![]() We can use integration to develop a formula for calculating mass based on a density function. We then turn our attention to work, and close the section with a study of hydrostatic force. Let’s begin with a look at calculating mass from a density function. In this section, we examine some physical applications of integration. 6.5.5 Find the hydrostatic force against a submerged vertical plate.6.5.4 Calculate the work done in pumping a liquid from one height to another.6.5.3 Calculate the work done by a variable force acting along a line.6.5.2 Determine the mass of a two-dimensional circular object from its radial density function.6.5.1 Determine the mass of a one-dimensional object from its linear density function.† † margin: y y x - 2 - 1 1 2 - 2 - 1 1 2 50 water line not to scale d ( y ) = 50 - y Figure 6.5.8: Measuring the fluid force on an underwater porthole in Example 6.5.4. The truth is that it is not, hence the survival tips mentioned at the beginning of this section. This is counter-intuitive as most assume that the door would be relatively easy to open. ![]() ![]() Most adults would find it very difficult to apply over 500 lb of force to a car door while seated inside, making the door effectively impossible to open. ![]() Using the weight-density of water of 62.4 lb/ft 3, we have the total force as We adopt the convention that the top of the door is at the surface of the water, both of which are at y = 0. Its length is 10 / 3 ft and its height is 2.25 ft. ![]() SolutionThe car door, as a rectangle, is drawn in Figure 6.5.7. ![]()
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