Physics 201: Lecture 6 Dynamics More on Forces Free Body Diagrams

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Physics 201 Lecture 6DynamicsMore on
ForcesFree Body Diagrams
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Dynamics

• Isaac Newton (1643 - 1727) published Principia
  Mathematica in 1687. In this work, he proposed
  three laws of motion
• Law 1 An object subject to no net external
  force is at rest or moves with a constant
  velocity, (if viewed from an inertial reference
  frame).

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Newtons First Law

• An object subject to no external forces is at
  rest or moves with a constant velocity if viewed
  from an inertial reference frame.
• If no forces act, there is no acceleration.
• The following statements can be thought of as the
  definition of inertial reference frames.
• An IRF is a reference frame that is not
  accelerating (or rotating) with respect to the
  fixed stars.
• If one IRF exists, infinitely many exist since
  they are related by any arbitrary constant
  velocity vector!

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Is Madison a good IRF?

• Is Madison accelerating?
• YES!
• Madison is on the Earth.
• The Earth is rotating.
• What is the centripetal acceleration of Madison?
• T 1 day 8.64 x 104 sec,
• R RE 6.4 x 106 meters .
• Plug this in aM .034 m/s2 ( 1/300 g)
• Close enough to 0 that we will ignore it.
• Madison is a pretty good IRF.

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Newtons Second Law

• For any object,
• The acceleration a of an object is proportional
  to the net force FNET acting on it.
• The constant of proportionality is called mass,
  denoted m.
• This is the definition of mass.
• The mass of an object is a constant property of
  thatobject, and is independent of external
  influences.
• Force has units of MxL / T2 kg m/s2 N
  (Newton)

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The Normal Force
When person is holding the bag above the table he
must supply a force. When the bag is placed on
the table, the table supplies the force that
holds the bag on it That force is perpendicular
or normal to the surface of table
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Newtons Third Law

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

• Finger pushes on box
• Ffinger?box force exerted on box by finger

• Box pushes on finger
• Fbox?finger force exerted on finger by box

• Third Law
• Fbox?finger - Ffinger?box

Action - Reaction Pair.
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Newton's Third Law...

• FA ,B - FB ,A. is true for all types of
  forces

Whenever one body exerts a force on a second
body, the first body experiences a force that is
equal in magnitude and opposite in direction to
the one it exerts.
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Example of Bad Thinking

• Since Fm,b -Fb,m why isnt Fnet 0, and a 0 ?

Fb,m
Fm,b
a ??
ice
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Example of Good Thinking

• Consider only the forces on the box!
• Fon box mabox Fm,b

What about forces on man?
Fb,m is the force on the man
Fb,m
Fm,b
abox
ice
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Question 1
Consider a car at rest. We can conclude that the
downward gravitational pull of Earth on the car
and the upward contact force of Earth on it are
equal and opposite because 1. The two forces
form an action-reaction pair 2. The net force
on the car is zero 3. Neither of the above
The two forces cannot be an action-reaction pair
because they act on the same object (car). Car is
at rest - therefore, it has no net forces acting
on it. The forces acting on it add up to zero
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System of Interest
The net external force acting on the system of
interest is Fwall on feet
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Problem Analysis Free Body Diagram
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System of Interest
f - All forces opposing the motion
System 1 Acceleration of the professor and the
cart System 2 Force the professor exerts on the
cart
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Question 2
Consider a person standing in an elevator that is
accelerating upward. The upward normal force N
exerted by the elevator floor on the person
is a) larger than b) identical to c) less
than the downward weight W of the person.
Person is accelerating upwards - net upwards
force is non zero
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Frictional Force

• Friction
• Opposes motion between systems in contact
• Parallel to the contact surface
• Depends on the force holding the surfaces
  together
• Normal force (N)
• Static friction
• Force required to move a stationary object
• fs is less than or equal to ms N
• Kinetic friction
• Frictional force on an object in motion
• Can be less than static friction
• fk mk N

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Question 2
You are pushing a wooden crate across the floor
at constant speed. You decide to turn the crate
on end, reducing by half the surface area in
contact with the floor. In the new orientation,
to push the same crate across the same floor with
the same speed, the force that you apply must be
about a) four times as great b) twice as
great c) equally as great d) half as
great e) one-fourth as great as the force
required before you changed the crate orientation.
Frictional force does not depend on the area of
contact. It depends only on the normal force and
the coefficient of friction for the contact.
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Friction Car Tires

• Friction keeps the car wheels from spinning in
  place
• You want the tires to roll
• You want the friction to be high
• The contact point is at rest - although the car
  is in motion
• What matters is the coefficient of static
  friction!

Consider Newtons 3rd law
Froad on car
Fcar on road
Froad on car is the actual force ON the
car. Static Friction msN is its maximum value
Maximum Static friction ( gt Fcar on road for car
not to spin in place!)
weight
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Tension
Tension can be transmitted around corners If
there is no friction in the pulleys, T
remains the same
Tension is a force along the length of a medium
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Question 3 Pulley I

• What is the tension in the string?
• A) TltW
• B) TW
• C) WltTlt2W
• D) T2W

Same answer
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Question 4 Pulley II

• What is the tension in the string?
• A) TltW
• B) TW
• C) WltTlt2W
• D) T2W

a
a
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Question 5
In the 17th century, Otto von Guricke, a
physicist in Magdeburg, fitted two hollow bronze
hemispheres together and removed the air from the
resulting sphere with a pump. Two eight-horse
teams could not pull the halves apart even though
the hemispheres fell apart when air was
readmitted! Suppose von Guricke had tied both
teams of horses to one side and bolted the other
side to a heavy tree trunk. In this case, the
tension on the hemisphere would be a) twice
what it was b) exactly what it was c) half
what it was
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Solving Problems

• Identify force using Free Body Diagram
• This is the most important step!
• Set up axes and origin
• x and y
• Write Fnetma for each axis (components of
  forces)
• Calculate acceleration components
• Setup kinematic equations
• Solve!
• Strong suggestion
• work problem algebraically
• plug in numbers only at the end

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Example 1
?k 0.2
v0 8 m/s
Find stopping distance
Normal force is balanced by gravity because there
is no vertical motion, i. e., N Mg, if M is the
mass of the object Kinetic frictional force that
decelerates the block is, f mk N mk
Mg Therefore, deceleration (direction opposite of
v0), a -f/M -mk g Given deceleration use
kinematics equation to obtain the
answer. Answer 16.3 m - is independent of the
mass
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Example 2
Frictional force, f mkMg opposes the tension
T Net force, Fnet Tf Acceleration, a Fnet /
M ((50 - 0.2 x 5 x 9.8) / 5) m/s2 Answer 8.04
m/s2
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Example 3
Hints Resolve T in x and y components Draw
FBD Normal force is smaller Tension component
along horizontal is also smaller Answer 6.0
m/s2
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Lecture 6, Pre-Flight 1 2

• A locomotive pulls a series of wagons. Which is
  the correct analysis of the situation?
• The train moves forward because the locomotive
  pulls forward slightly harder on the wagons than
  the wagons pull backward on the locomotive.
• Because action always equals reaction, the
  locomotive cannot pull the wagons since the
  wagons pull backward just as hard as the
  locomotive pulls forward, so there is no motion.
• The locomotive gets the wagons to move by giving
  them a tug during which the force on the wagons
  is momentarily greater than the force exerted by
  the wagons on the locomotive.
• The locomotives force on the wagons is as strong
  as the force of the wagons on the locomotive, but
  the frictional force on the locomotive is forward
  and large while the backward frictional force on
  the wagons is small.
• The locomotive can pull the wagons forward only
  if it weighs more than the wagons.

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Lecture 6, Pre-Flight 3 4

• Consider a car at rest. We can conclude that the
  downward gravitational pull of Earth on the car
  and the upward contact force of Earth on it are
  equal and opposite because
• The two forces form an action-reaction pair
• The net force on the car is zero
• Neither of the above

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Lecture 6, Pre-Flight 5 6

• An airplane is flying from Truax Field to O'Hare
  Field. Many forces act on the plane, including
  weight (gravity), drag (air resistance), the
  thrust of the engine, and the lift of the wings.
  At some point during its trip the velocity of the
  plane is measured to be constant (which means its
  altitude is also constant). At this time, the
  total force on the plane 1. is pointing
  upward2. is pointing downward 3. is pointing
  forward 4. is pointing backward5. is zero

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Lecture 6, Pre-Flight 7 8

• In the 17th century, Otto von Guricke, a
  physicist in Magdeburg, fitted two hollow bronze
  hemispheres together and removed the air from the
  resulting sphere with a pump.Two eight-horse
  teams could not pull the halves apart even though
  the hemispheres fell apart when air was
  readmitted. Suppose von Guricke had tied both
  teams of horses to one side and bolted the other
  side to a heavy tree trunk. In this case, the
  tension on the hemispheres would be
• Twice what it was before
• Exactly the same as what it was before
• Half what it was before

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Lecture 6, Pre-Flight 9 10

• Suppose you are an astronaut in outer space
  giving a brief push to a spacecraft whose mass is
  bigger than your own.
• 1) Compare the magnitude of the force you exert
  on the spacecraft, FS, to the magnitude of the
  force exerted by the spacecraft on you, FA, while
  you are pushing1. FA FS 2. FA gt FS3. FA
  lt FS

Third Law!
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Lecture 6, Pre-Flight 11 12
For the same situation as previous question,
compare the magnitudes of the acceleration you
experience, aA, to the magnitude of the
acceleration of the spacecraft, aS, while you are
pushing 1. aA aS 2. aA gt aS 3. aA lt aS
aF/m F same ? lower mass give larger a
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Lecture 6, Pre-Flight 13

• You are watching an old episode of Vampires from
  Outer Space, your favorite Sci-Fi TV show, when
  you see the following scene A starship is shown
  cruising through space with a constant velocity,
  it's engines turned on full blast. As the
  starship nears the space station it wants to
  visit, the captain turns the engines off and the
  ship is shown gliding to a stop. Looking at this
  through the eyes of a physicist, briefly explain
  what things are wrong with this scene.

If the engines are on full blast, the spaceship
would be accelerating. If the starship has a
constant velocity, then its acceleration is zero.
So having the engine on full blast should
accelerate the starship. Secondly, if the
captain turns the engines off, he should continue
to glide for eternity in the absence of any
outside forces. Thirdly, I thought vampires came
from Transylvania, unless of course they decided
to leave and colonize somewhere in outer space
and then come back ... Vampires wouldn't survive
in space. Vampires arent real. This whole thing
is absurd.