For example, suppose that in a setting similar to the problem posed in Preview Activity 6. You plan to store mercury (w 849 lb/ft3) in a vertical rectangular tank with a 1 ft square base side whose interior side wall. Find the fluid force on one side of the rectangular plate, where the dimensions are given in feet, and the tank is full of water (62.4 lbs/cu.ft.) arrowforward. What is the meaning of the value you find? Why?īecause work is calculated by the rule \( W = F \cdot d\), whenever the force \( F\) is constant, it follows that we can use a definite integral to compute the work accomplished by a varying force. Round your answer to one decimal place.) arrowforward. Evaluate the definite integral \( \int^50_0 B(h) dh\).To find the area, we will multiply all of that by the change in height, which is Δx.= B(h)\Delta h\) measure for a given value of \( h\) and a small positive value of \( \Delta h\)? Now we can find the area of the trapezoid, which is the base added to double the width of the triangle (a), since the triangle is on both sides of the trapezoid. This is equal to the line from the base to the surface of the water (2 - x) divided by a, which is the width at 2-x. Set up the equation so that you divide the total height (4m) by the maximum width of this section (2m since (8m - 4m)/2, there's 2m on each side). Find the fluid force on the vertical side of the tank, where the dimensions are given Trapezoid 4 feet across the top, height of 3 feet, 2 feet across the Top Specialists Top specialists are the best in their field and provide the highest quality care. Calculate the total force (in Newton) on a side of the plate in the figure, submerged in a fluid of mass density 800 kg / m 3, if a 2 m and b 6 m. First you need to find an area equation for the triangle section of the trapezoid where the width is increasing from 4m to 8m, keeping in mind that we're only interested in the area that is submerged in water (2m).
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