p250c1

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Force and Motion Some History The Copernican
Revolution with Copernicus, Galileo, Kepler
... Newtons Principia laws of motion physics
and calculus
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The First Law of Motion (The Law of Inertia) An
object at rest will remain at rest and an object
in motion will remain in motion (at constant
velocity) unless acted upon by an external
force. An object has a constant velocity unless
there is a net force acting on it. Forces are the
causes of changes in motion. forces on an
object arise from interactions with other
objects. forces are vectors the net force on an
object is the vector sum of the individual forces
acting on that object The inertia of an object is
its resistance to changes in its motion. Mass is
a measure of inertia. Inertial Frame of
Reference a frame of reference in which Newtons
Law of Inertia holds constant velocity! counter
examples not an accelerating aircraft or a
rotating merry go round
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The Second Law of Motion The rate of change of
momentum with time is proportional to the net
applied force and is in the same direction as the
net force momentum mass x velocity mv
Force causes acceleration! Mass is the measure
of inertia Units 1 Newton 1N 1 kg m/s2
1N 1/4 pound
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Example What force is necessary to give a 0.80
kg cart a horizontal acceleration of 1.5 m/s2?
What is the acceleration of the cart if only 1/3
of this force is applied to the cart?
Example A fully loaded Lockheed L-1011 has a
mass of 2.17E5 kg. When it accelerates at full
throttle down a runway, the engines provide a
combined force of 753 kN. If the plane starts
from rest, how far will it go during the 33.5 s
that it takes to liftoff?
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Weight the force exerted by earth (via gravity)
on an object In free fall, gravity is the only
force acting on the object F ma mg w Weight
(mass)(acceleration of gravity) Example what
is the weight of a two liter soda bottle which
has a mass of 2.0 kg?
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Normal Force the contact force exerted by the
surface of a rigid object
Normal Force N
Normal Force N
weight w
weight w
Normal means perpendicular Normal force
prevents object from sinking into
surface Example A large crate of mass m is
placed on a frictionless ramp. The ramp makes an
angle q with respect to the horizontal. What is
the acceleration of the crate? What is the
normal force of the ramp on the crate?
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Newtons Third Law For every action there is an
equal and opposite reaction For every action
(force) there is a reactive force and the action
and reaction forces are equal in magnitude and
opposite in direction, and act upon different
bodies. If body A exerts a force FAB on body B,
then B exerts a force FBA on A so that FAB - FBA
Action/Reaction
Forces on an Object
reaction force of table on computer
reaction force of table on computer
force of computer on table
weight of computer
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Example A 68 kg passenger rides in an elevator
that is accelerating upward at 1.00 m/s2. What
is the normal force of the floor on the
passenger? What is the force exerted by the
passenger on the floor of the elevator?
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• Problem Solving Strategies
• Draw a free body diagram
• all forces on each object are shown
• Choose the object to be isolated. Draw it and
  any geometric aspects are important. Keep it
  simple!
• Draw all forces on that object as vector arrows,
  approximately to scale and in the correct
  direction. Label all forces clearly!
• Choose a coordinate system and indicate it on the
  diagram. Shown the positive direction of
  displacement, velocity, acceleration, etc.
  Resolve vectors into components as necessary.
• repeat for each object in the problem.

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T
()
wB-TFB
T-wAFA
()
w
A
B
mA 15kg
mB 30kg
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Example A block of mass M is on a frictionless
inclined plane joined by a string over a pulley
to a suspended mass m. What is the magnitude of
the acceleration if the incline is at an angle of
20º from horizontal?
Example 4.11 a bit too elaborate...
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Friction opposes motion due to surfaces sticking
together Kinetic Friction surfaces are moving
relative to each other a.k.a. Sliding Friction
Static Friction surfaces are not moving
relative to each other. Static Friction prevents
stationary objects from moving until sufficient
force has been applied.
Coefficient of Friction Frictional forces depend
upon how hard the surfaces are being pressed
together -gt force perpendicular to the surface
normal force the types of surfaces that are in
contact -gt coefficient of friction
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Equilibrium Static Equilibrium no acceleration
with bodies at rest. Dynamic Equilibrium no
acceleration with moving bodies Equilibrium
implies SFi 0 so that SFxi 0 and SFyi
0 Stable, unstable and neutral equi. Example A
child sits on a sled that rests on a snow-covered
hill making an angle q to the horizontal. If the
coefficient of friction is 0.10, what is the
maximum angle at which the sled will remain at
rest?
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Example A lantern of mass 1 kg is suspended by a
string that is joined to two other strings as
shown. What is the tension in each string if the
top strings make an angle of 35º to the ceiling?
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Example A child of mass 30 kg sits on a light
swing suspended by a rope of negligible mass.
His sister pushes him forward with a horizontal
force until the rope is at an angle of 20º from
the vertical. What is the tension in the rope
and how much horizontal force is required to hold
the child in that position?