4 Topics force and net force types of

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. 1

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 2

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

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

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

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

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 7

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

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

g’s • one “g” of acceleration = 9. 8 m/s/s • “two g’s” = 19. 6 m/s/s, etc. • Example: What is the net force on a 2100 kg SUV that is accelerating at 0. 75 g? 10

units • • Force units (SI): newton, N 4. 45 N = 1 lb. 1 N = (1 kg)(1 m/s/s) N/kg = m/s/s 11

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

30 60 90 Mg, 300 deg. 30

• Fxnet = FNcos 90 + mgcos 300 = (0. 02)(a) • = 0 + (0. 02)(9. 8)(0. 5) = (0. 02)a • accel = 4. 9 m/s/s • Fynet = FNsin 90 + mgsin 300 = (0. 02)(0) • FN + (0. 02)(9. 8)(-. 866) = 0 • FN = 0. 17 N

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 15

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 16

Ex: Newton’s 2 nd Law Fnet acceleration upward (decreasing) velocity 17

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

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

Friction • Surfaces “stick” when at rest, this “static” friction varies from 0 to “fs, max” • Moving friction is called “fk” (~ indep. of v) • Characterized by “coefficients”, “ 0” = frictionless, “ 1” is high value • e. g. teflon around 0. 05, • Rubber on concrete around 1. 0 20

Coefficient of Static Friction dimensionless (no units) • Ex. 10 kg block sits on level surface with static coeff. frict. = 0. 50. Force needed to budge = 0. 50 Fn • = 0. 50 mg • = 0. 50(10 kg)(9. 8 N/kg) = 49 N. 21

Coefficient of Sliding Friction dimensionless (no units) • Ex. 10 kg moving on level surface with sliding frict. coef. 0. 30. Force needed to keep it at const. vel. = 0. 30 Fn = 0. 30 mg • =0. 30(10 kg)(9. 8 N/kg)= 29 N. 22

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

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

Block on Frictionless Incline • a = wx/m =mgsinq/m • a = gsinq. • F n = w y. 25

Two-Box Horizontal 26

One-Box Vertical 27

Two-Box Vertical 28

Force Diagrams: Free-fall vs. Terminal Velocity 29

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: 30

31

Two Connected Blocks 32

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 33

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 + 34

What is the magnitude of the acceleration? 35

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 36

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

1. (cont) 38

Q 1. What are ax and FN if angle is 30? 39

Interaction Notation • Since all forces are ‘pairs’, label as interactions, e. g. 1 on 2, 2 on 1, etc. • F 12 = “force of object 1 on object 2” • F 21 = “force of object 2 on object 1” • F 34 = “force of object 3 on object 4” • Etc. 40

Interaction Notation Symbols • • F 12 – general force, 1 on 2 N 12 – normal contact force, 1 on 2 f 12 – frictional force, 1 on 2 W 12 – gravitational force, 1 on 2 T 12 – tension force, 1 on 2 m 12 – magnetic force, 1 on 2 e 12 – electrical force, 1 on 2 41

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 42

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

Diagrams with Interaction Notation • If f 21 exists, then f 12 also exists, and is opposite in direction to f 21. • f 21 and f 12 act on different objects. 44