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30 Cards in this Set
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 Back
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!
