Answer:
W = 1.06 MJ
Explanation:
- We will use differential calculus to solve this problem.
- Make a differential volume of water in the tank with thickness dx. We see as we traverse up or down the differential volume of water the side length is always constant, hence, its always 8.
- As for the width of the part w we see that it varies as we move up and down the differential element. We will draw a rectangle whose base axis is x and vertical axis is y. we will find the equation of the slant line that comes out to be y = 0.5*x. And the width spans towards both of the sides its going to be 2*y = x.
- Now develop and expression of Force required:
F = p*V*g
F = 1000*(2*0.5*x*8*dx)*g
F = 78480*x*dx
- Now, the work done is given by:
W = F.s
- Where, s is the distance from top of hose to the differential volume:
s = (5 - x)
- We have the work as follows:
dW = 78400*x*(5-x)dx
- Now integrate the following express from 0 to 3 till the tank is empty:
W = 78400*(2.5*x^2 - (1/3)*x^3)
W = 78400*(2.5*3^2 - (1/3)*3^3)
W = 78400*13.5 = 1058400 J
That was a lucky pick.
Twice each each lunar month, all year long, whenever the Moon,
Earth and Sun are aligned, the gravitational pull of the sun adds
to that of the moon causing maximum tides.
This is the setup at both New Moon and Full Moon. It doesn't matter
whether the Sun and Moon are both on the same side of the Earth,
or one on each side. As long as all three bodies are lined up, we
get the biggest tides.
These are called "spring tides", when there is the greatest difference
between high and low tide.
At First Quarter and Third Quarter, when the sun, Earth, and Moon form a
right angle, there is the least difference between high and low tide. Then
they're called "neap tides".
