Transcript Kinematics equations for constant acceleration

Kinematics equations for motion with constant
acceleration
v  v 0  at
(1)
1 2
x  x0  v0t  at
2
(2)
v  v  2a( x  x0 )
(3)
v0  v
x  x0  (
)t
2
(4)
2
2
0
Position ( x ):
A quantity which describes the location of the object in one, two, or three dimensions.
v
Velocity ( ):
A quantity which describes the change of position with respect to time
Acceleration (a ):
A quantity which describes the change of velocity with respect to time
Derivation of Kinematic Equations of motion at
Constant Acceleration
Testing Kinetics for a=9.80m/s2
Free Fall
1 2
y  at
2
v  at
All objects fall with the same constant acceleration!!
• In air…
– A stone falls faster than a
feather
• Air resistance
affects stone
less
• In a vacuum
– A stone and a feather will
fall at the same speed.
Newton’s Laws of Motion
Newton's Principal Contributions
• The laws of motion
• The law of gravity
• The nature of light
• Calculus (Method of Fluxions)
• Mathematical approximation
methods
(1642 – 1727)
Newton’s First Law of Motion
An object at rest will
stay at rest, and an
object in motion will
stay in motion at
constant velocity as
long as no force acts
on it
Newton’s First Law of Motion
“Law of Inertia”
Inertia: the tendency of an object to resist
changes in its state.
The First Law states that all objects have
inertia. The more mass an object has, the
more inertia it has (and the harder it is to
change its state).
Wear seat belts!
Newton’s Second Law of Motion
If we want to change the state of an object, we should
apply force on it.
“The net force on an object is equal to the product
of its mass and acceleration, or F=ma.”
Contact Force = acts on an
object only by touching it.
Long-Range Force = forces that
are exerted without contact or
forces resulting from action-ata-distance
Short-Range Force
Newton’s Third Law of Motion: Action- Reaction
For every action there is an
equal and opposite reaction.
pulling a sled, Michelangelo’s assistant
FGP = - FPG
Force exerted on the
Ground by the Person
Force exerted on the
Person by the Ground
pulling a sled, Michelangelo’s assistant
Michelangelo’s assistant has been assigned the task of moving a block of marble using a sled. He
says to his boss, "When I exert a forward force on the sled, the sled exerts an equal and opposite
force backward. So, how can I ever start it moving? No matter how hard I pull, the backward
reaction force always equals my forward force, so the net force must be zero
For forward motion: FAG> FAS FSA > FSG
Derivation of the Lorentz transformation
The simplest linear trans formation
x'   ( x  vt)
x   ' ( x'vy)
 ' 
Principle of relativity
Consider expanding light
ct'   (ct  vt)
ct   (ct'vt' )
v
t '   t ' (1  )
c
2
v
Divide each t '  t (1  )
c
equation by c
v
t  t ' (1  )
c
Substitute 1/c
from the
lower to the
upper equation
Solve for
2
2 
1
2
1 v
1
 
c
2
1 v
2
c2
Find transformation for the time t’
We had
x   ' ( x' vt ' )
x'   ( x  vt )
 '
v
t '  t (1  )
c
x
t
c
vx
2
vx
c
t '   (t  2 ) 
c
v2
1
c
t