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3 years ago

A water tank holds 1,000 gallons of water. How many cubic meters is this?

1 answer:

4 0

I have no idea what the exact answer is, so sorry in advance but ik it’s definitely less than four, but greater than three.. lol hope that helps some

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How does an ocean wave transfer energy across the ocean?

Alborosie

The energy travels in a disturbance, in an ocean that disturbance is a wave, so the wave makes energy and moves it through the water

3 0

4 years ago

The inner cylinder of a long, cylindrical capacitor has radius r and linear charge density +λ. It is surrounded by a coaxial cyl

Ulleksa [173]

Hi there!

We can begin by using the equation for energy density.

$U = \frac{1}{2}\epsilon_0 E^2$

U = Energy (J)

ε₀ = permittivity of free space

E = electric field (V/m)

First, derive the equation for the electric field using Gauss's Law:
$\Phi _E = \oint E \cdot dA = \frac{Q_{encl}}{\epsilon_0}$

Creating a Gaussian surface being the lateral surface area of a cylinder:
$A = 2\pi rL\\\\E \cdot 2\pi rL = \frac{Q_{encl}}{\epsilon_0}\\\\Q = \lambda L\\\\E \cdot 2\pi rL = \frac{\lambda L}{\epsilon_0}\\\\E = \frac{\lambda }{2\pi r \epsilon_0}$

Now, we can calculate the energy density using the equation:
$U = \frac{1}{2} \epsilon_0 E^2$

Plug in the expression for the electric field and solve.

$U = \frac{1}{2}\epsilon_0 (\frac{\lambda}{2\pi r \epsilon_0})^2\\\\U = \frac{\lambda^2}{8\pi^2r^2\epsilon_0}$

Now, we can integrate over the volume with respect to the radius.

Recall:
$V = \pi r^2L \\\\dV = 2\pi rLdr$

Now, we can take the integral of the above expression. Let:
$r_i$ = inner cylinder radius

$r_o$ = outer cylindrical shell inner radius

Total energy-field energy:

$U = \int\limits^{r_o}_{r_i} {U_D} \, dV = \int\limits^{r_o}_{r_i} {2\pi rL *U_D} \, dr$

Plug in the equation for the electric field energy density and solve.

$U = \int\limits^{r_o}_{r_i} {2\pi rL *\frac{\lambda^2}{8\pi^2r^2\epsilon_0}} \, dr\\\\U = \int\limits^{r_o}_{r_i} { L *\frac{\lambda^2}{4\pi r\epsilon_0}} \, dr\\$

Bring constants in front and integrate. Recall the following integration rule:
$\int {\frac{1}{x}} \, dx = ln(x) + C$

Now, we can solve!

$U = \frac{\lambda^2 L}{4\pi \epsilon_0}\int\limits^{r_o}_{r_i} { \frac{1}{r}} \, dr\\\\\\U = \frac{\lambda^2 L}{4\pi \epsilon_0} ln(r)\left \| {{r_o} \atop {r_i}} \right. \\\\U = \frac{\lambda^2 L}{4\pi \epsilon_0} (ln(r_o) - ln(r_i))\\\\U = \frac{\lambda^2 L}{4\pi \epsilon_0} ln(\frac{r_o}{r_i})$

To find the total electric field energy per unit length, we can simply divide by the length, 'L'.

$\frac{U}{L} = \frac{\lambda^2 L}{4\pi \epsilon_0} ln(\frac{r_o}{r_i})\frac{1}{L} \\\\\frac{U}{L} = \boxed{\frac{\lambda^2 }{4\pi \epsilon_0} ln(\frac{r_o}{r_i})}$

And here's our equation!

3 0

2 years ago

When you stretch a spring 33 cm past its natural length, it exerts a force of 6 N. What is the spring constant of this spring?

PilotLPTM [1.2K]

The spring formula:

   Force = - (spring constant) · (distance stretched or squashed)

   6 N = - (spring constant) · (33 cm)

   = - (0.33 m) · (spring constant)

Spring constant = - (6 N) / (0.33 m)

=    - 18.18 N/meter .

The negative signs means that the spring always wants to go in the
opposite direction from where you forced it, and return to its relaxed
length. If you stretch it, it tries to get shorter, and if you compress it,
it tries to get longer.

6 0

3 years ago

Read 2 more answers

A resistance training system that is a variation of circuit training and that alternates upper body and lower body exercises thr

dlinn [17]

Answer:

Peripheral heart action.

Explanation:

The Peripheral heart action purpose is to keep the blood circulation throughout the body at time of workout.

This is specially proceed through the small central muscles which goes around your heart.

After that it is followed by the peripheral muscles which lies in the arms, legs and in the abs part.

6 0

4 years ago

Which statement best describes the density of the outer planets?

gavmur [86]

Answer:

Saturn is mainly composed of the lightest two gases known, hydrogen and helium. It is the only planet in our solar system whose density is less than water.

Explanation:

5 0

4 years ago

Read 2 more answers