1 4 Newton’s Laws Force, net-force, mass & inertia Newton’s Laws of Motion Weight, Contact Forces Labeling & Diagramming Hk: 37, 49, 53, 57, 59, 61, 65, 67.

22 Force Concept Contact Forces Ex: sliding, bouncing Non-Contact Ex: magnetism, gravity /

33 Inertia is ‘resistance’ to change in velocity Measurement: Mass SI Unit: Kilogram (Kg) /

44 units Force units (SI): newton, N 1N ≈ ¼ lb. 1N = (1kg)(1m/s/s) N/kg = m/s/s

5 Net Force vector sum of all forces acting on an object

66 1. An object maintains constant velocity when the Net-Force on it is zero. 3. Forces always occur in pairs equal in size and opposite in direction. 2. An object’s acceleration equals the Net-Force on it divided by its mass. Newton’s Laws of Motion

7 Weight Force

8 Contact Forces Surfaces in contact are often under compression: each surface pushes against the other. The outward push of each object is called the Normal Force. If the objects move (even slightly) parallel to their surface the resistance force experienced is called the frictional force.

9 Tension & Compression Compressed objects push outward away from their center (aka Normal Force). Stretched objects pull toward their center. This is called the Tension Force.

10 Force Label Notation F = general force F N = normal force f = frictional force w = mg = F g = weight T = tension force /

11 Net Force = change of motion vector sum of all forces acting on an object

12 Problem Solving Template: Two Equations – Two Unknowns

13 velocity Example: Ball rolls along a smooth level surface Force Diagram table force weight force

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

15 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

16 upward (decreasing) velocity F net acceleration Ex: Ball rolling up & slowing down (Use PHET Vector Addition for net-force)

17 Ex. m=3kg, F=86N, 60° below horizontal.

18 Ex. Continued

19 Block on Inclined Plane

20 Ex. Calculate Acceleration of Block on a Frictionless Plane inclined 30°

21 Ex. Calculate Normal Force on a Block on a Plane inclined 30°

22 VelocityAccelerationNet Force ++ –+ +– –– Complete the table below for the sign of the net force. Sketch a motion diagram for each case.

23 Newton’s 3 rd Law of Motion equal-sized oppositely-directed forces Independent of mass Pair-notation x x

24 Newton’s 3 rd Law Pair Notation use “x” marks on forces that are 3 rd Law pairs. Use “xx” for a different interaction, etc.

25 Force Diagram each object. Which has greater acceleration when released? Spring Force Spring Force xx Acceleration = F/m Acceleration = F/(2m)

26 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.

27 Solving Two Body Problems Force diagram each object & system (usually with one axis parallel to the acceleration). Use clockwise coordinates for problems with pulleys. System has a force-pair that cancels out Solve simplest diagram first, then use this information in another diagram “ma” is not a force /

28 Two Connected Blocks

29 4 Summary Zero net-force; constant velocity Acceleration = net-force/mass All forces are pairs Labeling & diagramming Solving problems using x, y force template Solving two body problems /

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

31 Newton’s 2 nd Law Examples

32 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

33 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 +

34 What is the magnitude of the acceleration?

35 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:

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

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

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40 2) 3kg box at rest on frictionless 30° inclined plane. F acts 40° below horizontal.

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42 Check of Previous Problem:

43 Q2. 3kg box at rest on frictionless 30° inclined plane. F acts horizontally. Calculate F and Fn.

44 3. Three boxes are pushed by force F along a horizontal frictionless surface. F=26N 3kg 5kg 2kg Force diagram object 1 (left box) F12, surface reaction force 3kg

45 F21, surface reaction force 5kg F23, surface reaction force F32, surface reaction force 2kg Diagram object 2: Diagram object 3:

46 Object1: 3kg Object2: 5kg Object3: 2kg Object1+2+3: 3kg+5kg+2kg

47 3kg 5kg 2kg Summary: Stimulus=26N Reactions: 18.2N, 5.2N

48 Q3. Recalculate problem3 with order switched to 5kg, 3kg, 2kg. F=26N 3kg 5kg 2kg 3kg

49 4. Modified Atwood Machine with frictionless plane Let m1 = 1kg, m2 = 2kg,  = 30°. solve for a and T in terms of m1, m2:

50 Q4. Recalculate problem4 with m1 = 6kg m2 = 1kg. Note that T > (m2)g

51 2. Block stays at same place on frictionless wedge. a) Draw a force diagram for the block with the forces to correct relative scale.

52 b) Use sum of vertical forces to calculate the size of Fn. c) Use Fn to calculate the size of the acceleration in m/s/s.

53 1. A 0.88 kg block projected up plane. Acceleration is 5.5m/s/s directed down the plane. Sliding friction is present. Name(s):___________________________________________ a) Draw a force diagram for the block after projection and moving up the plane. Label each force clearly.

54 b) Calculate the kinetic frictional coefficient. c) The block is projected down the plane. Draw a force diagram for the block after projection and moving down the plane. Label each force clearly.

55 d) Calculate the net force acting down the plane in newtons. e) Calculate the acceleration of the block in m/s/s. f) Is the acceleration i) up the plane, or ii) down the plane?