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3 years ago

12. A sprinter has an acceleration of 5m/s” during the first 2 seconds of the race. What

Physics

1 answer:

Gala2k [10]3 years ago

7 0

Answer:

v=10m/s

Explanation:

$a=\frac{vf-vi}{t}\\ 5m/s^{2}=\frac{vf-0}{2}\\ vf=5*2\\vf=10 m/s$

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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

What is the acceleration due to gravity in a region where a simple pendulum having a length 75.000 cm has a period of 1.7357 s?

Ksju [112]

Answer:

Explanation:

T = 2π $\sqrt{L/g}$

(T / 2π)² = L/g

g = 4π²L/T²

g = 4π²(0.75000)/(1.7357)²

g = 9.82814766...

g = 9.8281 m/s²

6 0

2 years ago

Why do things become hot or cold? Relate to Thermal Energy and The Law of Conservation of Energy

Mekhanik [1.2K]

Answer:

Things become hot and cold because of the transfer of energy.

Explanation:

The energy possessed by an object or system is called thermal energy and heat is the flow of this energy. While the law of conversation of energy states that energy is not destroyed or created, it just transfers from one object to another.

When a hot object is placed in normal conditions, it transfers heat to the environment until both are at the same temperature and heat transfers from the environment to the cold objects placed in normal conditions.

4 0

3 years ago

Based on your knowledge of the electromagnetic spectrum, why are radio waves considered harmless while ultraviolet waves and x-r

Goryan [66]

The correct answer of this question is : A) Radio waves have longer wavelengths, lower frequency, and lower energy than ultraviolet waves and x-rays.

EXPLANATION :

Before going to answer this question, first we have to know the electromagnetic spectrum.

Electromagnetic spectrum is the arrangement of electromagnetic waves in the ascending order of frequency or descending order of wavelength.

When the waves are arranged in the ascending order of their frequency, then perfect order is given below as such -

Radio wave < Micro wave < Infrared wave < Visible light < U.V ray< X-ray < Gamma ray .

Hence, we see that radio wave has the least frequency, and gamma ray has the most frequency.

We know that wavelength and frequency are inversely are inversely proportional to each other. Hence, radio wave has more wavelength and less frequency.

The wave having more frequency is more energetic. Hence, gamma is more energetic and radio wave is less energetic .

4 0

4 years ago

Read 2 more answers

Considering the symmetry of the charge distribution, determine the symmetry of the electric field and choose one of the followin

BaLLatris [955]

Answer:

my name jeff hahahhahahahahahhahhahhahhahhahhah the correct a

Explanation:

4 0

4 years ago