Title: Chapter 4 Forces and the Laws of Motion
1Chapter 4 Forces and the Laws of Motion
2Aristotles view on motion
3Two types of Motion
- Natural motion either straight up or down
- Violent motion was imposed motion, result of a
force.
4Force
- A push or a pull exerted on some object.
5- The cause of an acceleration, or the change in an
objects speed.
6Galileos view dispelled Aristotles
- A force is not necessary to keep an object
moving. - Introduced friction,
7Friction
- Force between materials that are moving past one
another. - Force that opposes motion.
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10Newton (N)
- SI/Metric unit of force.
- Is the amount of force that, when acting on a 1
kg mass, produces an acceleration of 1 m/s2.
11A dyne is the measurement of force when using
grams and centimeters.
12Weight
- Is the measure of the gravitational force exerted
on an object.
13Conversion Factor
- 1 N 0.225 lb
- 1 lb 4.448 N
14Figure out what your weight is in Newtons.
15190 lb 4.448 N 1 lb
16Forces can act through
- Contact
- At a distance
17Contact Forces
- A force that arises from the physical contact of
two objects. - Ex Throwing a ball or pulling a sled.
18Field Forces
- A force that can exist between objects, even in
the absence of physical contact between the
objects.
19- Ex force of gravity or attraction/repulsion of
electrical charges.
20 - The effect of a force depends upon the magnitude
of the force and the direction of the force. - Therefore, a force is a vector.
21Force Diagram
- Is a diagram, in which, all forces acting on an
object are represented by vector arrows. - Sometimes these are called free-body diagrams.
22Look at figures 4 3 4 4 on pages 126 128
.
23Section 4 2 Newtons First Law
24- An object at rest remains at rest, and an object
in motion will continue in motion with a constant
velocity, unless the object experiences a net
external force. -
25Inertia
- Is the tendency of an object to maintain its
state of motion.
26- Galileo said that every material object has a
resistance to the change of its state of motion.
27Newtons first law is sometimes called the Law
of Inertia
- Meaning that in the absence of force a body will
preserve its state of motion.
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32What is mass?
- The amount of matter an object contains.
- Mass measures the inertia of an object.
33- All objects made of matter have inertia - that
is, they resist accelerations (Newtons First
Law), but some objects resist more than others.
34Mass is not Volume.
- Mass is a scalar quantity.
- SI unit of mass is the kilogram (kg).
35Mass is not Weight
- Mass is a property of an object that measures how
much it resists accelerating. - An object is difficult to accelerate because it
has mass
36Net External Force (Fnet)
- Is the total force resulting from a combination
of external forces on an object sometimes called
the resultant force.
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38- The downward force due to gravity is the
object/bodys weight. - The upward force is due to the force exerted by
the contact surface on the object.
39Ex 1 A man is pulling on his dog with a force of
70 N directed at an angle of 30 degrees to the
horizontal. Find the x and y components of the
force.
40Force diagram
70 N
41Force diagram
70 N
y
x
Q 30
42- X component since we have a right triangle and
know the angle and the hypotenuse. We will use
the cosine trig function.
43 adjcos q ----- hyp
- Fx hyp cos q
- Fx 70 cos 30
- Fx
44- y component since we have a right triangle and
know the angle and the hypotenuse. We will use
the sine trig function.
45 oppsin q ----- hyp
- Fy hyp sin q
- Fy 70 sin 30
- Fy
46Ex 2 A crate is pulled to the right with a force
of 82 N, to the left with a force 115 N, upward
with a force of 565 N, and downward with a force
of 236 N. Find the Fnet and Angle
47Force Diagram
565 N
115 N
82 N
236 N
48A) Find the net external force in the x direction.
- Remember right is () and left is (-)
- Fx 82 N (- 115 N)
- Fx
49B) Find the net external force in the y direction.
- Remember up is () and down (-)
- Fy 565 N (- 236 N)
- Fy 329 N
50C) Find magnitude and direction of the Fnet on
the crate.
Fnet
329 N
- 33 N
51Use the Pythagorean Theorem to find Fnet and the
inverse tangent function to find the direction.
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60Since we are on the negative x-axis, this is the
same as an angle of 95.7o from the positive
x-axis.
61In your notes do problems 3 4 on HPg 133.
62Mass is a measurement of inertia.
- Ex A golf ball and a basketball, if the same
Fnet acts on both, the golf ball will accelerate
more.
63Equilibrium
- The state in which there is no change in the
bodys motion. -
64Equilibrium Means "Zero Acceleration"
Forces in balance Equilibrium
65- An object is in equilibrium when the vector sum
of the forces acting on it is equal to zero.
66Can the object moving?
- Yes, but at constant velocity.
67Section 4-3 Newtons Second and Third Laws
68Force is proportional to mass and acceleration
- Think about pushing a stalled car. If you try to
push it by yourself, you can move it, but not
very fast.
69- However, if a couple of friends help, then it is
much easier to move and you can make it move
faster quicker.
70Newtons 2nd Law
- The acceleration of an object is directly
proportional to the Net External Force (Fnet)
acting on the object and inversely proportional
to the objects mass.
71From this law we get
Normally it is written as
72a F / m
73a F / m
2a 2 F / m
74a F / m
2a 2 F / m
a 2 F / 2m
75a F / m
76a F / m
a/2 F /2m
77a F / m
a/2 F /2m
a/3 F / 3m
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79Note remember that it is the Fnet that cause the
object to move.
80Note
81Ex 3 Nathan applies a force of 20 N, causing the
book to accelerate at a rate of 1.25 m/s2. What
is the mass of the book?
82- G a 1.25 m/s2, Fnet 20 N
- U m ?
- E Fnet ma or m Fnet/a
- S m 20 N / 1.25 m/s2
- S m
83Ex 4 The Fnet on the propeller of a 3.2 kg
model airplane is 7.0 N forward. What is the
acceleration of the airplane?
84- G Fnet 7.0 N, m 3.2 kg
- U a ?
- E Fnet ma or a Fnet/m
- S a
- S a
85On pg 138 (HP), Do Practice 4B 3 5.
86Forces always exist in pairs.
- Ex When you push against the wall, the wall
pushes back. The forces are equal, but opposite.
87Newtons 3rd Law
88- If two objects interact, the magnitude of the
force exerted on object 1 by object 2 is equal in
magnitude of the force simultaneously exerted on
object 2 by object 1, and these two forces are
opposite in direction.
89A simpler alternative statement for Newtons 3rd
Law
- For every action, there is an equal and opposite
reaction.
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91Action-reaction pair
- A pair of simultaneously equal, but opposite
forces resulting from the interaction of 2
objects.
92Action-Reaction forces each act on different
objects.
- They do not result in equilibrium.
- Reread pg 139
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95Recoil is an example of the 3rd Law
96Field Forces also exist in pairs.
- Newtons 3rd Law also applies to field forces.
97When an object is falling, its falling due to the
force exerted by the earth, the reaction force is
that the body is exerting an equal and opposite
force on the earth.
98Why dont we notice the this reaction force?
- Because of Newtons 2nd Law, the mass of the
earth is so great that the acceleration is so
small it is negligible.
99Section 4-4 Everyday Forces
100Weight (Fg)
- The force of gravity acting on an object.
- Weight is NOT mass!
101- The weight of an object depends on the objects
mass. - In fact, an objects weight is directly
proportional to the objects mass.
102- The weight of an object also depends on the
objects location.
103- The weight of an object also depends on the
objects location. - In fact, an objects weight is directly
proportional to its free fall acceleration, g at
its current location.
104Fg mg
- Where g 10 m/s2, unless otherwise specified.
- Weight is dependent on the force of gravity. It
depends upon location. And acts downward.
105The farther away from the center of the earth,
the less g becomes.
106- Also, the gravitational pull of the moon is about
1/6th of the earths. - So if you way 180 lb or 900 N on earth youd
weigh 30 lb or 150 N on the moon.
107- EX 5 A rocket with a mass of 10 kg is launched
vertically with a force of 150 N. What is the
rockets net force? What is the acceleration
produced by this net force?
108What forces are acting on this object?
- Draw Block diagram Weight downward
- Force of Engine - upward
109Feng
Fg
110- G m 10 kg, g 10 m/s2 Fengine 150 N
- U Fnet ?
- E Fnet Fengine - Fg
- Fnet Fengine - mg
- S Fnet
- S Fnet
111Remember the net force is what accelerates the
object.
- U a ?
- E a Fnet /m
- S a
- S a
112- EX 6 A 20 kg rocket is accelerated upwards
(vertically) at 3 m/s2. What is the Force that
provides this acceleration, this is the net
force? What is the force provided by the rockets
engine?
113- Remember the Net Force causes the object to
accelerate.
114- G a 3 m/s2, m 20 kg, g 10 m/s2
- U Fnet ?
- E Fnet ma
- S Fnet
- S Fnet
115- U Fnet Fengine - Fg
- Fengine Fnet Fg
- Fengine Fnet mg
- Fengine
- Fengine
116Normal Force (FN)
- A force exerted by one object on another in a
direction perpendicular to the surface of contact.
117N
118The normal force is always to the surface of
contact, but is not always in the opposite
direction of gravity.
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120FN Fg, but opposite if
- The FN can be calculated by the equation FN
mgcosq, if the object is on an inclination.
121The value for q is the same for both.
q
FN
Fg
q
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123Force of Friction
- Is the force that opposes motion.
- There are 2 types of friction
124Static Friction (Fs)
- The resistive force that opposes relative motion
of 2 contacting surfaces that are at rest with
respect with one another.
125As long as an object does not move when a force
is applied
- As the applied force increase, the force of
static friction increases. It increases until it
reaches its max value Fs,max.
126Once you exceed the max value the object begins
to move.
127Kinetic Friction (Fk)
- The resistive force that opposes the relative
motion of two contacting surfaces that are moving
past one another.
128Since it is easier to keep an object moving than
it is to start it moving, the kinetic friction is
less than static friction.
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131Frictional forces arise from the complex
interaction of the surfaces, at a microscopic
level.
132Its easier to push a chair than it is to move a
desk at the same speed.
- Since the desk is heavier, it has a greater
normal force.
133Therefore, the force of friction is proportional
to the normal force.
- Also, friction depends upon the nature of the
surfaces in contact.
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135The frictional force between a chair and tile
floor is less than the the force between a chair
and carpet.
136Coefficient of Friction (m)
- Is the ratio of the force of friction and the
normal force acting between the objects.
137 Ffriction m ---------- Fnormal
138Note The coefficient of friction has no units.
From the equation the units cancel out.
139Coefficient of Kinetic Friction
140Coefficient of Static Friction
141- Remember that on a horizontal surface the normal
force is equal to the objects weight.
142On HPg 144, are values for the coefficient of
friction, for both static and kinetic.
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144Ex 8 A 19 kg crate initially at rest, on a
horizontal floor, requires a 75 N forces to set
it in motion. Find the coefficient of static
friction.
145- G m 19 kg, F Fs 75 N
- U ms ?
- E Fs Fs
- ms ----- ------
- FN mg
146- S
- s ---------------------
-
- S ms
147From the Coefficient of friction what are the two
surfaces in contact?
148- B.) What applied force is necessary to keep the
object moving at a constant speed?
149Overcoming Friction Example
150- Ex 9 Andy pulls a wagon with a force of 90 N at
an angle of 30o to a horizontal surface. The mass
of the wagon is 20 kg, and the coefficient of
kinetic friction between the wagon and the side
walk is 0.50. Find the acceleration of the wagon
due to the net force.
151FN
Fapplied
Fk
Fg
152Which way does the object accelerate?
153In order to find the acceleration, we will use
Newtons 2nd Law.
- Fnet,x max
- We dont know the Fnet,x, so we need to find it.
154Since the object doesnt move in the Y
direction the Fnet,y 0 N. We need to find the
net force in the x direction.
155Fnet,x Fapplied,x Fk
- Since the applied force is at an angle, we only
want the x-component.
156Fapp,x Fapp cosq
- Fapp,x 90 N cos(30)
- Fapp,x
157Next find the Fk
- Fk mkFN
- We need to find the Normal Force. Does it equal
the weight?
158NO, since the Fapp has a y-component.
- We know the net force in the y-direction is zero,
so - Fnet,y FN Fapp,y - Fg 0
159FN Fapp,y - Fg 0
160Fg mg
161- Fapp,y Fapp sinq
- Fapp,y
- Fapp,y
162FN Fapp,y - Fg 0
- FN Fg - Fapp,y
- FN 200 N - 45N
- FN
163Fk mk FN
164Now, find the Fnet,x
- Fnet,x Fapp,x - Fk
- Fnet,x
- Fnet,x
165Now, find the horizontal acceleration.
166Air Resistance is a form of friction (FAR)
- When an object moves through a fluid, that fluid
provides resistance in the direction opposite of
the objects motion.
167- When a free falling body accelerates, the
objects velocity increases. As the velocity
increases, the objects air resistance increases.
168- When the air resistance balances the force of
gravity, the net force is zero. The objects
continues to move downward at a constant maximum
speed.
169Terminal Velocity
- The maximum speed a free-falling body reaches due
to air resistance equaling the force of gravity.
170Terminal velocity is reached when the force R of
air resistance becomes equal to the force
exertedby the earth, and the object reaches
equilibrium.
171Why does the heavierperson fall faster?
172What does Pressure mean to you?
- Under Pressure
- Peer Pressure
- Feeling Pressured
- Air/Atmospheric
- Tire
173Pressure
- The amount of force per unit area.
174- Force
- Pressure ----------
- Area
175F
P
A
176Pressure Units
- N/m2
- 1 N/m2 1 Pascal (Pa)
177Ex