4' Motion and Force: Dynamics

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4. Motion and Force Dynamics

• We have discussed how to describe motion using
• Displacement
• Time
• Velocity
• Acceleration
• (mostly for the case of uniform acceleration)
• This is called kinematics.

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New subject Dynamics What makes an object move?
Answer Forces.
What is a force? Anything that makes an object
move is called a force on that object. It is
always exerted by another object.
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Quantitative definition of force
Verbal definition (something that makes an
object move) is not quantitative. Suppose only
one force F acts on an object. Example --
astronaut pushes on meteorite in deep space
Meteorite will accelerate to the left
Can we represent the force quantitatively by F
a?
Only if every object pushed by this force had the
same acceleration!
In fact, it takes twice the force to accelerate
an object twice as big F2 2 a .
What should we call the factor (1 or 2) in front
of a, that describes how hard we have to push it
to make it move?
or inertia
How about mass? So in general F m a.
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Objects with many forces
So When only ONE force acts on an object, we can
use F1 m a as the definition of F1.
But what if there are 2 forces?
What acceleration is produced by both forces
together?
Experimentally, is given by ma SF F1 F2 !
a
So in this form (where SF is the sum of all the
forces), this is a law of nature
Newtons 2nd Law SF ma
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Newtons First Law
If there is no force on an object (SF 0) then
Newtons 2nd law (SF ma) implies that
a 0.
Newtons 1st Law If SF 0, then a 0
(Special case of Newtons 2nd law)
Paraphrase If there is no force on an object, it
will continue with the same velocity (i.e. in a
straight line at constant speed). If it is
initially stationary (v 0 ) it will remain
stationary.
If this is a special case, why do we dignify it
with its own number? Because a lot of people
didnt believe it. If we dont keep pushing on
an object, it doesnt keep going forever
friction! It took people a long time to realize
that if you could remove all forces (including
friction) an object would keep moving forever.
(Easier to see in deep space.)
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The realization that in the absence of friction,
they would continue forever, is attributed to
Galileo.
Belief that objects naturally slow down is
usually attributed to Aristotle.
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Newtons 3rd Law
(What happens to the astronaut?)
B
The astronaut recoils to the right.
A
This means there must be a force on him
Newtons 3rd Law There is a force F on the
astronaut.
More generally if object A exerts a force F on
object B, then B also exerts a force F on A.
We write FBA - FAB
This other force is called a reaction force.
This is true even when it is less obvious when I
press down on a table, the table presses up on me.
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More examples of Newtons 3rd Law
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Important example of force Weight
What do we know about a mass M near the surface
of the earth? (with no forces except gravity)
M 2 kg
It falls with acceleration a g (0,-g,0)
So Newtons second law says there must be a force
on it F M a M g
W M g
We call this force its weight W M g
Numerically, the magnitude W M g 2 kg 9.8
m/s2 19.6 kg m/s2
Define a unit of force, Newton 1 N 1 kg
m/s2, so
W 19.6 N
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Example Estimate the net force needed to
accelerate a 1000 kg car at ½ g.
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Example What net force is required to bring a
1500 kg car to rest from a speed of 100 km/h
within a distance of 55 m?
To answer this question we need to combine
Newtons second law with the equations of motion.
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Free Body Diagrams
Draw a diagram of the object showing all forces
acting on the object, including any forces you
are trying to find. Draw an arrow for each
force vector, being sure the direction is correct
and the magnitude is approximately
correct. Label each force. Resolve all vectors
into components in perpendicular directions
(Usually the X and Y directions). Find the net
force in each perpendicular direction. Apply
Newtons 2nd law to each direction. (Fx max,
Fy may)
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Free Body Diagrams (object is not moving in this
example). Determine the normal force!
FH
FH
FH FN mg ma 0 FN mg FH
FH mg FN ma 0 FN FH mg
FN mgma0 FNmg
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A box with a mass of 10 kg is resting on a table.
A string is attached to it and somebody pulls
upward with the force Fp. What is happening?
Three forces are acting on the object. The net
force, determining the acceleration according
to Newtons 2nd law, is the sum of them. FN goes
to zero once the object is moving for Fp gt FW.
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Example A 1000 kg (one metric ton) stone block
can move friction free. Two workers are pulling
with a force of 100 N each into perpendicular
directions. What will be the acceleration of the
block?
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Example The air exerts a forward force of 10 N
on the propeller of a 0.2 kg model airplane. If
the plane accelerates forward at 2.0 m/s2, what
is the magnitude of the resistive force exerted
by the air on the airplane?
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Example A fisherman yanks a fish out of the
water with an acceleration of 4.5 m/s2 using a
very light fishing line that has a test
value of 22 N. The fisherman unfortunately loses
the fish as the line snaps. What can you say
about the mass of the fish?
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• Example
• Two blocks with mass m1 and m2 (m1gtm2) are placed
  on a
• frictionless (horizontal) table. A force F is
  pushing on both of
• them. Which statement is true
• The magnitude of the contact force between the
  two blocks
• is the same for F applied to m1 or m2.
• The magnitude of the contact force will be larger
  if F is
• applied to m1.
• The magnitude of the contact force will be
  smaller is F is
• applied to m1.

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Example Two masses are suspended over a pulley
by a cable. This elevator mechanism is called
an Atwood machine. Let one mass be 1500 kg, the
counter weight 1000 kg. What is the tension in
the cable?
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Example Two masses (2.2 kg and 3.2 kg) are
suspended over a pulley by a cable. They are
initially 1.8 m above the ground, and
the massless frictionless pulley is 4.8 m above
the ground. What maximum height does the lighter
object reach after the system is released?
m12.2 kg m23.2 kg
4.8 m
m2
m1
1.8 m
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• Example
• Two blocks with mass m1 and m2 (m1gtm2) are placed
  on a
• frictionless (horizontal) table. A force F is
  pushing on both of
• them. Which statement is true
• The magnitude of the contact force between the
  two blocks
• is the same for F applied to m1 or m2.
• The magnitude of the contact force will be larger
  if F is
• applied to m1.
• The magnitude of the contact force will be
  smaller is F is
• applied to m1.