Say we have a cylinder
that has a height of dx, we see that the cylinder has a volume of: <span>
<span>Vcylinder = πr^2*h = π(5)^2(dx) = 25π dx
Then, the weight of oil in this cylinder is:
Fcylinder = 50 * Vcylinder = (50)(25π dx) = 1250π dx.
Then, since the oil x feet from the top of the tank needs to
travel x feet to get the top, we have:
Wcylinder = Force x Distance = (1250π dx)(x) = 1250π x dx.
<span>Integrating from x1 to x2 ft gives the total work to be: (x1
= distance from top liquid level to ground level; x2 = distance from bottom
liquid level to ground level)</span>
<span>W = ∫ 1250π x dx
<span>W = 1250π ∫ x dx
W = 625π * (x2 – x1)</span></span></span></span>
<span>x2 = 14 ft + 15 ft = 29 ft</span>
x1 = 14 ft + 1 ft = 15
ft
<span>
W = 625π * (29^2 - 15^2)
<span>W = 385,000π ft-lbs
= 1,209,513.17 ft-lbs</span></span>
Answer:
50°C = 122 Fahrenheit
Explanation:
Here, we need to convert 50°C to F i.e. Fahrenheit. The conversion formula from degree Celsius to Fahrenheit is as follows :
Where, 
So, 50 degree Celsius is equal to 122 degree Fahrenheit. Hence, this is the required solution.
Explanation:
The net force along the horizontal direction is
where f is the frictional force. We can find the frictional force by looking at the vertical forces acting on the couch:
From the definition of frictional force,
Therefore, the net force on the couch is
Answer:
Explanation:
By conservation of energy, the sum of the kinetic and gravitational potential energies at the surface of the Earth must be equal than their sum at infinity, so we have:
Where 
is the gravitational constant,
and 
are the mass and radius of the Earth, <em>m </em>is the mass of the particle, 
its velocity at the surface of the Earth (which would be its escape velocity) and 
and 
are the velocities and distance at infinity, which would be null and infinity respectively, so the right hand side of our equation is 0J, which leaves us with:
Also, since the force the molecule experiments is the force of gravity (disregarding drag), we can write its weight in terms of Newton's Law of Gravitation:
Which means that:
So finally putting all together we can write:
Answer:
The oceans' deepest area is the Mariana Trench, also called the Marianas Trench, which is in the western part of the Pacific Ocean. The trench is 1,554 miles long and 44 miles wide, or 120 times larger than the Grand Canyon. According to the National Oceanic and Atmospheric Administration, the trench is almost 5 times wider than it is deep.
Explanation:
