Week 13

By Pedro James,2014-03-01 07:39
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Week 13

Week 13

    Chapter13 Kinetics of a Particle: Force and Acceleration Sec. 13.1 ~ 13.6 . Homework Prob. 15, 25, 58, 79, 101, 107

    13.1 Newtons Laws of Motion

    1st Law: If a particle, originally at rest or moving with a constant velocity, is not subjected to an

    unbalanced force, then it will remain in this state.

    2nd Law:

    3rd Law: The mutual forces of action and reaction between two particles are equal, opposite, and


    13.4 Motion in Rectangular Coordinates


     FmaFmaFma???; ; ;;;xxyyzz

    Procedure for analysis

     Select the inertial coordinate system.

     Draw the free-body diagram.

     Identify the acceleration to show the kinetic diagram.

     List the equations of motion.

     Solve the kinematics problem.

    Important Points for Solving Problem

    Equations of motion

     Friction: Ff = k N. Ff always opposes the motion of the particle relative to the

    contacting surface.

     Spring: Fs = k (l l0).


     a = a(t); v(t) = ?a(t)dt s(t) = ?v(t)dt

     a = a(s); ?a(s)ds = ?v(s)dv

     Make sure the positive inertial coordinate directions used for writing the kinematic

    equations are the same as those used for writing the equations of motion. Example 3:

    The 2-lb collar C fits loosely on the smooth shaft. If the spring is unstretched when s

    = 0 and the collar is given a velocity of 15 ft/s, determine the velocity of the collar

    when s = 1 ft. (Prob. 13-38)


13.5 Motion in N-T Coordinates


    FmaFmaF???; ; 0 ;;;ttnnb

    3 22~?dy,? 1;?,:(2dx ;)dvv?,??aa??? and tn2 dtdy

    2 dx

Example 6:

    The package has a weight of 5 lb and slides down the chute. When it reaches the

    curved portion AB, it is traveling at 8 ft/s ( = 0o). If the chute is smooth, determine the speed of the package when it reaches the intermediate point C ( = 30o) and when

    it reaches the horizontal plane ( = 45o). Also, find the normal force on the package at C. (Prob. 13-70)

Example Prob. 13-77;p133


13.6 Motion in Cylindrical Coordinates


    2 !!!FmrrFmrrFmz?;?;?(); (2); ;;;rz

A positive ( means that it’s measured in the positive direction of .


Example 7:

    Rod OA rotates counterclockwise with a constant angular velocity of 5 rad/s. The double collar B is pin-connected together such that one collar slides over the rotating rod and the other slides over the horizontal curved rod, of which the shape is described by the equation r = 1.5(2 - cos) ft. If both collars weight 0.75 lb, determine

    the normal force which the curved rod exerts on one collar at the instant = 120o. Neglect friction. (Prob. 13-89)

Example 9:

    Using air pressure, the 0.5-kg ball is forced to move through the tube lying in the horizontal plane and having the shape of a logarithmic spiral. If the tangential force exerted on the ball due to the air is 6 N, determine the rate of increase in the ball’s speed at the instant = /2. What direction does it act in? (Prob. 13-106)


13.3 Equation of Motion for a System of Particles

    The Equation of motion will be extended to a System of Particles. For ith particle:

    maFFf??; iiiii

    FandfiiHere represent the resultant external force and internal force respectively.

    All these equations are added together vectorially, we obtain: ;?;;;maFf ;?;maF iiiiiii

     and no mass is leaving the system, we have: And consider the relation ;?mrmriiG

     and maF?; ;?mamaGiiG


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