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Question 5 +(-12) and y= la. We assume that the density of We want to compute the centre- f mass (or centroid) of the r...
The centroid of a region R in the ry-plane having area A is the point with Cartesian coordinates (T, y) given by 3. -JIRZ dz dy, 9-Jl.ydzdy. The centroid would be the centre of mass if a plate in the...
The centroid of a region R in the ry-plane having area A is the point with Cartesian coordinates (T, y) given by 3. -JIRZ dz dy, 9-Jl.ydzdy. The centroid would be the centre of mass if a plate in the shape of R was made out of a uniform density material.) Find the centroid (, ) of the circular sector given by the polar coordinate inequal- ities, where 0 < θ。< π/2. You are given the area A = R300....
Use polar coordinates to find the centroid of the following constant-density plane region The reg...
Use polar coordinates to find the centroid of the following constant-density plane region The region bounded by the cardioid r4+4cos0. Set up the double integral that gives the mass of the region using polar coordinates. Use increasing limits of integration. Assume a density of 1 dr d0 (Type exact answers.) Set up the double integral that gives My the plate's first moment about the y-axis using polar coordinates. Use increasing limits of integration. Assume a density of M,-J J O...
р Question 5 Consider the region that is bounded by y = and y= Væ. Show...
р Question 5 Consider the region that is bounded by y = and y= Væ. Show your work in detail. (1) Sketch the region and find algebraically the intersections of y = ? and y = V. Label your scales. (2) Find exactly the following without using a calculator (i) total mass: m (ii) the first moment about the x-axis: M, (iii) the y coordinate of the centroid (x.y) of the region R. 12pt Paragraph Β Ι Ο Α Αν...
QUESTION 2 ONLY Question 1:(1 point) Consider the curves y = 7z2 +4x and y =-z2 + 4 a) Determine their points of interse...
QUESTION 2 ONLY
Question 1:(1 point) Consider the curves y = 7z2 +4x and y =-z2 + 4 a) Determine their points of intersection (x^,y1) and (x2,2),ordering them such that xi < x2 What are the exact coordinates of these points? ,y1= b) Find the area of the region enclosed by these two curves. t0.001 Give its approximate value within Answer: Question 2: (1 point) Let S be the solid with flat base, whose base is the region in the...
Consider a cylinder of mass M, radius R and length L. (a) Calculate the inertia tensor...
Consider a cylinder of mass M, radius R and length L. (a) Calculate the inertia tensor for rotations about the center of mass in the frame where the z axis is along the axis of the cylinder. Use cylindrical coordinates, where x = r cos θ and y = r sin θ. (b) Find the inertia tensor in the frame where the center of the “bottom side” is at the origin with the z axis along the axis of the...
Hi, I need help solving number 13. Please show all the steps, thank you. :) Consider the solid Q bounded by z-2-y2;z-tx at each point Р (x, y, z) is given by mass of Q [15 pts] 9. x-4. The density Z/...
Hi, I need help solving number 13. Please show all the steps,
thank you. :)
Consider the solid Q bounded by z-2-y2;z-tx at each point Р (x, y, z) is given by mass of Q [15 pts] 9. x-4. The density Z/m 3 . Find the center of (x, y, z) [15 pts] 10. Evaluate the following integral: ee' dy dzdx [15 pts] 11. Use spherical coordinates to find the mass m of a solid Q that lies between the...
Please help with questions 6 and 7. The exponential Eiffel Tower 501 Guided Project 72: The...
Please help with questions 6 and 7.
The exponential Eiffel Tower 501 Guided Project 72: The exponential Eiffel Tower Topics: Integration, center of mass Completed just one month before the opening of the 1889 Exposition Universelle (World's Fair) in Paris, the Eiffel Tower is one of the most recognizable landmarks in the world. It rises 300 meters from a 100 square base to a 10-meter-square observation deck. Surprisingly the project's chief engine tr no detailed structural analysis that explained the...
Question I.5 Figure 1.5 shows a frame with loads at A and D. Select the closest...
Question I.5 Figure 1.5 shows a frame with loads at A and D. Select the closest value for the magnitude of the total reaction at B. Assume the weight of the frame is zero. 40 kN VE 96.2 kN (a) (Ь -40 kN 5 m (c) -87.5 kN 30 kN (d) 57 kN 4m ao 1 m (e) 50 kN Figure L.5 Low mass frame Question I.6 In the shear and bending moment equations for beams, which of the following...
Consider a cylindrical capacitor like that shown in Fig. 24.6. Let d = rb − ra...
Consider a cylindrical capacitor like that shown in Fig. 24.6. Let d = rb − ra be the spacing between the inner and outer conductors. (a) Let the radii of the two conductors be only slightly different, so that d << ra. Show that the result derived in Example 24.4 (Section 24.1) for the capacitance of a cylindrical capacitor then reduces to Eq. (24.2), the equation for the capacitance of a parallel-plate capacitor, with A being the surface area of...
The centroid of a region R in the ry-plane having area A is the point with Cartesian coordinates (T, y) given by 3. -JIRZ dz dy, 9-Jl.ydzdy. The centroid would be the centre of mass if a plate in the shape of R was made out of a uniform density material.) Find the centroid (, ) of the circular sector given by the polar coordinate inequal- ities, where 0 < θ。< π/2. You are given the area A = R300....
Use polar coordinates to find the centroid of the following constant-density plane region The region bounded by the cardioid r4+4cos0. Set up the double integral that gives the mass of the region using polar coordinates. Use increasing limits of integration. Assume a density of 1 dr d0 (Type exact answers.) Set up the double integral that gives My the plate's first moment about the y-axis using polar coordinates. Use increasing limits of integration. Assume a density of M,-J J O...
р Question 5 Consider the region that is bounded by y = and y= Væ. Show your work in detail. (1) Sketch the region and find algebraically the intersections of y = ? and y = V. Label your scales. (2) Find exactly the following without using a calculator (i) total mass: m (ii) the first moment about the x-axis: M, (iii) the y coordinate of the centroid (x.y) of the region R. 12pt Paragraph Β Ι Ο Α Αν...
QUESTION 2 ONLY
Question 1:(1 point) Consider the curves y = 7z2 +4x and y =-z2 + 4 a) Determine their points of intersection (x^,y1) and (x2,2),ordering them such that xi < x2 What are the exact coordinates of these points? ,y1= b) Find the area of the region enclosed by these two curves. t0.001 Give its approximate value within Answer: Question 2: (1 point) Let S be the solid with flat base, whose base is the region in the...
Hi, I need help solving number 13. Please show all the steps,
thank you. :)
Consider the solid Q bounded by z-2-y2;z-tx at each point Р (x, y, z) is given by mass of Q [15 pts] 9. x-4. The density Z/m 3 . Find the center of (x, y, z) [15 pts] 10. Evaluate the following integral: ee' dy dzdx [15 pts] 11. Use spherical coordinates to find the mass m of a solid Q that lies between the...
Please help with questions 6 and 7.
The exponential Eiffel Tower 501 Guided Project 72: The exponential Eiffel Tower Topics: Integration, center of mass Completed just one month before the opening of the 1889 Exposition Universelle (World's Fair) in Paris, the Eiffel Tower is one of the most recognizable landmarks in the world. It rises 300 meters from a 100 square base to a 10-meter-square observation deck. Surprisingly the project's chief engine tr no detailed structural analysis that explained the...
Question I.5 Figure 1.5 shows a frame with loads at A and D. Select the closest value for the magnitude of the total reaction at B. Assume the weight of the frame is zero. 40 kN VE 96.2 kN (a) (Ь -40 kN 5 m (c) -87.5 kN 30 kN (d) 57 kN 4m ao 1 m (e) 50 kN Figure L.5 Low mass frame Question I.6 In the shear and bending moment equations for beams, which of the following...
Consider a cylindrical capacitor like that shown in Fig. 24.6. Let d = rb − ra be the spacing between the inner and outer conductors. (a) Let the radii of the two conductors be only slightly different, so that d << ra. Show that the result derived in Example 24.4 (Section 24.1) for the capacitance of a cylindrical capacitor then reduces to Eq. (24.2), the equation for the capacitance of a parallel-plate capacitor, with A being the surface area of...
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