Download Unit 5 and 6

Unit 5
Graphical Vector Addition
and Newton’s Law
© 2001-2005 Shannon W. Helzer. All Rights Reserved.
Vectors
 Vectors are physical quantities that not only have a magnitude (size) but
also that have a direction in which they act.
 For instance, we have already used the velocity triangle.
 Velocity is the speed of a body in a given direction.
 Another vector quantity commonly used is displacement which is a
distance traveled in a specific direction.
 Yet another vector used in our every day lives is the force vector made
up of a push or a pull in a given direction.
 In the next slide we will exam the nature of the displacement vector.
5-1
© 2001-2005 Shannon W. Helzer. All Rights Reserved.
Vectors vs Scalars



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
Suppose the three friends below drive their four wheelers a distance of 100.0 m.
Will they end up in the same place? Why or why not.
No, 100.0 m is a scalar and does not specify a specific direction.
Now suppose they drive 175.0 m due East.
Will they end up in the same place? Why or why not.
Yes, 175.0 m East is a vector and specifies a specific direction.
5-2
© 2001-2005 Shannon W. Helzer. All Rights Reserved.
Identical Vectors
 If any two vectors have
the same magnitudes
and directions, then
they are identical
vectors.
 Here vectors B and D
are identical even
though they are in
different places.
B
Protractor
D
Protractor
5-3
© 2001-2005 Shannon W. Helzer. All Rights Reserved.
Adding Vectors Graphically
 Vectors are always added “head
to tail.”
 Always measure the angle from
the +x axis.
 What are the two parts of a
vector?
 Given vectors A and B, find
vector C.
C=A+B

A  2.83 @ 45


B  4.50 @153
B
C
Protractor
A
Protractor

C ?
5-4
© 2001-2005 Shannon W. Helzer. All Rights Reserved.
Hand Glider Trip
5-5
© 2001-2005 Shannon W. Helzer. All Rights Reserved.
Graphical Vector Addition – Hand Glider
 On the first part of a hand glider
flight, a pilot flies her glider 300.0
m due East (A = 300 m @ 0).
 Afterwards, she turns North West
and flies 450.0 m (B = 450 m @
135 ).
 Finally, she turns due South and
flies 250.0 m (C = 250 m @ 270)
 What is her displacement (D) from
her takeoff point?
 D=A+B +C
5-6
© 2001-2005 Shannon W. Helzer. All Rights Reserved.
Graphical Vector Addition - Robots
 Three Physics track robots pull
on a book as shown.
 They pull with the following
forces: 7.0 N @ 45, 8.0 N @
180, and 5.0 N @ 270 .
 Find the net force applied to this
most valuable book.
5-7
© 2001-2005 Shannon W. Helzer. All Rights Reserved.
Graphical Vector Addition - Robots
 Three Physics track robots
pull on a book as shown.
 They pull with the
following forces: 7.0 N @
45, 8.0 N @ 180, and 5.0
N @ 270 .
 Find the net force applied
to this most valuable book.
5-8
© 2001-2005 Shannon W. Helzer. All Rights Reserved.
Force and Interactions
 Force – a “push or pull”
 Contact Force – you physically pushing (touching) on a wall
 Long-range Force – like magnets or like Weight (gravity)
 Force – a vector quantity. Has what two parts?
 SI Unit – the Newton abbreviated as “N”
 Superposition of Forces – forces combine according to vector addition

R
Push

F1
  
R  F1  F2

F2

F1

R
Pull

F2
5-9
© 2001-2005 Shannon W. Helzer. All Rights Reserved.
Newton’s First Law of Motion – At Rest
 An object remains at rest, or in uniform motion in a straight line, unless it
is compelled to change by an externally imposed force.
 Here, the skateboard/log combination is at rest until acted on by the force
imposed by the rocket.
5-10
© 2001-2005 Shannon W. Helzer. All Rights Reserved.
Newton’s First Law of Motion – In Motion
 For an object in motion, the object will continue in a straight line until
acted on by some “outside” force.
 Consider the space shuttle turning while in space flight. What produces
the forces?
5-11
© 2001-2005 Shannon W. Helzer. All Rights Reserved.
Newton’s First Law of Motion – In Motion
 For an object in motion, the object will continue in a straight line until
acted on by some “outside” force.
 Consider the space shuttle when landing. What produces the forces?
5-12
© 2001-2005 Shannon W. Helzer. All Rights Reserved.
Newton’s Second Law of Motion
 Relationship between the acceleration of a body and the force that
produced the acceleration.
 Newton’s Second Law – If there is a non-zero net force on a body, then it
will accelerate.
 In equation form the relationship can be expressed in two ways as
follows:

 F
a
m


F  ma
5-13
© 2001-2005 Shannon W. Helzer. All Rights Reserved.
Newton’s Second Law – Non-Equilibrium Situation
   

F  F1  F2  F3...  ma
 The net result of a Non-Equilibrium situation is that the body, upon which
the net force acts, will begin to accelerate.

F1

F1
 

F  F1  ma

F2
  

F  F1  F2  ma
5-14
© 2001-2005 Shannon W. Helzer. All Rights Reserved.
Newton’s Third Law
 Newton’s Third Law - If body A exerts a force on body B (action),
then body B exerts a force on body A (the reaction). These two forces
have the same magnitude but are opposite in direction.
 Newton’s Third Law - for every action force there is an equal, but
opposite, reaction force.
 Example - you sitting on your seat. Your weight (a force) is pressing
down on your seat. The seat is pushing back up on your butt. As a
result of these two equal but opposite actions, you do not fall through
the seat and to the ground.
 Action-Reaction Force Pair – the forces involved in Newton’s Third
Law
5-15
© 2001-2005 Shannon W. Helzer. All Rights Reserved.
Newton’s Third Law - Example
 Consider a book resting on a table.
 Why doesn’t the book fall through the table?
 The weight, W, and the normal force, N,
comprise an action-reaction pair.
 The normal force is the force which opposes
the weight of the book.
 It always acts perpendicular to the surface
upon which the body rests.
 They balance each other; therefore, the book
does not fall through the table.


W  N


N   mg


W  mg
5-16
© 2001-2005 Shannon W. Helzer. All Rights Reserved.
Newton’s Laws – A Review
 Newton’s First Law - An object remains at rest, or in uniform motion in a
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
straight line, unless it is compelled to change by an externally imposed
force.
Newton’s first law describes an Equilibrium Situation.
An Equilibrium Situation is one in which the acceleration of a body is
equal to zero.
Newton’s Second Law – If there is a non-zero net force on a body, then it
will accelerate.
Newton’s Second Law describes a Non-equilibrium Situation.
A Non-equilibrium Situation is one in which the acceleration of a body is
not equal to zero.
 Newton’s Third Law - for every action force there is an equal, but opposite,
reaction force.
5-17
© 2001-2005 Shannon W. Helzer. All Rights Reserved.
Net Force – Equilibrium at Rest
 What is the downward force on the crate pictured?
 Weight (W) – a force resulting from the gravitational acceleration acting
upon a body.
 What is the upward force acting on the crate?
 The Normal Force (N) – the upward force exerted on a body by the surface
upon which it rest. Always acts perpendicular to the surface.
 Net Force – What is the net force acting on the crate? Remember
Newton’s third law.
FNET  N  W  0
 The forces are equal and opposite.
 Will this crate accelerate in the vertical direction?
 Why or why not?


N   mg


W  mg
5-18
© 2001-2005 Shannon W. Helzer. All Rights Reserved.
Net Force – Equilibrium in Motion
 What forces are acting on the train while it is moving in a straight line
at a constant speed?
 Engine Force (FE) – Force applied to propel the train along the tracks.
 Opposition Force (Fo) – friction between the tracks, wind resistance,
etc. that attempts to slow the train down.
 What is the acceleration of the train? Negative, Zero, or Positive.
 Is this an equilibrium or non-equilibrium situation?

FO

FE
5-19
© 2001-2005 Shannon W. Helzer. All Rights Reserved.
Net Force – Non-Equilibrium
 Describe what happens in the animation below.
 What forces were acting on the train?
 Engine Force (FE) – Force applied to propel the train along the tracks.
 Opposition Force (Fo) – friction between the tracks, wind resistance, etc.
that attempts to slow the train down.
 Which force was larger?
 What is the acceleration of the train? Negative, Zero, or Positive.
 Is this an equilibrium or non-equilibrium situation?

FO

FE
5-20
© 2001-2005 Shannon W. Helzer. All Rights Reserved.
Net Force – Non-Equilibrium
 Describe what happens in the animation below.
 What forces were acting on the train?
 Opposition Force (Fo) – friction between the tracks, wind resistance, etc.
that attempts to slow the train down.
 What is the acceleration of the train? Negative, Zero, or Positive.
 Is this an equilibrium or non-equilibrium situation?

FO
5-21
© 2001-2005 Shannon W. Helzer. All Rights Reserved.
Equilibrium or Non-equilibrium
 When the helicopter is on the




ground, what state is it in?
Why isn’t it accelerating?
In order to get it accelerating,
what would we need?
What state is it in when it is
hovering in place?
In order to get it to accelerate,
what would we need?
5-22
© 2001-2005 Shannon W. Helzer. All Rights Reserved.
Example 1
 A 3.5 kg block being pushed across a floor experiences an acceleration of
4.0 m/s2.
a. What is the net force acting on the block?
b. If F1 is 16 N, then what is the magnitude of the force of friction, F2,
opposing F1?
  

F  F1  F2  ma

F1

F2
5-23
© 2001-2005 Shannon W. Helzer. All Rights Reserved.
Example 2
 A 5.0 kg block being acted upon by three horizontal forces as shown below.
 When F1 acts alone on the block, it produces an acceleration of 1.8 m/s2 to
the right. Likewise, F3 produces an acceleration of 1.1 m/s2 to the right.
 When all three forces are acting on the block, it experiences an
acceleration of 2.3 m/s2
a. What is the magnitude and direction of force F2 acting on the block?

F2

F1

F3
   

F  F1  F2  F3  ma
5-24
© 2001-2005 Shannon W. Helzer. All Rights Reserved.
What can help?
 A Large 4X4 is stuck on a sheet of ice. What could the driver do to drive
her truck on the ice?
 How about a set of tire spikes?
 What interaction occurs between the spikes and the ice?
5-25
© 2001-2005 Shannon W. Helzer. All Rights Reserved.
Frictional Forces
 Whenever two bodies interact by direct contact of their surfaces, we call the
interaction forces “contact forces.”
 Can you name one contact force we have already discussed?
 The Normal Force.
 Name another contact Force?
 Friction Force.
 Frictional forces results from the intermolecular (electrical) forces.
 As one body slides across another, these forces continually form and break.
5-26
© 2001-2005 Shannon W. Helzer. All Rights Reserved.
Frictional Forces
 There are two kinds of friction forces: Kinetic and Static Forces.
 Kinetic Frictional Forces – the kind of friction that acts when a body slides
over a surface. Better thought of as “sliding” friction.
 The coefficient of kinetic friction is denoted as k. k is a proportionality
constant.
5-27
© 2001-2005 Shannon W. Helzer. All Rights Reserved.
Frictional Forces
 If the body is at rest and you try to push it across the floor with an ever
increasing force, then initially the box will not move because the frictional
force between the body and the floor exerts an equal, but opposite, force
against the body.
 This force is known as the static friction force.
5-28
© 2001-2005 Shannon W. Helzer. All Rights Reserved.
Static Friction v. Kinetic Friction
 Static friction exist when an object wants to move but is held in
place by the force of friction.
 This force of friction is greater than the component of the weight
acting down the plane.
 If we continue to rotate the plane, the component of the weight
acting down the plane will eventually become larger than the
normal force.
 When this happens, the object will begin to slide changing from
static friction to kinetic friction.
Force of Friction v. Time
1
0
Friction (N)
-1 0
2
4
6
-2
-3
-4
-5
-6
-7
Time (s)
© 2001-2005 Shannon W. Helzer. All Rights Reserved.
8
10
Presence of Frictional Forces
 In the presence of friction, which ball do you think would go the farthest?
 Why?
5-29
© 2001-2005 Shannon W. Helzer. All Rights Reserved.
Absence of Frictional Forces
 In the absence of friction where would a ball originally positioned as shown
stop?
 Why?
5-30
© 2001-2005 Shannon W. Helzer. All Rights Reserved.
Newton’s Laws Applications
 What type of friction acts on the piano as it slides down the ramp?
5-31
© 2001-2005 Shannon W. Helzer. All Rights Reserved.
Newton’s Laws Applications
 What type of friction acts on the piano as it rests on the ramp?
 Draw the Free Body Diagram for the piano.
 The Normal force is always ______________ to the surface.
5-32
© 2001-2005 Shannon W. Helzer. All Rights Reserved.
Newton’s Laws Applications – Free Body Diagrams
 Two tractors pull on a crate as shown.
 How many forces are acting on the crate?
 If the crate started from rest, then which way did it accelerate?
 Draw the FBD for the crate.
 What type of a situation is depicted below?
Dig
Dug
5-33
© 2001-2005 Shannon W. Helzer. All Rights Reserved.
Setting the Standard
 When we do problems involving
kinematics, it is important that
we stick to a standard when
imputing data into the knowwant table.
 This standard enables us to take
into account the vector nature of
acceleration, velocity,
displacement, etc.
 Here is a diagram we will use in
order to help us correctly input
data into the table.
 This standard is based upon the
Cartesian Coordinate system.
 If a body travels West, then what
sign would you give its velocity?
 If a body travels at an angle of
90 degrees, then what sign
would you give its velocity?
3-3
© 2001-2005 Shannon W. Helzer. All Rights Reserved.
Forces on a Car – Free Body Diagrams






What is the name of the force exerted by the car onto the road?
The weight.
What force opposes the weight of the car?
The normal force acting perpendicularly to the surface of the road.
The normal force is always perpendicular to the surface.
Draw the FBD for the car.

N

W
© 2001-2005 Shannon W. Helzer. All Rights Reserved.
5-34
Newton’s Laws Applications
 The recoil caused by a cannon firing a cannonball demonstrates which of
Newton’s Laws?
 Draw the FBD for the cannon as the gun powder explodes.
5-35
© 2001-2005 Shannon W. Helzer. All Rights Reserved.
Net Force – Non-Equilibrium
 Describe what happens in the animation below.
 Now, draw the FBD.
5-36
© 2001-2005 Shannon W. Helzer. All Rights Reserved.
Newton’s Laws Applications
 Watch the two shots below.
 Which one demonstrates Newton’s first law?
 Which one demonstrates Newton’s second law?
5-37
© 2001-2005 Shannon W. Helzer. All Rights Reserved.
Newton’s Laws Applications
 Use Newton’s Laws to describe what happened…
 To the hatchet as it was thrown.
 As it flies towards the log.
 When it hits the log.
 What about the log itself?
5-39
© 2001-2005 Shannon W. Helzer. All Rights Reserved.
Setting the Standard - Torque
 a
m2
m1
© 2001-2005 Shannon W. Helzer. All Rights Reserved.
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© 2001-2005 Shannon W. Helzer. All Rights Reserved.