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Newton’s laws of motion
•Net force
•Action/reaction
•Inertial Reference frame
•Non-inertial Ref frame
•Mass
•Acceleration
•Friction
•Inertial Force
•Non-inertial Force
Q: Define as many of
these concepts as you
can?
First Law: Law of Inertia
Q: How does this animation relate to first law?
Q: What is state of motion?
Q: Where is unbalanced force applied ?
An object at rest (v=0) remains at rest AND
an object at constant velocity (v=c) remains
at constant velocity UNLESS acted upon by
an unbalanced force (Fnet not equal zero).
Second Law: force definition
Acceleration is produced when a
unbalanced force acts on a mass.
The greater the mass of the object
being accelerated the greater the
amount of force needed to
accelerate the object.
Third law: action/reaction
For every action, there is an equal and
opposite reaction.
Force is always an interaction between two
objects that occurs and an action/reaction
force pair.
No one object applies a force, both apply
equal and opposite force on each other.
If force was not always an action reaction
pair, momentum would NOT be conserved.
The rocket's action is to push down on the
ground with the force of its powerful engines,
and the reaction is that the ground pushes the
rocket upwards with an equal force.
Three Laws of classical mechanics
1. In the absence of a net force, a body either is at rest or moves in a straight line with
constant speed.
2. A body experiencing a force F experiences an acceleration a related to F by F = ma,
where m is the mass of the body. Alternatively, force is equal to the time derivative of
momentum.
3. Whenever a first body exerts a force F on a second body, the second body exerts a
force −F on the first body. F and −F are equal in magnitude and opposite in direction.
First Law Redux
Newton's first law is also called the law of inertia. It states that if the vector sum of all forces (that is,
the net force) acting on an object is zero, then the acceleration of the object is zero and its velocity is
constant.
The first point needs no comment, but the second seems to violate everyday experience. For example,
a hockey puck sliding along ice does not move forever; rather, it slows and eventually comes to a stop.
According to Newton's first law, the puck comes to a stop because of a net external force applied in the
direction opposite to its motion. This net external force is due to a frictional force between the puck
and the ice, as well as a frictional force between the puck and the air. If the ice were frictionless and
the puck were traveling in a vacuum, the net external force on the puck would be zero and it would
travel with constant velocity so long as its path were unobstructed.
Implicit in the discussion of Newton's first law is the concept of an inertial reference frame, which for
the purposes of Newtonian mechanics is defined to be a reference frame in which Newton's first law
holds true. There is a class of frames of reference (called inertial frames) relative to which the motion
of a particle not subject to forces is a straight line. Newton placed the law of inertia first to establish
frames of reference for which the other laws are applicable.To understand why the laws are restricted
to inertial frames, consider a ball at rest inside an airplane on a runway. From the perspective of an
observer within the airplane (that is, from the airplane's frame of reference) the ball will appear to
move backward as the plane accelerates forward. This motion appears to contradict Newton's second
law (F = ma), since, from the point of view of the passengers, there appears to be no force acting on
the ball that would cause it to move. However, Newton's first law does not apply: the stationary ball
does not remain stationary in the absence of external force. Thus the reference frame of the airplane is
not inertial, and Newton's second law does not hold in the form F = ma.
Second law redux
Newton's second law states that the force applied to a body produces a
proportional acceleration; the relationship between the two is
where F is the force applied, m is the mass of the body, and a is the body's
acceleration. If the body is subject to multiple forces at the same time, then the
acceleration is proportional to the vector sum (that is, the net force):
The second law can also be shown to relate the net force and the momentum p
of the body:
Therefore, Newton's second law also states that the net force is equal to the
time derivative of the body's momentum:
Second Law redux: Impulse
An impulse I occurs when a force F acts over an interval of time Δt, and it is given by
Since force is the time derivative of momentum, it follows that
This relation between impulse and momentum is closer to Newton's wording of the
second law.
Impulse is a concept frequently used in the analysis of collisions and impacts.
The laws: relationship to the conservation laws
In modern physics, the laws of conservation of momentum, energy, and angular
momentum are of more general validity than Newton's laws, since they apply to both
light and matter, and to both classical and non-classical physics.
This can be stated simply, "Momentum, energy and angular momentum cannot be
created or destroyed.“
Because force is the time derivative of momentum, the concept of force is redundant
and subordinate to the conservation of momentum, and is not used in fundamental
theories (e.g. quantum mechanics, quantum electrodynamics, general relativity, etc.).
Analysis of ball and feather fall in vacuum
•A vacuum is required to prove gravitational acceleration of an object is
independent of its mass. The vacuum means that no air molecules are
present to create friction on the falling object.
•This friction would resists the objects acceleration (greater velocity).
•Thus, any friction means that an object cannot be in a free-fall state.
•The vacuum is NOT why the feather and ball fall at same rate: i.e., hit
the bottom at same time with same velocity.
•The fact that gravity would be very constant over a few 10’s of meters is
also NOT why the masses fall at same rate.
•So, why does the feather and ball fall at same rate in a frictionless
(airless) environment?
Why acceleration is independent of mass (without friction)
Larger Mass = Larger gravity force
Larger Mass = Larger inertial force
So, Larger gravity force is resisted by larger inertial force
This means acceleration is independent of mass
Position, velocity and acceleration
1-D kinematic equations of motion
Projectile velocity along path
x: position (m)
v: velocity (m/s)
a: acceleration (m/s2)
a = ∆v/ ∆t (m/s/s = m/s*1/s = m/s2 )
v = ∆x/ ∆t (m/s
= m/s)
What is relation between x and t?
What is acceleration at vy = 0 point?
acceleration
In physics, and more specifically kinematics,
acceleration is the change in velocity over
time.[1] Because velocity is a vector, it can
change in two ways: a change in magnitude
and/or a change in direction. In one dimension,
i.e. a line, acceleration is the rate at which
something speeds up or slows down. However,
as a vector quantity, acceleration is also the rate
at which direction changes.[2][3] Acceleration has
the dimensions L T−2. In SI units, acceleration is
measured in metres per second squared (m/s2).
Acceleration is the rate of change of
velocity. At any point on a trajectory,
the magnitude of the acceleration is
given by the rate of change of
velocity in both magnitude and
direction at that point. The true
acceleration at time t is found in the
limit as time interval Δt → 0.
In common speech, the term acceleration
commonly is used for an increase in speed (the
magnitude of velocity); a decrease in speed is
called deceleration. In physics, a change in the
direction of velocity also is an acceleration: for
rotary motion, the change in direction of
velocity results in centripetal (toward the
center) acceleration; where as the rate of
change of speed is a tangential acceleration.
Linear free-fall: Zero to 30 m/s (60 mph) in 3 seconds!
Orbital free-fall
•If initial ball velocity this is slow (A,B) , the
ball falls back to earth tracing out a parabolic
path. Called ballistic trajectory.
•If initial ball velocity is too fast (E) (>escape
velocity) , the ball leaves earth traveling
outward towards infinity and never comes
back.
•Given correct initial ball velocity (C), the ball
will go into orbit which means it is in
continual free-fall as pull of gravity acts
perpendicular to velocity vector to accelerate
ball towards earth by the same amount that
the earth’s surface curves away.
•Question: what would happen if you were
placed at 1000 km above the earth and let go
with no initial velocity ?
Centripetal acceleration
Why if string breaks does ball
moves off in a straight line?
Gravity field in Space shuttle
The gravity field strength diminishes as 1/r2 where r is reckoned with respect to center
of the earth.
At earth’s surface 6400 km from center of earth, the gravity field strength is 9.8 m/s2.
So what is gravity field strength at 380 km above the earth’s surface which is the normal
height that the space shuttle orbits.
2
2
2
 r 
 6371 
2
g (r  dr )  g (r  6371) * 

9.81*

9.81
0.94

8.
7
4
m
/
s





 r  dr 
 6371  380 
Orbital velocity at 380 km height is about 17,400 miles per hour (7800 m/s).
The Orbital period at 380 km height is about 92 minutes.
Centripetal acceleration for stable orbit must be: a = v2/r = 78002 / 6.75e6 =9.01 m/s2 .
Does 8.74 = 9.01 m/s2 , it is close. I used approximate numbers from the web.
The gravity field is 88% of the gravity at the surface. So, why are the people weightless?
Weightlessness in orbit
Weightlessness in an orbiting spacecraft is physically
identical to free-fall, with the difference that gravitational
acceleration causes a net change in the direction, rather than
the magnitude, of the spacecraft's velocity. This is because
the acceleration vector is perpendicular to the velocity
vector.
In typical free-fall, the acceleration of gravity acts along the
direction of an object's velocity, linearly increasing its speed
as it falls toward the Earth, or slowing it down if it is moving
away from the Earth. In the case of an orbiting spacecraft,
which has a velocity vector largely perpendicular to the force
of gravity, gravitational acceleration does not produce a net
change in the object's speed, but instead acts centripetally,
to constantly "turn" the spacecraft's velocity as it moves
around the Earth. Because the acceleration vector turns
along with the velocity vector, they remain perpendicular to
each other. Without this change in the direction of its
velocity vector, the spacecraft would move in a straight line,
leaving the Earth altogether.
Terminal velocity (falling through fluid)
In fluid dynamics an object is moving at its terminal
velocity if its speed is constant due to the restraining
force exerted by the air, water or other fluid through
which it is moving.
A free-falling object achieves its terminal velocity when
the downward force of gravity (Fg) equals the upward
force of drag (Fd). This causes the net force on the
object to be zero, resulting in an acceleration of zero.[1]
When a falling object has reached terminal velocity, is it still in free-fall state ?
Fields extend or propagate to infinite
•Gravity field from mass
•Electric field from charge
•Sound source wave field
•Electro-magnetic wave field
1
f (r )  2
r
For r=0, f(r) is undefined (infinite).
For limit as r →∞, f(r) = 0.
For all other r values (domain), f(r) is finite.
Moral of story: Fields never die. The gravitational effects of you, me, the planet,
anything, extends to infinity! Although at far distances, the effects becomes so small as
to not be measurable.