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30 Cards in this Set
- Front
- Back
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What is the arc length formula?
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∫sqrt[((d/dx)y)^2+((d/dx)x)^2]dt on a to b.
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When doing area, volume, and arc length, x ALWAYS GOES WITH ____ when finding the boundaries?
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X!!!!
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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. |
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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
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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. |
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What's the formula for mass?
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Mass = density*volume
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What's the density of water?
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1000 kg/m^3
or 1 g/cm^3 or 62.5 lb./ft^3 |
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What is the formula for pressure?
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P = ρgd
ρ = density g = gravity d = depth |
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What is the formula for hydrostatic force?
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Hydrostatic Force = Pi*Ai
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What are the units for pressure?
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Pascals
or N/m^2 |
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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)
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My = 3(-1) + 4(2) + 8(3)
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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)
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Mx = 3(1) + 4(-1) + 8(2)
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Once you've calculuated Mx and My, what do you do?
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Divide both by the mass. The mass = 3 + 4 + 8 = 15. So your interval is from (My/m,Mx/m)
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What's the formula for the x value of a center of mass on a lamina?
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[∫(x*f(x))dx]/[∫f(x)dx]
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What's the formula for the y value of a center of mass on a lamina?
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[∫0.5*(f(x))^2dx]/[∫f(x)dx]
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What does not matter when finding centers of mass?
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DENSITY!
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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 |
|
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What is the formula for hydrostatic force?
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Hydrostatic Force = Pi*Ai
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What are the units for pressure?
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Pascals
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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)
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My = 3(-1) + 4(2) + 8(3)
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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)
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Mx = 3(1) + 4(-1) + 8(2)
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Once you've calculuated Mx and My, what do you do?
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Divide both by the mass. So your interval is from (My/m,Mx/m)
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What's the formula for the x value of a center of mass on a lamina?
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[∫(x*f(x))dx]/[∫f(x)dx]
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What's the formula for the y value of a center of mass on a lamina?
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[∫0.5*(f(x))^2dx]/[∫f(x)dx]
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What does not matter when finding centers of mass?
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DENSITY!
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