Chapter 4 Forces and the Laws of Motion

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Chapter 4 Forces and the Laws of Motion
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Aristotles view on motion
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Two types of Motion

• Natural motion either straight up or down
• Violent motion was imposed motion, result of a
  force.

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Force

• A push or a pull exerted on some object.

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Galileos view dispelled Aristotles

• A force is not necessary to keep an object
  moving.
• Introduced friction,

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Friction

• Force between materials that are moving past one
  another.
• Force that opposes motion.

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• The cause of an acceleration, or the change in an
  objects speed.

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Newton (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.

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A dyne is the measurement of force when using
grams and centimeters.
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Weight

• Is the measure of the magnitude of the
  gravitational force exerted on an object.

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Conversion Factor

• 1 N 0.225 lb
• 1 lb 4.448 N

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Figure out what your weight is in Newtons.
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190 lb 4.448 N 1 lb

• 845.12 N

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Forces can act through

1. Contact
2. At a distance

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Contact Forces

• A force that arises from the physical contact of
  two objects.
• Ex Throwing a ball or pulling a sled.

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Field Forces

• A force that can exist between objects, even in
  the absence of physical contact between the
  objects.

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• Ex force of gravity or attraction/repulsion of
  electrical charges.

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• The effect of a force depends upon the magnitude
  of the force and the direction of the force.
• Therefore, a force is a vector.

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Force Diagram

• Is a diagram, in which, all forces acting on an
  object are represented by vector arrows.
• Sometimes these are called free-body diagrams.

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Look at figures 4 3 4 4 on pages 126 128
.
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Section 4 2 Newtons First Law
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• An object at rest remains at rest, and an object
  in motion will continue in motion with a constant
  velocity (in a straight line),

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• unless the object experiences a net external
  force.

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Inertia

• Is the tendency of an object to maintain its
  state of motion.

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• Galileo said that every material object has a
  resistance to the change of its state of motion.

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Newtons 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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What is mass?

• The amount of matter an object contains.
• Mass measures the inertia of an object.

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• All objects made of matter have inertia - that
  is, they resist accelerations (Newtons First
  Law), but some objects resist more than others.

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Mass is not Volume.

• Mass is a scalar quantity.
• SI unit of mass is the kilogram (kg).

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Mass 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

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Net 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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• 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.

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Ex 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.
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Force diagram
70 N
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Force diagram
70 N
y
x
Q 30
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• X component since we have a right triangle and
  know the angle and the hypotenuse. We will use
  the cosine trig function.

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adjcos q ----- hyp

• Fx hyp cos q
• Fx 70 cos 30
• Fx 60.6 N

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• y component since we have a right triangle and
  know the angle and the hypotenuse. We will use
  the sine trig function.

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oppsin q ----- hyp

• Fy hyp sin q
• Fy 70 sin 30
• Fy 35 N

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Ex 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.
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Force Diagram
565 N
115 N
82 N
236 N
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A) Find the net external force in the x direction.

• Remember right is () and left is (-)
• x 82 N (- 115 N)
• x - 33 N

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B) Find the net external force in the y direction.

• Remember up is () and down (-)
• y 565 N (- 236 N)
• y 329 N

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C) Find magnitude and direction of the Fnet on
the crate.
Fnet
329 N
- 33 N
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Use the Pythagorean Theorem to find Fnet and the
inverse tangent function to find the direction.
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Since we are on the negative x-axis, this is the
same as an angle of 95.7o from the positive
x-axis.
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In your notes do problems 3 4 on HPg 133.
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Mass 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.

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Equilibrium

• The state in which there is no change in the
  bodys motion.

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Equilibrium Means "Zero Acceleration"
Forces in balance   Equilibrium
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• An object is in equilibrium when the vector sum
  of the forces acting on it is equal to zero.

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Is the object moving?

• Yes, but at constant velocity.

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Section 4-3 Newtons Second and Third Laws
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Force 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.

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• However, if a couple of friends help, then it is
  much easier to move and you can make it move
  faster quicker.

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Newtons 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.

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From this law we get
Normally it is written as
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a F / m
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a F / m
2a 2 F / m
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a F / m
2a 2 F / m
a 2 F / 2m
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a F / m
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a F / m
a/2 F /2m
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a F / m
a/2 F /2m
a/3 F / 3m
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Note remember that it is the Fnet that cause the
object to move.
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Note
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Ex 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?
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• 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 16 kg

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Ex 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?
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• G Fnet 7.0 N, m 3.2 kg
• U a ?
• E Fnet ma or a Fnet/m
• S a 7.0 N / 3.2 kg
• S a 2.2 m/s2 forward

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Remember the from Ch. 2
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Remember the from Ch. 2
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Remember the from Ch. 2
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Ex 5 A 2 kg otter starts from rest at the top of
a muddy incline 0.85 m long and slides down to
the bottom in 0.5 sec. What is the net external
force?
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• G Dx .85 m, Dt 0.5s vi 0 m/s,
  m 2 kg
• U Fnet ?
• We need to find the acceleration, but we need
  final speed first.

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We need to find the average speed first, than use
that to find the final speed.
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Using the 2nd average speed equation.
Rearrange for final speed
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Now we can find acceleration.
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Now we can find Fnet

• E Fnet ma
• S Fnet (2 kg)(6.8 m/s2)
• S Fnet 13.6 N

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On pg 138 (HP), Do Practice 4B 3 5.
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Forces always exist in pairs.

• Ex When you push against the wall, the wall
  pushes back. The forces are equal, but opposite.

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Newtons 3rd Law
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• 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.

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A simpler alternative statement for Newtons 3rd
Law

• For every action, there is an equal and opposite
  reaction.

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Action-reaction pair

• A pair of simultaneously equal, but opposite
  forces resulting from the interaction of 2
  objects.

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Action-Reaction forces each act on different
objects.

• They do not result in equilibrium.
• Reread pg 139

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Recoil is an example of the 3rd Law
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Field Forces also exist in pairs.

• Newtons 3rd Law also applies to field forces.

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When 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.
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Why 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.

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Section 4-4 Everyday Forces
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Weight (Fg)

• The magnitude of the force of gravity acting on
  an object.
• Weight is NOT mass!

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• The weight of an object depends on the objects
  mass.
• In fact, an objects weight is directly
  proportional to the objects mass.

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• The weight of an object also depends on the
  objects location.

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• 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.

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Fg mg

• Where g 10 m/s2, unless otherwise specified.
• Weight is dependent on the force of gravity. It
  depends upon location. And acts downward.

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The farther away from the center of the earth,
the less g becomes.
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• 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.

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• EX 6 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?

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What forces are acting on this object?

• Weight downward
• Force of Engine - upward

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• G m 10 kg, g 10 m/s2 Fengine 150 N
• U Fnet ?
• E Fnet Fengine - Fg
• Fnet Fengine - mg
• S Fnet 150 N - (10)(10)
• S Fnet 50 N

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Remember the net force is what accelerates the
object.

• U a ?
• E a Fnet /m
• S a 50 N / 10 kg
• S a 5 m/s2

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• EX 7 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?

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• Remember the Net Force causes the object to
  accelerate.

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• G a 3 m/s2, m 20 kg, g 10 m/s2
  
• U Fnet ?
• E Fnet ma
• S Fnet (20 kg)(3 m/s2)
• S Fnet 60 N

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• U Fnet Fengine - Fg
• Fengine Fnet Fg
• Fengine Fnet mg
• Fengine 60 (20)(10)
• Fengine 260 N

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Normal Force (FN)

• A force exerted by one object on another in a
  direction perpendicular to the surface of contact.

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N
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The normal force is always to the surface of
contact, but is not always opposite the direction
of gravity.
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FN Fg, but opposite if

• The FN can be calculated by the equation FN
  mgcosq, if the object is on an inclination.

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The value for q is the same for both.
q
FN
Fg
q
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Force of Friction

• Is the force that opposes motion.
• There are 2 types of friction

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Static Friction (Fs)

• The resistive force that opposes relative motion
  of 2 contacting surfaces that are at rest with
  respect with one another.

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As 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.

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Once you exceed the max value the object begins
to move.
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Kinetic Friction (Fk)

• The resistive force that opposes the relative
  motion of two contacting surfaces that are moving
  past one another.

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Since 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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Frictional forces arise from the complex
interaction of the surfaces, at a microscopic
level.
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Its 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.

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Therefore, 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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The frictional force between a chair and tile
floor is less than the the force between a chair
and carpet.
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Coefficient of Friction (m)

• Is the ratio of the force of friction and the
  normal force acting between the objects.

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Ffriction m ---------- Fnormal
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Note The coefficient of friction has no units.
From the equation the units cancel out.
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Coefficient of Kinetic Friction
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Coefficient of Static Friction
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• Remember that on a horizontal surface the normal
  force is equal to the objects weight.

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On pg 144, are values for the coefficient of
friction, for both static and kinetic.
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Ex 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.
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• G m 19 kg, F Fs 75 N
• U ms ?
• E Fs Fs
• ms ----- ------
• FN mg

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• S 75 N
• s ---------------------
• (19 kg)(10 m/s2)
• S ms 0.39

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From the Coefficient of friction what are the two
surfaces in contact?

• Wood on Wood

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Overcoming Friction Example
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• 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.

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FN
Fapplied
Fk
Fg
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Which way does the object accelerate?

• Only in the x direction

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In 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.

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Since the object doesnt move in the Y
direction the Fnet,y 0 N. We need to find the
net force in the x direction.
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Fnet,x Fapplied,x Fk

• Since the applied force is at an angle, we only
  want the x-component.

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Fapp,x Fapp cosq

• Fapp,x 90 N cos(30)
• Fapp,x 77.9 N

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Next find the Fk

• Fk m FN
• We need to find the Normal Force. Does it equal
  the weight?

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NO, 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

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FN Fapp,y - Fg 0

• FN Fg - Fapp,y

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Fg mg

• Fg (20)(10)
• Fg 200 N

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• Fapp,y Fapp sinq
• Fapp,y 90N sin(30)
• Fapp,y 45N

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FN Fapp,y - Fg 0

• FN Fg - Fapp,y
• FN 200 N - 45N
• FN 155 N

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Fk mk FN

• Fk (0.50)(155 N)
• Fk 77.5 N to the left
• So Fk 77.5 N

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Now, find the Fnet,x

• Fnet,x Fapp,x - Fk
• Fnet,x (77.9 N - 77.5 N) Fnet,x 0.4 N

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Now, find the horizontal acceleration.

• ax Fnet,x /m
• ax 0.4 N / 20 kg
• ax 0.02 m/s2

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Air Resistance is a form of friction (FR)

• When an object moves through a fluid, that fluid
  provides resistance in the direction opposite of
  the objects motion.

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Terminal Velocity

• When a free falling body accelerates, the
  objects velocity increases. As the velocity
  increases, the objects air resistance increases.

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• 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.

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• The maximum speed a free-falling body reaches due
  to air resistance equaling the force of gravity.

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Eventually, the force R of air resistance becomes
equal to the force exertedby the earth, and the
object reaches equilibrium.
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Why does the heavierperson fall faster?
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What does Pressure mean to you?

• Under Pressure
• Peer Pressure
• Feeling Pressured
• Air/Atmospheric
• Tire

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Pressure

• The amount of force per unit area.

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• Force
• Pressure ----------
• Area

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F
P
A
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Pressure Units

• N/m2
• 1 N/m2 1 Pascal (Pa)

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Ex