4 Newtons Laws Force netforce mass inertia Newtons

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4 Newton’s Laws • • Force, net-force, mass & inertia Newton’s Laws of Motion

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. 1

Force Concept Contact Forces Ex: sliding, bouncing Non-Contact Ex: magnetism, gravity / 2

Force Concept Contact Forces Ex: sliding, bouncing Non-Contact Ex: magnetism, gravity / 2

Inertia • is ‘resistance’ to change in velocity • Measurement: Mass • SI Unit:

Inertia • is ‘resistance’ to change in velocity • Measurement: Mass • SI Unit: Kilogram (Kg) • / 3

units • • Force units (SI): newton, N 1 N ≈ ¼ lb. 1

units • • Force units (SI): newton, N 1 N ≈ ¼ lb. 1 N = (1 kg)(1 m/s/s) N/kg = m/s/s 4

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

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

Newton’s Laws of Motion 1. An object maintains constant velocity when the Net -Force

Newton’s Laws of Motion 1. An object maintains constant velocity when the Net -Force on it is zero. 2. An object’s acceleration equals the Net-Force on it divided by its mass. 3. Forces always occur in pairs equal in size and opposite in direction. 6

Weight Force 7

Weight Force 7

Contact Forces • Surfaces in contact are often under compression: each surface pushes against

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. 8

Tension & Compression • Compressed objects push outward away from their center (aka Normal

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. 9

Force Label Notation • • • F = general force FN = normal force

Force Label Notation • • • F = general force FN = normal force f = frictional force w = mg = Fg = weight T = tension force / 10

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

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

Problem Solving Template: Two Equations – Two Unknowns 12

Problem Solving Template: Two Equations – Two Unknowns 12

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

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

Example of a Force Diagram for a Sled net force equals the mass times

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

Force Diagrams • Object is drawn as a “point” • Each force is drawn

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 15

Ex: Ball rolling up & slowing down (Use PHET Vector Addition for net-force) Fnet

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

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

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

Ex. Continued 18

Ex. Continued 18

Block on Inclined Plane 19

Block on Inclined Plane 19

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

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

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

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

Complete the table below for the sign of the net force. Sketch a motion

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

Newton’s 3 rd Law of Motion • equal-sized oppositely-directed forces • Independent of mass

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

Newton’s 3 rd Law Pair Notation • use “x” marks on forces that are

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. 24

Force Diagram each object. Which has greater acceleration when released? Spring Force x Acceleration

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

Newton’s Second and Third Laws in Operation: Ball hits a large block on a

Newton’s Second and Third Laws in Operation: Ball hits a large block on a smooth level surface. Motion of Ball Force on Block Acceleration of Ball Acceleration of Block 26

Solving Two Body Problems • Force diagram each object & system (usually with one

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 • / 27

Two Connected Blocks 28

Two Connected Blocks 28

4 Summary • • Zero net-force; constant velocity Acceleration = net-force/mass All forces are

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 / 29

Example: Net Force = 0. Block on a surface inclined 30° from horizontal. Applied

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

nd 2 Newton’s Law Examples 31

nd 2 Newton’s Law Examples 31

A 3 kg object sits on a frictionless table. Two horizontal forces act, one

A 3 kg object sits on a frictionless table. Two horizontal forces act, one is 2 N in the y-direction, the other 4 N in the xdirection. A top-view diagram will be shown. What is the magnitude of the net-force acting? 2 Fnet 2 4 32

What direction does the 3 kg mass accelerate in? Its acceleration is parallel to

What direction does the 3 kg 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 + 33

What is the magnitude of the acceleration? 34

What is the magnitude of the acceleration? 34

Example: A 10 kg box is being pushed along a horizontal surface by a

Example: A 10 kg box is being pushed along a horizontal surface by a force of 15 N. A frictional force of 5 N 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 10 N horizontal (0 vertical) The x-acceleration is: 35

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Coefficients of Friction Ex: Block&Load = 580 grams If it takes 2. 4 N

Coefficients of Friction Ex: Block&Load = 580 grams If it takes 2. 4 N to get it moving and 2. 0 N to keep it moving 37

Q 1. What are ax and FN if angle is 30? 38

Q 1. What are ax and FN if angle is 30? 38

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

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

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Check of Previous Problem: 42

Check of Previous Problem: 42

Q 2. 3 kg box at rest on frictionless 30° inclined plane. F acts

Q 2. 3 kg box at rest on frictionless 30° inclined plane. F acts horizontally. Calculate F and Fn. 43

3. Three boxes are pushed by force F along a horizontal frictionless surface. 5

3. Three boxes are pushed by force F along a horizontal frictionless surface. 5 kg 3 kg 2 kg F=26 N Force diagram object 1 (left box) F 12, surface reaction force 3 kg 44

Diagram object 2: F 23, surface reaction force Diagram object 3: 5 kg F

Diagram object 2: F 23, surface reaction force Diagram object 3: 5 kg F 21, surface reaction force 2 kg F 32, surface reaction force 45

Object 1: 3 kg Object 2: 5 kg Object 3: 2 kg Object 1+2+3:

Object 1: 3 kg Object 2: 5 kg Object 3: 2 kg Object 1+2+3: 3 kg+5 kg+2 kg 46

3 kg 5 kg 2 kg Summary: Stimulus=26 N Reactions: 18. 2 N, 5.

3 kg 5 kg 2 kg Summary: Stimulus=26 N Reactions: 18. 2 N, 5. 2 N 47

Q 3. Recalculate problem 3 with order switched to 5 kg, 3 kg, 2

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

4. Modified Atwood Machine with frictionless plane solve for a and T in terms

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

Q 4. Recalculate problem 4 with m 1 = 6 kg m 2 =

Q 4. Recalculate problem 4 with m 1 = 6 kg m 2 = 1 kg. Note that T > (m 2)g 50

2. Block stays at same place on frictionless wedge. a) Draw a force diagram

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

b) Use sum of vertical forces to calculate the size of Fn. c) Use

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. 52

Name(s): ______________________ 1. A 0. 88 kg block projected up plane. Acceleration is 5.

Name(s): ______________________ 1. A 0. 88 kg block projected up plane. Acceleration is 5. 5 m/s/s directed down the plane. Sliding friction is present. a) Draw a force diagram for the block after projection and moving up the plane. Label each force clearly. 53

b) Calculate the kinetic frictional coefficient. c) The block is projected down the plane.

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. 54

d) Calculate the net force acting down the plane in newtons. e) Calculate the

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? 55