In Problems 17 to 30, for the curve
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- Answer question 5 in the attached image pleasearrow_forwardA frame consisting of a simple span BD, an overhang AB, and a bracket CEF, is supported by a pin at B and a roller at D (see Figure 2). The beam ABCD has a uniform cross section with a moment of inertia I = 0.00025 ft. The frame is subjected to a concentrated load P at point Fas shown in the figure. Take E = 32,000 ksi, L = 12 ft, a = 6 ft, and P = 900 lb. a) Draw the shear force and bending moment diagrams of the horizontal section ABCD using the graphical method. (Hint: use the method of sections to study CEF first) b) Using the method of superposition, find an expression for the elastic curve v(x) of the segment BC. x is a horizontal coordinate measured from point of A. (Hint: select appropriate cases from the table shown below and use superposition to find v(x) for 0≤ x' ≤3, then translate the origin of the coordinate system to point A to get the final expression in terms of x). c) Using the method of integration, find expressions for the elastic curve v(x) of the segments AB and…arrow_forwardThe Deligne Dam on the Cayley River is built so that the wall facing the water is shaped like the region above the curve y 0.3x² and below the line y 180. (Here, distances are measured in meters.) The water level is 36 meters below the top of the dam. Find the force (in Newtons) exerted on the dam by water pressure. (Water has a density of 1000kg/m³, and the acceleration of gravity is 9.8m/sec².) Answer:arrow_forward
- If you compute the surface area of a sphere as the volume of revolution of the parametric curve c(t) = (cos t, sin t), as t ranges from 0 to 27. you get 0. If you use the same parametrization, but restrict t to the range from () to T, you get 47 (the correct surface area for the sphere of radius 1). Why did you get 0 when t ranged from () to 27? O Having closed the circle parametrized by c, the displacement is zero, so the surface area is zero. O Sine has the same (unsigned) area of its positive part on 0, 27 as its negative part, but on 0, 7|, it is all positive. So the sine contribution cancels out on the longer interval and not on the shorter interval. O Correct. The contribution from t e [0, 7| is exactly cancelled by t e T, 27| because the positive contributions for y(t) = cos tin the first interval are exactly cancelled by the negative contributions in the second interval. O The arc length contribution from the upper semicircle is negative because x' (t) < 0 on that semicircle…arrow_forwardFf.158.arrow_forward- Another bowl has the shape of a paraboloid. The equation of the cross- section with the (x, z)-plane is x² = 2RAZ, where RA is the curvature radius at point A. One releases at a point with height z = h a point mass with initial velocity equal to 0. What is in this case the magnitude of the force exerted by the particle on the bowl when it passes point A?arrow_forward
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage