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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!