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30 Cards in this Set

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 What is the arc length formula? ∫sqrt[((d/dx)y)^2+((d/dx)x)^2]dt on a to b. When doing area, volume, and arc length, x ALWAYS GOES WITH ____ when finding the boundaries? X!!!! If we have y = x^2 + 2x, what can we use for y in the arc length formula on (0,1) to (4,5)? What are a and b in the integral? We can use 1 for y. a and b are 0 and 4. A particle is located x ft. from the origin, a force of x^2+2x lbs. acts on it. How much work is done in moving it from x=1 to x=3? WRITE OUT Fi = [(xi*)2 + 2(xi*)] Wi = [(xi*)2 + 2(xi*)]Δx W = lim(n->∞) Σ{[(xi*)2 + 2(xi*)]Δx} W = ∫(x^2+2x)dx from 1 to 3. What's the formula for mass? Mass = density*volume What's the density of water? 1000 kg/m^3 or 1 g/cm^3 or 62.5 lb./ft^3 What is the formula for pressure? P = ρgd ρ = density g = gravity d = depth What is the formula for hydrostatic force? Hydrostatic Force = Pi*Ai What are the units for pressure? Pascals or N/m^2 What is My in the following problem? Find the moments and center of mass of the system of objects that have masses 3,4,8 @ (-1,1),(2,-1), and (3,2) My = 3(-1) + 4(2) + 8(3) What is Mx in the following problem? Find the moments and center of mass of the system of objects that have masses 3,4,8 @ (-1,1),(2,-1), and (3,2) Mx = 3(1) + 4(-1) + 8(2) Once you've calculuated Mx and My, what do you do? Divide both by the mass. The mass = 3 + 4 + 8 = 15. So your interval is from (My/m,Mx/m) What's the formula for the x value of a center of mass on a lamina? [∫(x*f(x))dx]/[∫f(x)dx] What's the formula for the y value of a center of mass on a lamina? [∫0.5*(f(x))^2dx]/[∫f(x)dx] What does not matter when finding centers of mass? DENSITY! What is the arc length formula? ∫sqrt[((d/dx)y)^2+((d/dx)x)^2]dt on a to b. When doing area, volume, and arc length, x ALWAYS GOES WITH ____ when finding the boundaries? X!!!! If we have y = x^2 + 2x, what can we use for y in the arc length formula on (0,1) to (4,5)? What are a and b in the integral? We can use 1 for y. a and b are 0 and 4. A particle is located x ft. from the origin, a force of x^2+2x lbs. acts on it. How much work is done in moving it from x=1 to x=3? WRITE OUT Fi = [(xi*)2 + 2(xi*)] Wi = [(xi*)2 + 2(xi*)]Δx W = lim(n->∞) Σ{[(xi*)2 + 2(xi*)]Δx} W = ∫(x^2+2x)dx from 1 to 3. What's the formula for mass? Mass = density*volume What's the density of water? 1000 kg/m^3 or 1 g/cm^3 or 62.5 lb./ft^3 What is the formula for pressure? P = ρgd ρ = density g = gravity d = depth What is the formula for hydrostatic force? Hydrostatic Force = Pi*Ai What are the units for pressure? Pascals What is My in the following problem? Find the moments and center of mass of the system of objects that have masses 3,4,8 @ (-1,1),(2,-1), and (3,2) My = 3(-1) + 4(2) + 8(3) What is Mx in the following problem? Find the moments and center of mass of the system of objects that have masses 3,4,8 @ (-1,1),(2,-1), and (3,2) Mx = 3(1) + 4(-1) + 8(2) Once you've calculuated Mx and My, what do you do? Divide both by the mass. So your interval is from (My/m,Mx/m) What's the formula for the x value of a center of mass on a lamina? [∫(x*f(x))dx]/[∫f(x)dx] What's the formula for the y value of a center of mass on a lamina? [∫0.5*(f(x))^2dx]/[∫f(x)dx] What does not matter when finding centers of mass? DENSITY!