1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Law Incorporation [45]
3 years ago
14

A small sphere of

Physics
1 answer:
mixas84 [53]3 years ago
5 0

Answer:

θ = 39.7º

Explanation:

In this exercise we must use Newton's second law for the sphere, at the equilibrium point we write the equations in each exercise; we will assume that plate 1 is on the left

Y Axis

       T_{y} -W = 0

       T_{y} = W

X axis

         -F_{e1}<u> - F_{e2} + Tₓ = 0 </u>

<u> </u>

let's use trigonometry to find the components of the tension, we measure the angle with respect to the vertical

         sin θ = Tₓ / T

         cos θ = T_{y} / t

         Tₓ = T sin θ

         T_{y} = T cos θ

let's use gauss's law to find the electric field of each leaf; We define a Gaussian surface formed by a cylinder, so the component of the field perpendicular to the base of the cylinder is the one with electric flow.

         F = ∫ E. dA = q_{int} / ε₀

  in this case the scalar product is reduced to the algebraic product, the flow is towards both sides of the plate

        F = 2E A = q_{int} / ε₀

let's use the concept of surface charge density

        σ = q_{int} / A

we substitute

        2E A = σ A /ε₀

          E = σ / 2ε₀

this is the field created by each plate. The electric force is

        F_{e} = q E

for plate 1 with σ₁ = -30 10⁻⁶ C / m²

         F_{e1}  = q σ₁ /2ε₀

for plate 2 with s2 = ab 10⁻⁶ C / m², for the calculations a value of this charge density is needed, suppose s2 = 10 10⁻⁶ C / m²

          F_{e2} = q σ₂ /2ε₀

we substitute and write the system of equations

           T cos θ = mg

          - q σ₁ / 2ε₀  - q σ₂ /2ε₀  + T sinθ = 0

we introduce t in the second equations

          - q /2 ε₀  (σ₁ + σ₂) + (mg / cos θ) sin θ = 0

          mg tan θ = q /2ε₀   (σ₁ + σ₂)

          θ = tan -1 (q / 2ε₀ mg (σ₁ + σ₂)

data indicates the mass of 0.25 g = 0.25 10⁻³ kg

give the charge density on plate 2, suppose ab = 10 10⁻⁶ C / m²

let's calculate

         θ = tan⁻¹ (9.0 10⁻¹⁰ (30 + 10) 10⁻⁶ / (2  8.85 10⁻¹² 0.25 10⁻³ 9.8))

         θ = tan⁻¹ 8.3 10⁻¹)

         θ = 39.7º

You might be interested in
Based on its location on the periodic table, which element is a metal?
goldfiish [28.3K]

Sodium (Na) is a Alkali metal so that's the answer

6 0
2 years ago
Read 2 more answers
How did the astronomy of hipparchus and ptolemy violate the principles of early greek philosophers?
Mariana [72]

Answer: Hipparchus & Ptolemy believed sun and moon travel around circles with Earth in the middle (geocentric) while Plato and Aristotle believed Perfect unchanging heavens

Explanation: thus hipparchus and ptolemy violate early greek philosophy

8 0
2 years ago
How do you compare the energies of the different parts of the electromagnetic spectrum?
faltersainse [42]

The different types of radiation in electromagnetic spectrum are compared by the amount of energy found in the photons.

Radio waves have photons with low energies, microwave photons have a little more energy than radio-waves. Infrared photons still have more energy, then comes visible, ultraviolet, x-rays and the most energetic of all, gamma rays.

The energy associated with electromagnetic radiation is proportional to frequency and inversely proportional to wavelength. So, electromagnetic waves with shorter wavelengths have more energy.

On one end of the electromagnetic spectrum are radio waves, which have wavelengths billions of times longer than those of visible light. On the other end of the spectrum are gamma rays with wavelengths billions of times smaller than those of visible light.

To know more about electromagnetic spectrum:

brainly.com/question/27839167

#SPJ4

5 0
1 year ago
PLEASE HELP!!
Klio2033 [76]

Answer:

28.15

Explanation:

the ateps is in the photo

6 0
3 years ago
ver shines light up to the surface of a flat glass-bottomed boat at an angle of 30 relative to the normal. If the index of refr
Free_Kalibri [48]

Answer:

\beta = 41.68°

Explanation:

according to snell's law

\frac{n_w}{n_g} = \frac{sin\alpha}{sin30 }

refractive index of water n_w is 1.33

refractive index of glass  n_g  is 1.5

sin\alpha = \frac{n_w}{n_g}* sin30

sin\alpha = 0.443

now applying snell's law between air and glass, so we have

\frac{n_g}{n_a} = \frac{sin\alpha}{sin\beta}

sin\beta = \frac{n_g}{n_a} sin\alpha

\beta = sin^{-1} [\frac{n_g}{n_a}*sin\alpha]

we know that sin\alpha = 0.443

\beta = 41.68°

7 0
3 years ago
Other questions:
  • What is the total resistance of 3 resistors of 3ohms added together in series?
    9·1 answer
  • When responding to sound, the human eardrum vibrates about its equilibrium position. suppose an eardrum is vibrating with an amp
    5·1 answer
  • Please help me asapp!!!!!!!!!!!!!!!!
    10·2 answers
  • Two objects that are at different temperatures are added to a container of water and then the container is closed. The temperatu
    12·2 answers
  • When an object oscillating in simple harmonic motion is at its maximum displacement from the equilibrium position, which of the
    15·1 answer
  • A 1.6 Kg bird that is flying through the air has 220 J of kinetic energy. How fast is the bird flying?
    15·1 answer
  • A town requiring 2.0 m3/s of drinking water has two sources, a local well with 15 g/m3 nitrate (as N) and a distant reservoir wi
    6·1 answer
  • Which takes more energy, going from 0 to 30, or from 30 to 60?
    6·1 answer
  • Ultrasonic images are obtained from the inside organs of our body. This process uses which property of sound wave?
    10·1 answer
  • An object is moving along the x axis. At t = 5.6 s, the object is at x = +3.0 m and has a velocity of +5.7 m/s. At t = 8.5 s, it
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!