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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.
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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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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
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Net Force
FFFFnet
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vector sum of all forces acting on an object
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constant velocity
Force Diagram
Fnet = 0
a = 0
Example: Net Force = 0, Ball rolls along a smooth level surface
table force
weight force
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Example Motion Diagram when Fnet = 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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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
NF
w F
30
40
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Example of a Force Diagram for a Sled
net force equals the mass times its acceleration.
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Newton’s Second Law: acceleration equals Net External Force (on object) divided by object mass:
mass
Fa
Example Motion Diagrams when Fnet ≠ 0
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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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units
• Force units (SI): newton, N
• 4.45N = 1lb.
• 1N = (1kg)(1m/s/s)
• N/kg = m/s/s
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Inertia• is ‘resistance’ to change in velocity
• Ex: accelerating a ping pong ball• Ex: accelerating a train
• Measurement: Mass
• SI Unit: Kilogram (Kg)
3090
6030
Mg, 300 deg.
• 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
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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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Motion of Ball
Force on Ball Force on Block
Acceleration of BallAcceleration of Block
Newton’s Second and Third Laws in Operation: Ball hits a large block on a smooth level surface.
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upward (decreasing) velocity
Fnet
acceleration
Ex: Newton’s 2nd Law
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Contact Forces
• Normal Force – perpendicular to surfaces
• Frictional Force – along surface. f ~ FN and to types of surfaces
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Normal forces are?
1. Always vertically upward.
2. Always vertically downward.
3. Can point in any direction.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40
41 42 43 44 45
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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 concretearound 1.0
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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.
N
ss F
f max, dimensionless (no units)
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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.
N
kk F
f dimensionless (no units)
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Velocity Acceleration Net 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.
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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)
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Block on Frictionless Incline
• a = wx/m =mgsin/m
• a = gsin.
• Fn = wy.
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Two-Box Horizontal
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One-Box Vertical
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Two-Box Vertical
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Force Diagrams: Free-fall vs. Terminal Velocity
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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.
xx maNNNF 10515
0. yy maweightforceNormalF
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: ssmkg
N
m
Fa x
x //110
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Example:
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Two Connected Blocks
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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.
Fnet
What is the magnitude of the net-force acting?
4
22
2,
2, )()(|| ynetxnetnet FFF
490cos20cos4, xnetF
290sin20sin4, ynetF
NFnet 47.4)2()4(|| 22
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What direction does the 3kg mass accelerate in?
Its acceleration is parallel to Fnet by Newton’s 2nd Law. So we need to determine the direction of Fnet.
),.(180tan,
,1 IIIIIquadsF
F
xnet
ynet
6.26
4
2tan 1
N
N
We are in Quadrant I since x and y are both +
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What is the magnitude of the acceleration?
ssmkg
N
m
Fa
net//49.1
3
47.4
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Coefficients of FrictionEx: Block&Load = 580grams
NkgNkgmgFN 68.5)/8.9)(580.0(
If it takes 2.4N to get it moving and 2.0N to keep it moving
42.068.5
4.2max, N
N
F
f
N
ss
35.068.5
0.2
N
N
F
f
N
ks
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1. 3kg box on level frictionless surface. F=86N acts 60° below horizontal.
xy
300cos)270cos(90cos)300cos( FwFFF Nx
wFFwFFF NNy 866.0)270sin(90sin)300sin(
NF
F60w
Example:
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xy
0xa
0ya
xx maF
2/14
360cos86
60cos
sma
a
maF
x
x
x
yy maF
NF
F
wFF
N
N
N
8.103
)8.9(360sin86
060sin
1.(cont)
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Q1. What are ax and FN if angle is 30?NF
F30w
30cos)90cos(90cos)30cos( FwFFF Nx
wFFwFFF NNy 30sin)90sin()30sin(90sin
2/25
330cos86
30cos
sma
a
maF
x
x
x
NF
F
wFF
N
N
N
4.72
)8.9(330sin86
030sin
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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.
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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
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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
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Example: Net Force = 0. Block on a surface inclined 30° from horizontal. Applied force F acts 40° below horizontal.
NF
w F
30
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Net Force = 0
velocity = constant
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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.