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3 years ago

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Two particles, with identical positive charges and a separation of 2.85 x 10⁻² m, are released from rest. Immediately after the

release, particle 1 has an acceleration vector a₁ whose magnitude is 4.50 x 10³ m/s², while particle 2 has an acceleration vector a₂ whose magnitude is 8.15 x 10³ m/s². Particle 1 has a mass of 6.40 10⁻⁶ kg.
Find
(a) the charge on each particle _______ C and
(b) the mass of particle 2. ________ kg

1 answer:

PIT_PIT [208]3 years ago

5 0

Answer:

A, 5.1*10^-8C

B, 3.52*10^-6kg

Explanation:

See attachment

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A harmonic wave on a string is described by

xxMikexx [17]

$\huge{\bold{\orange{\underline{ Solution }}}}$

<h3><u>Given </u><u>:</u><u>-</u></h3>

A harmonic wave on a string is described by

$\sf{ Y( x, t) = 0.1 sin(300t + 0.01x + π/3)}$

x is in cm and t is in seconds

<h3><u>Answer </u><u>1</u><u> </u><u>:</u><u>-</u></h3>

<u>Equation </u><u>for </u><u>travelling </u><u>wave </u><u>:</u><u>-</u>

$\sf{ Y( x, t) = Asin(ωt + kx + Φ)...eq(1)}$

<u>Equation</u><u> </u><u>for </u><u>stationary </u><u>wave </u><u>:</u><u>-</u>

$\sf{ Y( x, t) = Acos(ωt - kx )...eq(2)}$

<u>Given </u><u>equation </u><u>for </u><u>wave </u><u>:</u><u>-</u>

$\sf{ Y( x, t) = 0.1 \:sin(300t + 0.01x + π/3)...eq(3)}$

<u>On </u><u>comparing </u><u>eq(</u><u>1</u><u>)</u><u> </u><u>,</u><u> </u><u>(</u><u>2</u><u>)</u><u> </u><u>and </u><u>(</u><u>3</u><u>)</u>

We can conclude that, Given wave represent travelling wave.

<h3><u>Answer </u><u>2</u><u> </u><u>:</u><u>-</u></h3>

From solution 1 , We can say that,

$\sf{ Y( x, t) = 0.1 \: sin(300t + 0.01x + π/3).}$

It is travelling from right to left direction

Hence, The direction of its propagation is right to left that is towards +x direction.

<h3><u>Answer </u><u>3</u><u> </u><u>:</u><u>-</u></h3>

Here, We have to find the wave period

<u>We </u><u>know </u><u>that</u><u>, </u>

Wave period = wavelength / velocity

<u>Wave </u><u>equation</u><u> </u><u>:</u><u>-</u>

$\sf{ Y( x, t) = 0.1 \:sin(300t + 0.01x + π/3).}$

ω = 300rad/s
k = 0.01

<u>We </u><u>know </u><u>that</u><u>, </u>

$\sf{v =}{\sf{\dfrac{ ω}{2π}}}{\sf{\: and\:}}{\sf{ λ =}}{\sf{\dfrac{ 2π}{k}}}$

<u>Subsitute </u><u>the </u><u>required </u><u>values</u><u>, </u>

$\sf{ wave\: period =}{\sf{\dfrac{ 2π/k}{ω/2π }}}$

$\sf{ wave \:period = }{\sf{\dfrac{k}{ω}}}$

$\sf{ wave\: period =}{\sf{\dfrac{ 0.01}{300}}}$

$\sf{ wave\: period = 0.000033\: s}$

<h3><u>Answer </u><u>4</u><u> </u><u>:</u><u>-</u></h3>

The wavelength of given wave

$\bold{ λ = }{\bold{\dfrac{2π}{k}}}$

<u>Subsitute </u><u>the </u><u>required </u><u>values</u><u>, </u>

$\sf{ λ = }{\sf{\dfrac{2 × 3.14 }{0.01}}}$

$\sf{ λ = }{\sf{\dfrac{6.28}{0.01}}}$

$\sf{ λ = 628 \: cm }$

<h3><u>Answer </u><u>5</u><u> </u><u>:</u><u>-</u></h3>

We have wave equation

$\sf{ Y( x, t) = 0.1 sin(300t + 0.01x + π/3).}$

<u>Travelling </u><u>wave </u><u>equation </u><u>:</u><u>-</u>

$\sf{ Y( x, t) = A\:sin(ωt + kx + Φ)...eq(1)}$

<u>Therefore</u><u>, </u>

Amplitude of the wave particle

$\sf{ A = 0.1 \: cm}$

Hence, The amplitude of the particle is 0.1 cm

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2 years ago

Write an equation for the magnetic field vector b generated by the current at an arbitrary point in terms of i, the length eleme

Lubov Fominskaja [6]

The magnetic field vector B generated by the current at an arbitrary point in terms of i, the length element dl, and the vector for the distance r from dl to the point is given by the equation dB = μ0/4 π ∫ (dl x r)/r $r^{3}$

<h3>Biot – Savart Law and its Applications:</h3>

The Biot – Savart Law gets its name from Jean-Baptiste Biot and Felix Savart. This is a formula that describes the relationship between force, displacement, and velocity. It plays a huge role in the branch of electromagnetism. This law is used to derive the equation between the magnetic field which is produced due to the flow of a constant electric current.

The equation of Biot – Savart law is

dB = μ0/4 π ∫ {(idl sinΦ)/r2}

Here,

I is the current,

dl is the small length of the wire. As the direction of this length is along the current hence it forms the vector idl.

r is the position vector of the point in question which is drawn from the current element and

Φ is the angle between the two.

<h3>Applications of Biot – Savart Law </h3>

• It helps in the calculation of magnetic field in an infinitely long straight wire with constant current,

• Calculation of magnetic field in the center of current carrying arc can be done by this,

• To calculate the magnetic field along the axis of a circular current carrying coil, this law can be used.

To know more about Biot - Savart Law visit:

brainly.com/question/14950341

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1 year ago

What is the relationship between the internal energy of a substance and its state of matter? A) As a gas loses internal energy i

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D)<span>As the internal energy increases a substance would go from solid to a liquid.</span>

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3 years ago

Read 2 more answers

True or false: The maximum tensile force a solid, cylindrical wire can withstand increases as the thickness of the wire increase

MaRussiya [10]

Answer:

True

Explanation:

The tensile stress, σ, on a solid cylindrical wire is given by the following relationship;

$\sigma = \dfrac{F_t}{A_o}$

Where;

$F_t$ = The tensile force

$A_o$ = The original cross sectional area of the cylindrical wire = π·R²

R = The radius of the wire

Therefore;

$F_t$ = σ × $A_o$ = σ × π × R²

Therefore, the tensile force is directly proportional to the square of the radius of the cylindrical wire, and as the radius of the wire increases, which is by increasing the thickness of the wire, the tensile force is largely increased

The correct option is; True.

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3 years ago

A flock of ducks is trying to migrate south for the winter, but they keep being blown off course by a wind blowing from the west

Minchanka [31]

The ducks' flight path as observed by someone standing on the ground is the sum of the wind velocity and the ducks' velocity relative to the wind:

ducks (relative to wind) + wind (relative to Earth) = ducks (relative to Earth)

or equivalently,

$\vec v_{D/W}+\vec v_{W/E}=\vec v_{D/E}$

(see the attached graphic)

We have

ducks (relative to wind) = 7.0 m/s in some direction <em>θ</em> relative to the positive horizontal direction, or

$\vec v_{D/W}=\left(7.0\dfrac{\rm m}{\rm s}\right)(\cos\theta\,\vec\imath+\sin\theta\,\vec\jmath)$

wind (relative to Earth) = 5.0 m/s due East, or

$\vec v_{W/E}=\left(5.0\dfrac{\rm m}{\rm s}\right)(\cos0^\circ\,\vec\imath+\sin0^\circ\,\vec\jmath)$

ducks (relative to earth) = some speed <em>v</em> due South, or

$\vec v_{D/E}=v(\cos270^\circ\,\vec\imath+\sin270^\circ\,\vec\jmath)$

Then by setting components equal, we have

$\left(7.0\dfrac{\rm m}{\rm s}\right)\cos\theta+5.0\dfrac{\rm m}{\rm s}=0$

$\left(7.0\dfrac{\rm m}{\rm s}\right)\sin\theta=-v$

We only care about the direction for this question, which we get from the first equation:

$\left(7.0\dfrac{\rm m}{\rm s}\right)\cos\theta=-5.0\dfrac{\rm m}{\rm s}$

$\cos\theta=-\dfrac57$

$\theta=\cos^{-1}\left(-\dfrac57\right)\text{ OR }\theta=360^\circ-\cos^{-1}\left(-\dfrac57\right)$

or approximately 136º or 224º.

Only one of these directions must be correct. Choosing between them is a matter of picking the one that satisfies <em>both</em> equations. We want

$\left(7.0\dfrac{\rm m}{\rm s}\right)\sin\theta=-v$

which means <em>θ</em> must be between 180º and 360º (since angles in this range have negative sine).

So the ducks must fly (relative to the air) in a direction 224º relative to the positive horizontal direction, or about 44º South of West.

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