Download phy211_4 - Personal.psu.edu

Physics 211
4: Classical Mechanics - Newtons Laws
•Force and Equilibrium
•Hookes Law
•Newtons Laws
•Weight
•Friction
•Free Body Diagrams
•Force Problems
How do we know if a Force is present ?
Newton discovered that it corresponds to a
change in velocity
Forces are vector quantities add together like vectors
The sum of all forces acting on an object
Net force = Total force = Resultant force
If net force is zero
body will stay at rest or travel at same
uniform velocity
If the velocity of an object is constant,
then the object is said to be in EQUILIBRIUM
•
•
•
•
•
Known types of basic forces
Gravitational (long range)
Electromagnetic (long range)
Strong Nuclear (short range)
Weak Nuclear (short range)
All known forces can be described in terms
of these forces
Measuring force
Hookes Law for elastic materials
F = -kd
Restoring force = [constant] X [displacement
from equilibrium position]
The magnitude of the force exerted
on an elastic object is equal to the
restoring force (when equilibrium is
reached) thus proportional to the
displacement d
Newtons Laws
First Law of Motion
An object at rest will remain at rest and an
object in motion will remain in motion with
constant velocity unless it experiences a net
external force
Fnet 

Fi  0  a  0
Inertial reference frame
•An inertial frame of reference is one in which an
object, subject to no force, moves with constant
velocity.
•A reference frame in which Newtons first law is
valid is an inertial frame of reference.
In all inertial reference frames
F net  0  a  0
•Can identify inertial frames of
reference with coordinate systems
moving with constant velocity
•If one finds one such frame, then all
frames moving with constant velocity
with respect to this one are also
inertial frames of reference
•Non inertial frames are ones that are
accelerating
•In such frames we observe fictitious
forces
Inertial mass
•If you attempt to change state of motion of an
object, the object will resist this change
•This is a consequence of inertia
•Mass is a measure of inertia
Gravitational mass
•Objects with mass exert gravitational forces on
each other
•The gravitational force exerted by a celestial
body (earth, moon, sun etc) on an object on (or
near) its surface is called the WEIGHT of the
object
the magnitude of the weight force is
proportional to the (gravitational) mass of the
object and the celestial body
mass measured through the effects of gravity
agrees with
mass measured through the effects of other
forces
mass of an object does not depend on
its position or relation to other objects
weight of an object does
The force of gravity acts at the center of
mass of an object
Newtons Second Law
the acceleration of an object is directly
proportional to the resultant force acting on it
and inversely proportional to its mass
F
SI units
net

F
i
: [ F ]  [ ma ]
 N
 ma

(Newton)
Force of gravity = weight
W  mg
kg m
s2
The MOMENTUM P of an object is defined to
be the mass of the object times its velocity
p  mv
kg m
m
p
v


[ ] [ ]
s
Momentum measures the tendency
SI units
:
of an object to keep moving
F net
dv
a 
dt
dv
d( mv ) dp
 m


dt
dt
dt
Newtons third law
If two objects interact, the force exerted on the first
object by the second is equal but opposite to the
force exerted by the second object on the first
F12

- F 21
(action force )  (reaction force )
 a single isolated force cannot exist.
Action force and reaction force act on
DIFFERENT objects
Friction
•Force exerted by a surface on an object on the surface
that resists motion of the object is called FRICTION
•Friction is a CONTACT force
•it is the result of electromagnetic forces
•If the force of friction is zero the surface is said to be
smooth.
•Friction opposes motion along the surface
•STATIC friction: force exerted when object is stationary
•DYNAMIC friction: force exerted when object is moving
N
Ffriction
Fexternal
W
magnitude
of
force of
friction
(N)
object moves
magnitude of external force (N)
Fstat.fric  mstat N
F kin.fric
 mkin N
N  constant NORMAL force
m = coefficients of friction
Normal force is the reaction force from the
surface to the force exerted by the object
on the surface. It is NOT the reaction force
to the weight of the object
If an object has zero component of
acceleration in a certain direction then
there is a NET FORCE of ZERO acting on the
object in that direction
Newtons Laws and circular motion
acceleration associated with uniform circular
motion must be produced a force
v2
Fcentripetal
rˆ
 m a  m ac  - m
r
tangential acceleration is zero

\ tangential force is zero



Free Body Diagrams
N
Fext
Ff
W
Draw all forces acting on the object of
interest
If the object is stationary then
the total net force on the object
MUST be zero
Thus the components of the net
force in any direction must be
zero
If the objects velocity in one
direction does not change then
the net force in that direction is
zero