Physics, 25.03.2020 06:29 sindy35111

) A circular swimming pool has a diameter of 16 m. The circular side of the pool is 4 m high, and the depth of the water is 3.5 m. (The acceleration due to gravity is 9.8 m/s2 and the density of water is 1000 kg/m3.) How much work (in Joules) is required to: (a) pump all of the water over the side

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Answer from: yurlgurllmay

Complete Question

A circular swimming pool has a diameter of 16 m. The circular side of the pool is 4 m high, and the depth of the water is 3.5 m. (The acceleration due to gravity is 9.8 m/s2 and the density of water is 1000 kg/m3.) How much work (in Joules) is required to:

(a) pump all of the water over the side

(b) pump all of the water out of an outlet 3 m over the side?

The work required is W_d = 14.25*10^6J

The work is $W_{d3} = 3.6 *10^7 J$

Explanation:

From the question we are told that

The diameter is d = 16m

The height of the circular side is H =4m

The depth of water is D = 3.5m

The acceleration due to gravity is g =9.81m/s^2

The density of water is $\rho_w = 1000kg/m^3$

The radius of the swimming pool is

$r = \frac{16}{2} = 8m$

The work is mathematically given as

W_d = Force * distance

Now force is mathematically given as

$F = density * area * height \ of \ pool$

$= \rho * (\pi r^2 ) dx$

Now the work done to pump all of the water over the side

$W_d = \int\limits^D_0 {\rho (\pi r^2 )(H-x)} \, dx$

$=\int\limits^D_0 {1000*9.81 *(\pi * 8^2) (4- x)} \, dx$

$= 64000 *9.8 \pi \int\limits^{3.5} _0 {(4-x)} \, dx$

$= 64000 * 9.8 \pi [4x - \frac{x^2}{2} ]\left {3.5} \atop {0} \right.$

$= 64000 *9.8 \pi [4(3.5) - \frac{3.5^2}{2} ]$

=14.25*10^6J

Now for 3 meters over the side the new height would be

$H_{new} = H +3$

= 4+3

=7m

Now applying the formula for work that is above

$W_{d3 }= \int\limits^D_0 {\rho g (\pi r^2)(H-x)} \, dx$

$= \int\limits^{3.5}_0 {1000 *9.8 * (\pi * 8^2)(7 - x)} \, dx$

$= 64000 * 9.8 \pi [7x - \frac{x^2}{2} ]\left {3.5} \atop {0} \right.$

$= 64000 *9.8 \pi[7(3.5) - \frac{(3.5)^2}{2} ]$

=3.6*10^7J

Answer from: Quest

answer: strength i guess

explanation:

Answer from: Quest

Answer:

the word that best describes martin luther king jr.'s tone in the video is dignified

explanation:

martin luther king, jr. was a social activist and baptist minister who played a key role in the american civil rights movement from the mid-1950s until his assassination in 1968. the video shows his manner and attitude having or showing a composed or serious manner that is worthy of respect so dignified is the correct answer

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) A circular swimming pool has a diameter of 16 m. The circular side of the pool is 4 m high, and th...