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omeli [17]
3 years ago
9

A well hole having a diameter of 5 cm is to be cut into the earth to a depth of 75 m. Determine the total work (in joules) requi

red to raise the earth material to the surface if the average mass of 1 m is 1830 kg. (Data: g = 9.81 m/s) (Hint: How much work is required to raise a volume of ad/4 x dx from a depth of x feet to the surface?
Physics
1 answer:
guapka [62]3 years ago
6 0

Answer:

total work is 99.138 kJ

Explanation:

given data

diameter = 5 cm

depth = 75 m

density = 1830 kg/m³

to find out

the total work

solution

we know mass of volume is

volume = \frac{\pi}{4} d^2 dx

volume = \frac{\pi}{4} d^2 1830 dx

so

work required to rise the mass to the height of x m

dw = \frac{\pi}{4} d^2 1830 gx dx

so total work is integrate it with 0 to 75

w = \int\limits^{75}_{0} {\frac{\pi}{4} d^2 1830 gx dx}

w = \frac{\pi}{4} × 0.05² × 1830× 9.81× (\frac{x^2}{2})^{75}_0

w = 99138.53 J

so total work is 99.138 kJ

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