summary

Let us now summarize the results found thus far for the fall of a solid object in a fluid and in a vacuum.
  1. For a body falling from rest in a vacuum

        (1.4)
        (2.5)
    Note that the velocity is independent of the mass, density or shape of the object. A skydiver or a steel sphere fall at the same velocity in a vacuum.

    The acceleration of the body is constant

        (1.2)
  2. When a body falls from rest in a fluid

        (3.4)
        (4.1)

    The acceleration of the body is not constant since
        (3.2)
    The initial acceleration is g but a decreases with t or y. If we insert equation (3.4) or (4.1) into equation (3.2), we see that as t or y gets large af goes to zero and vf becomes constant. We will make more of this starting in the Terminal Velocity section.

    An applet allows you to plot eqns (1.4), (2.5) and (1.2) to obtain the velocity and acceleration of bodies falling in a vacuum. Similarly plots of eqns (3.4), (4.1) and (3.2) allow you to obtain the velocity and acceleration of bodies falling in a fluid. Furthermore the value of k/m can be varied to show the effect of this parameter on the velocity and acceleration. Practice using the applet to get a feel for the aforementioned equations and the effect of k/m on the velocity and acceleration.


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