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1 4 Topics force and net force inertia and 1 st law acceleration and 2 nd law g notation force pairs and 3 rd law force diagrams equilibrium friction

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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

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

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4 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.

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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

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

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7 Newton’s Second Law: When a Net External Force acts on an object with mass m, the resulting acceleration of the object is parallel to the net external force and has magnitude of Example Motion Diagrams when F net ≠ 0

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8 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?

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

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10 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

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

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12 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

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

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

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

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16 Contact Forces Normal Force – perpendicular to surface Frictional Force – parallel to surface Static (no sliding)Kinetic (sliding)

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

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18 Static Friction Objects usually “stick” when at rest Must be “budged” to get them moving “Budging force” = f s,max. f s ranges from 0 to f s,max.

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19 Kinetic Friction After objects breaks free, friction decreases f k = force that just keeps object moving at a steady speed

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20 Coefficients of Friction dimensionless (no units) Ex. tire on dry road, static coeff. ~ 1.0 Ex. tire on dry road, kinetic coeff. ~ 0.8

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21 4 Summary Newton’s Laws of Motion force-diagrams and net force contact forces: normal, frictional, other equilibrium

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22 Newton’s 2 nd Law Examples

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23 Block on Frictionless Incline

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24 Two Connected Blocks

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25 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

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26 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 +

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27 What is the magnitude of the acceleration?

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28 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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30 Coefficients of Friction Ex: Block&Load = 580grams If it takes 2.4N to get it moving and 2.0N to keep it moving

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31 1. 3kg box on level frictionless surface. F=86N acts 60° below horizontal. Example:

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32 1.(cont)

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

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35 2) 3kg box at rest on frictionless 30° inclined plane. F acts 40° below horizontal.

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37 Check of Previous Problem:

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

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39 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

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

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

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42 3kg 5kg 2kg Summary: Stimulus=26N Reactions: 18.2N, 5.2N

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

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

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

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

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47 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.

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48 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.

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49 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.

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50 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?

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