Transcript hp1f2013_class03_NewtonsLaws_Forces

Honors Physics 1
Class 03 Fall 2013
Force
Newton’s Laws
Everyday Forces
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Newton’s Laws
Mechanics laws are hard to observe because
there are confounding forces, such as friction
and drag.
1rst Law – A body will continue to move with
constant velocity unless a net force acts on it.
2nd Law – F=ma (We need to define inertial
mass and force. We should write
acceleration as second derivative of position.)
3rd Law – Force is necessarily the result of
interaction between two systems.
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Questions
What is a force?
What is mass?
What is an isolated body?
How do we measure acceleration?
– Inertial reference frame.
When are Newton’s Laws true? Are there
any special conditions?
Note: Newton’s Laws are easy to apply when dealing
with “point” masses, but not for fluids.
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Simplifications
We will start by treating physical objects
as particles.
Particle: an object for which internal
structures and motions can be ignored
or all of whose parts move in the same
way.
Force: the interaction of an object with its
environment in ways that can influence
the motion of the object.
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Inertial systems
If the net force on an object is zero, then it is
possible to find a set of coordinate systems,
or reference frames, in which that body has
no acceleration.
Inertial frames are defined by the sentence
above.
The laws of Physics are the same in all inertial
frames.
Inertial frames are related by x’=x+vt+d
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Forces and accelerations are related
in the same way in different inertial
reference frames
Consider the motion of an object in one reference frame.
F  ma; v  v (t )
Now allow x '  x  v0t
dx ' dx
v'

 v0  v (t )  v0
dt
dt
dv ' dv dv0
a'


 a0
dt
dt dt
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Mass
The mass of an object is a quantitative
measure of the resistance of an isolated
body to acceleration for a given net
applied force.
mx
mstandard
astandard

ax
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Types of Forces
There are four (maybe five) “fundamental”
forces
- strong nuclear,
- weak nuclear,
- electromagnetic,
- gravity
- + maybe “dark”.
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Everyday forces in mechanics
Contact (Normal and/or Tension)
Gravity
Electromagnetic
Friction
Drag
Spring
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Using Newton’s Laws
1)
2)
Mentally divide the system of objects into smaller systems, until the
forces and motion of each can be analyzed.
Draw a force diagram for each mass.
A.
represent each object as a point mass or simple symbol.
B.
Draw a force vector on each mass for each force acting on the mass.
– Convention: Label forces with subscripts indicating which body the force is
acting on and which one the force is exerted by:
– FAB is the force on A due to B
»
3.
4.
5.
6.
Draw only forces acting on the object.
Choose a coordinate system
Take care to address interactions
Carefully consider and include constraints on the motion. (Sometimes
constraints are trivially included, sometimes not.)
Keep track of which variables are known, which are unknown, and
what is the goal of your calculation.
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Free-Body Diagrams
1.
Draw the object as a box or a circle, detached
from everything else. (“free-body”)
a
2.
Y
Draw and label the force arrows acting on the
object, with all tails on the object.
3.
It helps to put the coordinate axes in the diagram
to remember which direction is positive.
4.
If you know the direction of the acceleration it is
often helpful to pick that as one coordinate axis.
X
N
F
P
W = mg
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Normal force
The normal force FN acts perpendicular to the
point of contact between two objects.
When two objects are in contact and remain in
contact, the normal force is equal to the force
that the object exerts on the surface.
mg
FN
PHYS 1100 Summer 2013
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Tension
When a cord (or spring, cable, wire, chain,
band…) is attached to a body and pulled taut,
the cord pulls on the body with a force T that
is directed away from the body. This is called
the tension force.
PHYS 1100 Summer 2013
mg
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Friction
If we attempt to slide a body over a surface, the
motion is resisted by bonding between the
two surfaces. This friction force is directed
along the surface and is opposite to the
intended motion.
The magnitude of the friction force depends on
the normal force between two surfaces and
on the nature of the surfaces.
FF
FApplied
mg
FN Summer 2013
PHYS 1100
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Friction vs Applied Force
Starting
Friction
Frictional
Force
Static
Friction
Kinetic Friction
Motion
begins
(usually less than
starting friction)
Applied Force
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Coefficient of Friction
The friction force is equal to the applied force parallel to
a surface until the applied force exceeds the critical friction force.
The critical friction force is given by:
FF (crit )   S FN
 S  static friction coefficient (0 to 1, typical= 0.2)
Once the object is sliding, the force opposing motion is
FF (moving )   k FN
 k  kinetic friction coefficient (0 to 1, typical = 0.1)
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Illustration of Newton’s 3rd Law
Reaction force of
table on book
Force of book on
table
Reaction forces of floor on
table
Forces of table on floor
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Example 1: Two astronauts – tug of
war
Unequal strengths (A>B), unequal masses (A>B). Mass
of rope can be neglected.
Find their motion if each pulls on the rope as hard as he
can.
Make a sketch. Draw forces on each object.
Things to note:
–
–
–
–
–
Each astronaut can only apply force to the rope.
Make a sketch and force diagram
Newton’s third law applies between rope and each astro.
If rope mass is negligible then FAB=FBA
Forces must be equal and opposite. B must let rope slip and
A can’t exert max force.
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Activity
The motion of an asteroid is measured by the crew of
two space ships. Crew 1 observes that the asteroid
moves with v=1000m/s. Crew 2 observes that the
asteroid moves with v=2000 m/s.
Can they both be making their measurement from an
inertial frame?
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Activity
The motion of an asteroid is measured by the crew of
two space ships. Crew 1 observes that the asteroid
moves with v=1000m/s+10m/s2. Crew 2 observes
that the asteroid moves with v=2000 m/s+20m/s2.
The asteroid has a mass of 106 kg.
Do both crews measure the same force on the object.
Can both crews be in a inertial frame?
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Activity – Motion with constraints
Frictionless pulley and table.
Only net external force=gravity on mass 2.
Rope massless and fixed length.
Find acceleration of mass 1.
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