1. 1 4 Topics force and net force types of forces Newton’s Laws & force diagrams Ch.4 Homework: 1, 3, 5, 6, 8, 13, 16, 23, 26, 34, 39, 45, 49, 62, 63, 66, 68, 69, 72, 81, 87, 90, 97, 99, 101, 105.

2. 2 Force Concept Force = push or pull Contact Forces – requires touch Ex: car on road, ball bounce Non-Contact – does not require touch Ex: magnetism, gravity

3. 3 Force Label Notation Each force gets a distinctive label, and sketch & context supplies the interaction information F – general force F N – normal force f – frictional force W – weight T – tension force

4. 4 Net Force vector sum of all forces acting on an object

5. 5 constant velocity Force Diagram F net = 0 a = 0 Example: Net Force = 0, Ball rolls along a smooth level surface table force weight force

6. 6 Example Motion Diagram when F net = 0 Newton’s First Law: An object maintains an unchanged constant velocity unless or until it is acted on by a non- zero Net Force.

7. 7 Force Diagrams Object is drawn as a “point” Each force is drawn as a “pulling” vector Each force is labeled Relevant Angles are shown x, y axes are written offset from diagram Only forces which act ON the object are shown

8. 8 Example of a Force Diagram for a Sled net force equals the mass times its acceleration.

9. 9 Newton’s Second Law: acceleration equals Net External Force (on object) divided by object mass: Example Motion Diagrams when F net ≠ 0

10. 10 g’s one “g” of acceleration = 9.8m/s/s “two g’s” = 19.6m/s/s, etc. Example: What is the net force on a 2100kg SUV that is accelerating at 0.75g?

11. 11 units Force units (SI): newton, N 4.45N = 1lb. 1N = (1kg)(1m/s/s) N/kg = m/s/s

12. 12 Inertia is ‘resistance’ to change in velocity Ex: accelerating a ping pong ball Ex: accelerating a train Measurement: Mass SI Unit: Kilogram (Kg)

13. 30 90 60 30 Mg, 300 deg.

14. Fxnet = FNcos90 + mgcos300 = (0.02)(a) = 0 + (0.02)(9.8)(0.5) = (0.02)a accel = 4.9 m/s/s Fynet = FNsin90 + mgsin300 = (0.02)(0) FN + (0.02)(9.8)(-.866) = 0 FN = 0.17N

15. 15 Newton’s Third Law: Whenever one body exerts a force on a second body, the second body exerts an oppositely directed force of equal magnitude on the first body attraction repulsion

16. 16 Motion of Ball Force on BallForce on Block Acceleration of Ball Acceleration of Block Newton’s Second and Third Laws in Operation: Ball hits a large block on a smooth level surface.

17. 17 upward (decreasing) velocity F net acceleration Ex: Newton’s 2 nd Law

18. 18 Contact Forces Normal Force – perpendicular to surfaces Frictional Force – along surface. f ~ F N and to types of surfaces

19. 19 Normal forces are? 1.Always vertically upward. 2.Always vertically downward. 3.Can point in any direction.

20. 20 Friction Surfaces “stick” when at rest, this “static” friction varies from 0 to “f s,max ” Moving friction is called “f k ” (~ indep.of v) Characterized by “coefficients”, “0” = frictionless, “1” is high value e.g. teflon around 0.05, Rubber on concrete around 1.0

21. 21 Coefficient of Static Friction Ex. 10kg block sits on level surface with static coeff. frict. = 0.50. Force needed to budge = 0.50Fn = 0.50mg = 0.50(10kg)(9.8N/kg) = 49N. dimensionless (no units)

22. 22 Coefficient of Sliding Friction Ex. 10kg moving on level surface with sliding frict. coef. 0.30. Force needed to keep it at const. vel. = 0.30Fn = 0.30mg =0.30(10kg)(9.8N/kg)= 29N. dimensionless (no units)

23. 23 VelocityAccelerationNet Force ++ –+ +– –– Complete the table below for the sign of the net force. Sketch a motion diagram for each case. (+) is rightward direction, (-) is leftward direction.

24. 24 4 Summary if F net = 0, v = constant. F net = ma forces always occur in pairs of equal size and opposite direction various forces (& symbols) equilibrium problems (a = 0) dynamic problems (a ≠ 0)

25. 25 Block on Frictionless Incline a = w x /m =mgsin  /m a = gsin . F n = w y.

26. 26 Two-Box Horizontal

27. 27 One-Box Vertical

28. 28 Two-Box Vertical

29. 29 Force Diagrams: Free-fall vs. Terminal Velocity

30. 30 A 10kg box is being pushed along a horizontal surface by a force of 15N. A frictional force of 5N acts against the motion. We will want to (a) Calculate the net-force acting and (b) calculate the acceleration of the box. The net-horizontal force determines its x-acceleration The y-acceleration is known to be zero because it remains in horizontal motion, thus The net-force is 10N horizontal (0 vertical) The x-acceleration is: Example:

31. 31

32. 32 Two Connected Blocks

33. 33 A 3kg object sits on a frictionless table. Two horizontal forces act, one is 2N in the y-direction, the other 4N in the x- direction. A top-view diagram will be shown. F net What is the magnitude of the net-force acting? 4 2 2

34. 34 What direction does the 3kg mass accelerate in? Its acceleration is parallel to Fnet by Newton’s 2 nd Law. So we need to determine the direction of Fnet. We are in Quadrant I since x and y are both +

35. 35 What is the magnitude of the acceleration?

36. 36 Coefficients of Friction Ex: Block&Load = 580grams If it takes 2.4N to get it moving and 2.0N to keep it moving

37. 37 1. 3kg box on level frictionless surface. F=86N acts 60° below horizontal. Example:

38. 38 1.(cont)

39. 39 Q1. What are a x and F N if angle is 30?

40. 40 Interaction Notation Since all forces are ‘pairs’, label as interactions, e.g. 1 on 2, 2 on 1, etc. F12 = “force of object 1 on object 2” F21 = “force of object 2 on object 1” F34 = “force of object 3 on object 4” Etc.

41. 41 Interaction Notation Symbols F12 – general force, 1 on 2 N12 – normal contact force, 1 on 2 f12 – frictional force, 1 on 2 W12 – gravitational force, 1 on 2 T12 – tension force, 1 on 2 m12 – magnetic force, 1 on 2 e12 – electrical force, 1 on 2

42. 42 Gravitational Force All masses attract via gravitational force Attraction is weak for two small objects Ex: Attraction between two bowling balls is so small it is hard to measure. Force is proportional to mass product Force is inversely proportional to the square of the distance between objects

43. 43 Example: Net Force = 0. Block on a surface inclined 30° from horizontal. Applied force F acts 40° below horizontal. Net Force = 0 velocity = constant

44. 44 Diagrams with Interaction Notation If f21 exists, then f12 also exists, and is opposite in direction to f21. f21 and f12 act on different objects.