# Lecture 3 Kinematics in One Dimension Forces and Newtonâ€™s by umsymums38

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```									            Lecture 3:
Kinematics in One Dimension &
Forces and Newton’s Laws of Motion
Displacement, Velocity and Acceleration
Displacement:   X = X – X0
         
Average Velocity:    X  X 0 X
      (m/s)
t  t0   t

X
Instantaneous Velocity: V  lim             (m/s)
t  0 t
           
 v  v0 v
Average Acceleration: a                           (m/s2)
t  t0      t

          v
Instantaneous Acceleration: a  lim                 (m/s2)
t 0 t
Equations of Kinematics in Two Dimensions
X direction                   Y direction

x        x            x       y         y           y

x   Y                         y
x                             y

Y
x                x             y               y

Y
x            x            x   y             y           y
Applying the Equations of Kinematics in Two Dimensions
1   Make a drawing to represent the situation being studied.
.
2   Decide which directions are to be called positive (+) and negative (–) relative to a
.   conveniently chosen coordinate origin. Do not change your decision during the course
of a calculation.
3   Remember that the time variable t has the same value for the part of the motion along
.   the x axis and the part along the y axis.
4   In an organized way, write down the values (with appropriate + and – signs) that are
.   given for any of the five kinematic variables associated with the x direction and the y
direction. Be on the alert for “implied data,” such as the phrase “starts from rest,”
which means that the values of the initial velocity components are zero: v0x = 0 m/s
and v0y = 0 m/s. The data summary boxes used in the examples are a good way of
keeping track of this information. In addition, identify the variables that you are being
5   Before attempting to solve a problem, verify that the given information contains values
.   for at least three of the kinematic variables. Do this for the x and the y direction of the
motion. Once the three known variables are identified along with the desired unknown
variable, the appropriate relations from Table 3.1 can be selected.
6   When the motion is divided into “segments,” remember that the final velocity for one
.   segment is the initial velocity for the next segment.
7   Keep in mind that a kinematics problem may have two possible answers. Try to
.   visualize the different physical situations to which the answers correspond.
Projectile Motion
Projectile motion: two separate one dimensional motion

X direction: X, ax, Vx, t   where ax=0, Vx = constant
Y direction: Y, ay, Vy, t   where ay = 9.8 m/s2 and Vy is not a constant

http://galileo.phys.virginia.edu/classes/109N/more
_stuff/Applets/ProjectileMotion/enapplet.html
Projectile Motion

Break up the motion into X and Y direction

Horizontal Direction: V final = V initial, acceleration
in x direction = zero.

Vertical direction: Feels the effect of gravity, Y
component of velocity is not a constant
Forces and Newton’s Laws of motion
• Force: Push or pull
• Contact force versus non-contact force (effect of
gravity on sky diver)
• Mass – scalar quantity
• 17th century – Sir Isaac Newton – developed on
the theories of Galileo
• Came up with three important laws that deals
with forces and masses
• Newton’s laws of motion: Provides the basis for
understanding the effect that forces have on an
object
Sir Isaac Newton

Born: 4 Jan 1643 in Woolsthorpe, Lincolnshire, England
Died: 31 March 1727 in London, England
Newton’s First Law

• An object continues in a state of rest or in
a state of motion at a constant speed
along a straight line, unless compelled to
change that state by a net force.
• Net Force = Vector Sum of all forces
• State of rest and a state of constant
velocity are equivalent.
• Purpose of Net Force – to change velocity
Newton’s First Law

• Inertia: Natural tendency of an object to
remain at rest or in motion at a constant
speed along a straight line.
• Newton’s 1st law is also called the law of
inertia.
• Mass of an object is a quantitative
measure of the inertia (UNITS: Kg)
• Mass and Weight are not interchangeable
• Inertial frame of reference?
Newton’s Second Law

• 2nd law deals with what happens when a net force
acts on the object
• Greater force produces greater acceleration
• Same net force will exert lesser acceleration on a
massive object.
• Net Force =        
F
• Mass is another component that determines the
acceleration.

•  F              UNIT: Kg m/s2 = Newton
a      or  F  ma
m
Vector Nature of Newton’s Laws
     
 F  ma
      
 Fx  ma x
       
 F y  ma y
Newton’s Third Law

• Whenever one body exerts a force on a
second body, the second body exerts an
oppositely directed force of equal
magnitude on the first body.
• Also called “Action- Reaction” law.
• Every action has an equal and opposite
reaction.

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