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Euler's Method using Matlab

  1. Nov 6, 2011 #1
    1. The problem statement, all variables and given/known data

    Question :

    The ball is kicked at a 5m high vertical wall 20m away. The initial speed of the ball is Vm/s and its initial angle of motion is C degrees with the horizontal (both the speed and angle are inputs). When the ball strikes the wall it bounces back with coefficient of restitution e , eventually returning to ground between the wall and the kicker.

    The forces acting on the ball are gravity and a wind that acts at right angles to the initial motion of the ball, which generates a force of WN
    The ball has diameter of 1 metre and weighs 0.5 kg.
    Using Euler’s method,determine the location where the ball strikes the ground.

    2. The attempt at a solution

    I've never used matlab before,so i was looking for a tutorial about euler's method on matlab and i found this one : http://www.me.ucsb.edu/~moehlis/APC591/tutorials/tutorial1/node4.html

    So i came up with this :

    First i divided my work into 2 phases,first phase is when the ball hits the wall,the second one is when the ball bounces back and hit the ground.

    %input
    m = 0.5; %weighs
    g = 9.81; % gravity
    w = 1.06; %Wind Force
    h = 0.5; %timestep
    e = 0.78; % coefficient of restitution
    npoints = 41;
    %since my stationary point is at the centre of the ball so the distance between the Stationary point to the wall is now 20.5m(41xtimestep(0.5)=20.5)

    V = input('Initial Speed ');
    C = input('Initial Angle ');
    V;
    C;

    %Equation for the first phase (when ball hits the wall)
    % Centre of the ball as a stationary point
    % y''(doubledot)=-g
    % x''(doubledot)=0
    % z''(doubledot)=w/m


    %reduce to first oder equations
    % let m = y' , s = x' , r = z'


    x =zeros(npoints,1);%this initialize the vector y to being all zeros
    y =zeros(npoints,1);
    z =zeros(npoints,1);
    m =zeros(npoints,1);
    s =zeros(npoints,1);
    r =zeros(npoints,1);

    %Initial Condition
    x(1) = 0;
    y(1) = 0;
    z(1) = 0;
    m(1) = V*sind(C); %ydot(0)
    s(1) = V*cosd(C); %xdot(0)
    r(1) = 0; %zdot(0)




    for n=1:npoints-1 %loop over the timesteps

    m(n+1) = m(n) + h*-g;
    y(n+1) = y(n) + h*m(n);

    s(n+1) = s(n) + h*0;
    X(n+1) = x(n) + h*S(n);

    r(n+1) = r(n) + h*(w/m);
    z(n+1) = z(n) + h*r(n);

    end

    plot(x,y,z);

    ==================================================
    is that code right ?
    I have not tested yet because i dont have matlab on my laptop,i did that one notepad.
    If that is right,
    How do i calculate the new velocity of the ball when it bounces back using e (coefficient of restitution ) ?
    Once I get the new velocity,do I need to do the same step as above with different initial condition ?

    Thanks
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
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