Assignment 9

course Mth 174

Sorry this is late but i sent you an e-mail explaining why it is late.

???????Y???????assignment #009??n??????g???~w???Physics II

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10-17-2007

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23:18:05

what is the moment of the rod?

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RESPONSE -->

the moment of the rod is shown by the equation of

m ( l - x).

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23:19:58

What integral did you evaluate to get a moment?

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RESPONSE -->

i evaluated the integral to the left of the center of mass and to the right of the center of mass.

to the left of the center of mass the equation is 2 + 6x and to the right of the center of mass the equation is

2 - 6x

Using rho(x) for the density function:

To get the moment you integrate x * rho(x).

The integrand for the numerator is 2x + 6 x^2, antiderivative F(x) = x^2 + 2 x^3 and definite integral F(2) - F(0) = 20.

The moment of the typical increment has units of mass/unit length * length * distance from axis, or (g / m) * m * m = g * m.

The units of the integral are therefore g * m

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** To get the center of mass, which was not requested here, you would integrate x * p(x) and divide by mass, which is the integral of rho(x).

You get int(x(2+6x), x, 0, 2) / int((2+6x), x, 0, 2).

The integrand for the denominator is 2 + 6 x, antiderivative G(x) = 2x + 3 x^2 and definite integral G(2) - G(0) = 16 - 0 = 16.

The units of the denominator will be units of mass / unit length * length = mass, or in this case g / m * m = g.

So the center of mass is at x = 20 g * m /(16 g) = 5/4 (g * m) / g = 5/4 g. **

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23:24:47

what is the total mass of the region?

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RESPONSE -->

first we have to find the center of mass bye using just a area of the strip by using the equation of

A = Ax (x) delta (x)

After this is done we go on to find the density of the cardboard strip by using the equation of

z = integral (z) density (A)(z) dz / Mass

after this the total mass of the object came be found by using the same equation as before but just substituting in some things like the integral and the density found.

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23:25:01

What integral did you evaluate to obtain this mass?

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RESPONSE -->

it is shown in the before answer

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23:25:10

What is the mass of an increment at x coordinate x with width `dx?

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RESPONSE -->

shown in the before answer

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23:25:29

What is the area of the increment, and how do we obtain the expression for the mass from this area?

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RESPONSE -->

the area is shown in the very first answer pertaining to this problem

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23:25:48

How to we use the mass of the increment to obtain the integral for the total mass?

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RESPONSE -->

we use it in the equation explained in the answer before

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23:41:17

how much work is required to pump all the water to a height of 10 ft?

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RESPONSE -->

to calculate the work done here we have to use the equation

Work done = integral F(x) dx from a to b

but the real equation is W = Force * Distance

So first we have to find the Force which is

mass * acceleration

the amount of work done to pump the water up to a height of 10ft above the top of the tank is

2,822,909. 50 ft-lbs

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23:41:35

What integral did you evaluate to determine this work?

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RESPONSE -->

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23:42:02

Approximately how much work is required to pump the water in a slice of thickness `dy near y coordinate y? Describe where y = 0 in relation to the tank.

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RESPONSE -->

dont really understand the question because the thickness of a slice

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23:42:20

Explain how your answer to the previous question leads to your integral.

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RESPONSE -->

didnt answer the previous question because i didnt understand it.

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23:46:14

how much work is required to raise all the drink to a height of 15 cm?

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RESPONSE -->

the volume of the slice here has to be calculated by using the equation of

V = pi / 4 w^2 delta(h) m^3

then we find the force of gravity on the slice is calculated by the density * g * volume so the force is

800g * pi/4w^2 = 200pi * g * w^2 delta(h)

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23:46:25

What integral did you evaluate to determine this work?

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RESPONSE -->

shown on the previous answer

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23:47:44

Approximately how much work is required to raise the drink in a slice of thickness `dy near y coordinate y? Describe where y = 0 in relation to the tank.

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RESPONSE -->

the amount of work done here is calculated by the equation

Total work = lim Sum (total work done on strip) * pi * g * h^2 * vertical distance moved.

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23:47:49

How much drink is contained in the slice described above?

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RESPONSE -->

dont know

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23:47:59

What are the cross-sectional area and volume of the slice?

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RESPONSE -->

shown in previous answer

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23:48:03

Explain how your answer to the previous questions lead to your integral.

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RESPONSE -->

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23:48:20

Query Add comments on any surprises or insights you experienced as a result of this assignment.

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RESPONSE -->

didnt really understand the last few question about what they were wanting in their answer

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"

Not all the required information came through here. Please run through the program again and be sure to complete all necessary clicks and enter all necessary information. You should be able to copy the information shown here into the Query in just a few minutes, and resubmit.

You should also think about adding a little more of your reasoning process--informatin on how you set up the integrals.