Lecture 3 Kinematics in One Dimension Forces and Newton’s by umsymums38


									            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
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

            x                x             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
     asked to determine.
 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

                 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
            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
• 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 =        
• Mass is another component that determines the
•  F              UNIT: Kg m/s2 = Newton
  a      or  F  ma
   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

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