Work animations / Tank pumping exploration

Interface notes

Scenarios 1-4 simply provide animations of boxes lifted from a floor to a shelf. (These animations relate to "warm up" exercises involving work computations. See the associated worksheet for more details.) Interactivity is very limited. In 1-3 controls are provided to allow you to adjust your view on the 3D scene as the animation runs. Scenario 4 also allows you to pause the animation and adjust the animation speed. You change navigate among the animations by clicking on the numbers in the navigation bar at the top of the display. You change also reload the current page by clicking on the corresponding number.

Scenario 5 is a more flexible tool, designed to help you conceptualize and construct Riemann sum approximations to the work performed in pumping the fluid from a storage tank to a certain height. (Again, see the worksheet for more details.) The shape of the tank is determined by the formula you enter into the Meridian equation r= text entry field and numerical value you enter for Upper z limit. Your formula specifies the radius of the tank as a function of height above the base. It should assume positive values less than 5 for inputs between 0 and the upper z limit (which itself should be less than 8). Click Process new equation after changing the meridian equation and/or upper z limit to apply the changes. Click Animate pumping to view an animation of the tank's fluid pumped to height units. The fluid in the tank may be modelled approximately by a family of stacked cylindrical disks. To visualize such an approximation either click Discretize (to use the default number of disks), or adjust the Number of subdivisions slider. Then click Animate lifting to see the "layers" individually raised to height . While the animation is running the Animate lifting becomes a pause button. The speed of the animation can be controlled with the Animation speed slider. Also the scene may be repositioned or rotated while the animation is running, if desired. Clicking Process new equation, Animate pumping, or Discretize while the animation is running will abort the animation.