third Law • If you exert a force on a body, the body always exerts a force (the “reaction”) back upon you. • A force and its reaction force have the same magnitudebutopposite directions. • These forces act on different bodies.

42. Applying Newton’s Third Law: Objects at rest • An apple rests on a table. Identify the forces that act on it and the action-reaction pairs.

43. Applying Newton’s Third Law: Objects at rest • An apple rests on a table. Identify the forces that act on it and the action-reaction pairs.

44. Applying Newton’s Third Law: Objects at rest • An apple rests on a table. Identify the forces that act on it and the action-reaction pairs.

45. Applying Newton’s Third Law: Objects at rest • An apple rests on a table. Identify the forces that act on it and the action-reaction pairs.

46. Applying Newton’s Third Law: Objects in motion • A person pulls on a block across the floor. Identify the action-reaction pairs.

47. Applying Newton’s Third Law: Objects in motion • A person pulls on a block across the floor. Identify the action-reaction pairs.

48. Applying Newton’s Third Law: Objects in motion • A person pulls on a block across the floor. Identify the action-reaction pairs.

49. Applying Newton’s Third Law: Objects in motion • A person pulls on a block across the floor. Identify the action-reaction pairs.

50. A paradox? • If an object pulls back on you just as hard as you pull on it, how can it ever accelerate?