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    Vector Mechanics For Engineers: Dynamics

    Uploaded by

    Joshua
    This document discusses kinematics and kinetics concepts related to particle dynamics. It covers rectilinear and curvilinear motion, determining the motion of a particle given its acceleration as a function of time, position or velocity. Examples are provided to demonstrate solving problems involving uniformly accelerated and uniformly decelerated rectilinear motion.

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    © All Rights Reserved
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    Vector Mechanics For Engineers: Dynamics

    Uploaded by

    Joshua
    59 views8 pages
    This document discusses kinematics and kinetics concepts related to particle dynamics. It covers rectilinear and curvilinear motion, determining the motion of a particle given its acceleration as a function of time, position or velocity. Examples are provided to demonstrate solving problems involving uniformly accelerated and uniformly decelerated rectilinear motion.

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    Original Title

    RECTILINEAR MOTION

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    This document discusses kinematics and kinetics concepts related to particle dynamics. It covers rectilinear and curvilinear motion, determining the motion of a particle given its acceleration as a function of time, position or velocity. Examples are provided to demonstrate solving problems involving uniformly accelerated and uniformly decelerated rectilinear motion.

    Copyright:

    © All Rights Reserved
    Download as DOCX, PDF, TXT or read online from Scribd
    Download as docx, pdf, or txt
    59 views8 pages

    Vector Mechanics For Engineers: Dynamics

    Uploaded by

    Joshua
    This document discusses kinematics and kinetics concepts related to particle dynamics. It covers rectilinear and curvilinear motion, determining the motion of a particle given its acceleration as a function of time, position or velocity. Examples are provided to demonstrate solving problems involving uniformly accelerated and uniformly decelerated rectilinear motion.

    Copyright:

    © All Rights Reserved
    Download as DOCX, PDF, TXT or read online from Scribd
    Download as docx, pdf, or txt
    of 8

    VECTOR MECHANICS FOR ENGINEERS: DYNAMICS

     Kinematic relationship are used to help us determine the trajectory of a golf ball,
    the orbital speed of a satellite, and the accelerations during acrobatic flying.
    DYNAMICS INCLUDES:
     KINEMATICS – Study of the geometry of motion
     Relates displacement, velocity, acceleration, and time without reference
    to the cause of motion
     KINETICS – Study of the relations existing between the forces acting on a body,
    the mass of the body, and the motion of the body. Kinetics is used to predict the
    motion caused by given forces or to determine the forces required to produce a
    given motion.
    PARTICLE KINETICS INCLUDES:
     RECTILINEAR MOTION – position, velocity, and acceleration of a particle as it
    moves along a straight line.
     CURVILINEAR MOTION – position, velocity and acceleration of a particle as it
    moves along a curved line in two or three dimensions.

    RECTILINEAR MOTION: POSITION, VELOCITY & ACCELERATION


    CONCEPT QUIZ
    1. What is true about the kinematics of a particle?
    The velocity of a particle is equal to the slope of the position-time graph.

    DETERMINATION OF THE MOTION OF A PARTICLE


     We often determine accelerations from the forces applied (kinetics will be
    covered later)
     Generally have three classes of motion
    o acceleration given as a function of time, a = f(t)
    o acceleration given as a function of position, a = f(x)
    o acceleration given as a function of velocity, a = f(v)
    ACCELERATION AS A FUNCTION OF TIME, POSITION, OR VELOCITY

    SAMPLE PROBLEM 11.2


    A ball tossed with 10 m/s vertical velocity
    from window 20 m above ground.
    DETERMINE:
     Velocity and elevation above
    ground at time t.
     Highest elevation reached by ball
    and corresponding time, and
     Time when ball will hit the ground
    and corresponding velocity.
    SOLUTION:
     Integrate twice to find v(t) and y(t).
     Solve for t when velocity equals
    zero (time for maximum elevation) and evaluate corresponding altitude
     Solve for t when altitude equals zero (time for ground impact) and evaluate
    corresponding velocity.
    UNIFORM RECTILINEAR MOTION
    During free-fall, a parachutist reaches terminal velocity when her weight equals
    the drag force. If motion is in a straight line, this is uniform rectilinear motion.
     For a particle in uniform rectilinear motion, the acceleration is zero and the
    velocity is constant.
    dx
    =v=constant
    dt
    X t

    ∫ dx=v ∫ dt
    x0 0

    x−x 0=vt

    x=x 0 +vt

     Careful – these only apply to uniform rectilinear motion!


     For a particle in uniformly accelerated rectilinear motion, the acceleration of the
    particle is constant. You may recognize these constant acceleration equations
    from your physics courses.
    v t
    dv
    =a=constant ∫ dv=a∫ dt v =v 0 +at
    dt v 0 0

    x t
    dx 1 2
    =v 0 +at ∫ dx=∫ ( v 0 ¿ +at)dt x=x 0 + v 0 t + a t ¿
    dt x0 0 2
    v x
    dv 2 2
    v =a=constant ∫ vdv =a∫ dx v =v 0+ 2a ( x−x 0)
    dx v 0 x 0

     Careful – these only apply to uniformly accelerated rectilinear motion!


    SAMPLE PROBLEM 11.4
    Ball thrown vertically from 12 m level in
    elevator shaft with initial velocity of 18
    m/s. At same instant, open-platform
    elevator passes 5 m level moving upward
    at 2 m/s
    DETERMINE
    a) when and where ball hits elevator
    and
    b) relative velocity of ball and elevator
    at contact
    SOLUTION:
     Substitute initial position and
    velocity and constant acceleration
    of ball into general equations for
    uniformly accelerated rectilinear
    motion.
     Substitute initial position and constant velocity of elevator into equation for
    uniform rectilinear motion.
     Write equation for relative position of ball with respect to elevator and solve for
    zero relative position, i.e., impact.
     Substitute impact time into equation for position of elevator and relative velocity
    of ball with respect to elevator.

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