Physics, 02.04.2020 03:21 wendyyy7774

A tank in the shape of an inverted right circular cone has height 4 meters and radius 2 meters. It is filled with 3 meters of hot chocolate. Find the work required to empty the tank by pumping the hot chocolate over the top of the tank. The density of hot chocolate is δ=1020 kg/m3.δ=1020 kg/m3. Your answer must include the correct units.

Answers: 2

Show answers

Answers

Answer from: RebelZane18

The required work to empty the the tank is 247401 J.

Explanation:

Given that,

A tank is in the shape of right circular cone.

The radius of the tank= 2 m

The height of the tank = 4 m

The relation between the radius and the height is

$\frac{r}{h}=\frac{2}{4}$

$\Rightarrow r= \frac12 h$

Let h be the height of hot of chocolate any time t.

The volume of a cone is $= \frac 13 \pi r^2 h$

$=\frac13 \pi (\frac h2)^2h$

$=\frac16 \pi h^3$

The volume of the chocolate is $=\frac16 \pi h^3$

The mass of the chocolate is(M)= Density × Volume

$=1020(\frac16 \pi h^3)$ Kg

$=170\pi h^3$ kg

$\frac{dM}{dh}= 170\pi (3h^2)$

$\Rightarrow dM=510\pi h^2\ dh$

Work done = Force × displacement

= Mass × acceleration×displacement

Here acceleration= acceleration due to gravity = 9.8 m/s²

The displacement when the hot chocolate level is h is = (4-h)

Work done (dw) $=(510\pi h^2 )(9.8)(4-h)dh$ $=4998\pi h^2 (4-h)dh$

Work done = W $=\int_0^34998\pi h^2 (4-h)dh$

$=\int_0^34998\pi [4h^2-h^3]dh$

$=4998\pi [4\frac{h^3}{3}-\frac{h^4}{4}]_0^3$

$=4998\pi [(4\frac{3^3}{3}-\frac{3^4}{4})-(4\frac{0^3}{3}-\frac{0^4}{4})]$

=247401 J

The required work to empty the the tank is 247401 J.

Answer from: Quest

does anyone know or what?

Answer from: Quest

Answer

the order for strong to weak forces such as

strong nuclear force → electromegnetic force → weak nuclear force → gravitational force

explanation

the fundamental forces are those forces that act between to objects or element to make interactions. there are four types of fundamental forces such as strong and weak nuclear forces (due to protons and electrons), electromagnetic force (due to the motion of electrons) and gravitational force (due to orbital movement of the planet). if these forces are arranged on the basis of their maximum strength then the order is

strong nuclear force → electromegnetic force → weak nuclear force → gravitational force

Another question on Physics

Physics, 23.06.2019 01:20

What is the state of matter with a specific volume but no definite shape

Answers: 1

Answer

Physics, 23.06.2019 01:30

"if the pressure acting on an ideal gas at constant temperature is tripled, its volume isa) reduced to one-third.b) increased by a factor of three.c) increased by a factor of two.d) reduced to one-half"

Answers: 2

Answer

Physics, 23.06.2019 03:50

Asimple electrochemical cell contains two electrodes? t or f

Answers: 2

Answer

Physics, 23.06.2019 06:00

The buildup of charges on an object is called

Answers: 1

Answer

You know the right answer?

A tank in the shape of an inverted right circular cone has height 4 meters and radius 2 meters. It i...