The amount of work done in emptying the tank by pumping the water over the top edge is 163.01* 10³ ft-lbs.
Given that, the tank is 8 feet across the top and 6 feet high
By the property of similar triangles, 4/6 = r/y
6r = 4y
r = 4/6*y = 2/3*y
Each disc is a circle with area, A = π(2/3*y)² = 4π/9*y²
The weight of each disc is m = ρw* A
m = 62.4* 4π/9*y² = 87.08*y²
The distance pumped is 6-y.
The work done in pumping the tank by pumping the water over the top edge is
W = 87.08 ∫(6-y)y² dy
W = 87.08 ∫(6y³ - y²) dy
W = 87.08 [6y⁴/4 - y³/3]
W = 87.08 [3y⁴/2- y³/3]
The limits are from 0 to 6.
W = 87.08 [3*6⁴/2 - 6³/3] = 87.08* [9*6³ - 2*36] = 87.08(1872) = 163013.76 ft-lbs
The amount of work done in emptying the tank by pumping the water over the top edge is 163013.76 ft-lbs.
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Answer:
A combination of longitudinal & transverse
Explanation:
Explanation:
a) We need to write down first Newton's 2nd law as applied to the given system. The equations of motion for the x- and y-axes can be written as follows:


From Eqn(2), we see that

so using Eqn(3) on Eqn(1), we get

Solving for the acceleration, we see that


b) Now that we have the acceleration, we can now solve for the velocity of the crate at the bottom of the plane. Using the equation

Since the crate started from rest,
Thus our equation reduces to



The problem is basically asking us to find a way to find the sound intensity I, in terms dependent on the sound level and the reference intensity
.For this purpose we can start from the unit used in the scale logarithmic decibel, that is

Where
I = Acoustic intensity on the linear scale
Hearing threshold
Using the logarithmic properties of the exponents the above expression can be described as:

that is the expression or technique to find the intensity of sound.
Answer:
(a) 
(b) 
Explanation:
Given data
Distance r₁=50 m
Distance r₂=2 m
Intensity I₂=2.0 W/m²
To find
(a) The Sound Intensity I₁
(b) The Sound Intensity level β
Solution
For (a) the Sound Intensity I₁

For (b) the Sound Intensity level β
The Sound Intensity level β is calculated as follow
