Motion: Forces influence motion

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Motion Forces influence motion

• How do we describe motion?
• Displacement
• Velocity
• Acceleration

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Position Displacement
The position (r) of an object describes its
location relative to some origin or other
reference point.
The displacement is the change in an objects
position. It depends only on the beginning and
ending positions.
? is a symbol. ? r does not mean ? times r
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Vector Subtraction

• A-B A(- B)
• -B same magnitude as B but opposite direction
• B-A -( A- B) The order matters

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Example (text problem 3.4) Margaret walks to the
store using the following path 0.500 miles west,
0.200 miles north, 0.300 miles east. What is her
total displacement? Give the magnitude and
direction.
Take north to be in the y direction and east to
be along x.
r2
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Example continued
The displacement is ?r rf ? ri. The initial
position is the origin what is rf?
The final position will be rf r1 r2 r3.
The components are rfx ?r1 r3 ?0.2 miles
and rfy r2 0.2 miles.
Using the figure, the magnitude and direction of
the displacement are
N of W.
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• What distance did Margaret walk?
• This is not the same as her displacement
• Why?
• Is displacement a Vector or scalar?
• Is distance a Vector or scalar?
• Think of hitting a home run. What is the
  displacement? What is the distance the runner
  travels?

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Velocity
Velocity is a vector that measures how fast and
in what direction something moves.
? is a symbol it is not a quantity
Speed is the magnitude of the velocity. It is a
scalar.
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Velocity

• The velocity is a vector. It changes if we change
• the speed
• the direction i.e. driving around a curve even at
  constant speed.

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Fig. 03.09
T 12 seconds
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vav is the constant speed that results in the
same displacement in a given time interval.
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At what point of the butterflys path does the
velocity change?

1. At almost every point
2. Only at the beginning and end
3. It is constant the whole time
4. We cant tell unless we know the speed
   everywhere.

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Example (text problem 3.4) Margaret walks to the
store using the following path 0.500 miles west,
0.200 miles north, 0.300 miles east. What is her
total displacement? Give the magnitude and
direction.
Take north to be in the y direction and east to
be along x.
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Example Consider Margarets walk to the store in
the earlier example. If the first leg of her
walk takes 10 minutes, the second takes 8
minutes, and the third 7 minutes, compute her
average velocity and average speed during each
leg and for the overall trip.
Use the definitions
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Example continued
Leg ?t (hours) vav (miles/hour) Average speed (miles/hour)
1 0.167 3.00 (west) 3.00
2 0.133 1.50 (north) 1.50
3 0.117 2.56 (east) 2.56
Total trip 0.417 0.679 (45? N of W) 2.40
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Instantaneous velocity
If ?t becomes very small we call v the
instantaneous velocity Your speedometer reads
instantaneous speed
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On a graph of position versus time, the average
velocity is represented by the slope of a chord.
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This is represented by the slope of a line
tangent to the curve on the graph of an objects
position versus time.
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Fig. 03.10
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• As you drive around a corner you are careful to
  keep the speedometer reading at 30 km/hr. You
  have been moving at
• Constant speed
• Constant velocity
• Both constant speed and velocity
• Neither constant speed nor constant velocity

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Finding d when we know v Consider only x
component ?x vx ?t If vx v1 (constant) This
is the same as the area in graph of v /t
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If V is not constant we can still use area in
graph
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A particle moves along the gold path as shown.
At time t1 its position is ri and at time t2 its
position is rf.
y
x
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Example (text problem 3.24) Speedometer readings
are obtained and graphed as a car comes to a stop
along a straight-line path. How far does the car
move between t 0 and t 16 seconds?
Since there is not a reversal of direction, the
area between the curve and the time axis will
represent the distance traveled.
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acceleration

• Acceleration is a vector
• (since v is a vector)

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Fig. 03.18
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• Which has a greater acceleration an airplane
  going from 1000 km/hr to 1005 km/hr in 5 seconds
  or a skateboarder going from 0 to 5 km/hr in 1
  second?
• The airplane
• The skateboarder

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Example (text problem 3.39) If a car traveling
at 28 m/s is brought to a full stop 4.0 s after
the brakes are applied, find the average
acceleration during braking.
Given vi 28 m/s, vf 0 m/s, and ?t 4.0 s.
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Fig. 03.17
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A particle moves along the gold path as shown.
At time t1 its position is ri and at time t2 its
position is rf.
y
vi
x
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Motion Forces influence motion

• How do we describe motion?
• F ma

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Exam!

• Monday Oct. 5
• Up to and including todays lecture
• Review

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Question

• You put your notebook on the front seat of your
  car. When your car stops, the notebook
• slides off forward. Why?
• A) A net force acted on it.
• B) No net force acted on it.
• C) It remained at rest.
• D) It didn't move, but only seemed to.
• E) Gravity briefly stopped acting on it.

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Question

• A book is sitting on a desk top. Identify the
  3rd law partner of the weight of the book.
• A) The force of the desk on the book.
• B) The force of the book on the desk.
• C) The force of the earth on the book.
• D) The force of the book on the earth.

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Question

• A box of mass m sits on an inclined plane. What
  is the relationship between the weight of the
  box, W, and the normal force exerted on the box,
  N?
• A) W gt N
• B) W N
• C) W lt N
• D) can't tell

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Question

• For which arrangement of (moving) boxes is the
  force of friction larger? The two boxes are
  identical.
• A) The stacked boxes. (1)
• B) The side-by-side boxes (2).
• C) The force is the same.

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acceleration

• Acceleration is a vector
• ?v a ?t

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If V is not constant we can still use area in
graph
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Fig. 03.23
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Fig. 03.22
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Example (text problem 3.47) At the beginning of
a 3 hour trip you are traveling due north at 192
km/hour. At the end, you are traveling 240
km/hour at 45? west of north.
(a) Draw the initial and final velocity vectors.
450
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Find ?v Find aav
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Which of the following controls can be used to
accelerate your car? A) Gas pedal B) Brake
C) Steering wheel D) All of the above
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Newtons 2nd Law
The acceleration of a body is directly
proportional to the net force acting on the body
and inversely proportional to the bodys mass.
Mathematically
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• An objects mass is a measure of its inertia.
  The more mass, the more force is required to
  obtain a given acceleration.
• If F is fixed and m is doubled a is
• Doubled
• Halved
• Remains the same
• What should F be if a is to be the same?
• What if m is halved?

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The net force is just the vector sum of all of
the forces acting on the body, often written as
?F.
If a 0, then ?F 0. This body can have
Speed 0 which is called static equilibrium,
or speed ? 0, but constant and same direction,
which is called dynamic equilibrium.