A system of four particles moves along a dimension. The center of mass is at rest, and the particles do not interact with any objects outside of the system. Find the velocity of v4 at t=2.83 seconds given the details for the motion of particles 1,2,3

Explanation:

(a) Given that,

Area of a parallel plate capacitor, [tex]A=1.8\ cm^2=1.8\times 10^{-4}\ m^2[/tex]

The separation between the plates of a capacitor, [tex]d=0.01\ mm = 10^{-5}\ m[/tex]

The dielectric constant of, k = 2.1

When a dielectric constant is inserted between parallel plate capacitor, the capacitance is given by :

[tex]C=\dfrac{k\epsilon_o A}{d}[/tex]

Putting all the values we get :

[tex]C=\dfrac{2.1\times 8.85\times 10^{-12}\times 1.8\times 10^{-4}}{0.01\times 10^{-3}}\\\\C=3.345\times 10^{-10}\ F\\\\C=334.5\ pF[/tex]

(b) We know that the Teflon has dielectric strength of 60 MV/m, [tex]E=60\times 10^6\ V/m[/tex]

The voltage difference between the plates at this critical voltage is given by :

[tex]V=Ed\\\\V=60\times 10^6\times 0.01\times 10^{-3} \\\\V=600\ V[/tex]

or

V = 0.6 kV

We have that the Capacitance and potential difference is mathematically given as



Question Parameters:

having a plate area of 1.80 cm2 and a plate separation of 0.010 0 mm

having a plate area of 1.80 cm2 and a plate separation of 0.010 0 mm.

a)

Generally the equation for the Capacitance  is mathematically given as

[tex]C=\frac{ke_0A}{d}\\\\Therefore\\\\C=\frac{2.1*1.80e-4*8.85e12}{0.01e-3}\\\\[/tex]

C=334.68pF

b)

Generally the equation for the Capacitance  is mathematically given as

[tex]Vmax=\frac{Q}{C}[/tex]

Where

Q is the charge on the plates, and hence not given

Therefore, maximum potential difference is

[tex]Vmax=\frac{Q}{334.68pF}[/tex]

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Answer:

1. Energy: ultraviolet>> visible> infrared

2. Frequency: ultraviolet>> visible > infrared

3. Wavelength: infrared >> visible > ultraviolet

Explanation:

Electromagnetic waves are a class of waves that do not require material medium for their propagation, and travel at the same speed. They are arranged with respect to either their decreasing wavelength or increasing frequency to form a spectrum called an electromagnetic spectrum.

Comparing the energy, frequency and wavelength of ultraviolet, infrared and visible regions, it can be deduced that:

1. Energy: ultraviolet has the highest energy, then followed by visible, and infrared has the lowest energy.

i.e energy: ultraviolet>> visible> infrared

2. Frequency: ultraviolet radiation has the highest frequency, visible region has a greater frequency than that of infrared.

i.e frequency: ultraviolet>> visible > infrared

3. Wavelength: infrared radiation has the highest wavelength, followed by visible region, and ultraviolet radiation has the lowest wavelength.

i.e  wavelength: infrared >> visible > ultraviolet

In terms of lowest to the highest energy,frequency, and wavelength is;

Energy: infrared > visible light > ultraviolet

Frequency: infrared > visible light > ultraviolet

Wavelength: ultraviolet > visible light > infrared

The electromagnetic spectrum is made up of all the electromagnetic waves (ultraviolet, infrared, and visible) arranged according to their energy,frequency, and wavelength.

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Answer:

to overcome the out of friction we must increase the angle of the plane

Explanation:

To answer this exercise, let's propose the solution of the problem, write Newton's second law. We define a coordinate system where the x axis is parallel to the plane and the other axis is perpendicular to the plane.

X axis

       fr - Wₓ = m    a                      (1)

Y axis  

       N- [tex]W_{y}[/tex] = 0

       N = W_{y}

let's use trigonometry to find the components of the weight

        sin θ = Wₓ / W

        cos θ = W_{y} / W

        Wₓ = W sin θ

        W_{y} = W cos θ

the friction force has the formula

         fr = μ N

         fr = μ Wy

         fr = μ mg cos θ

from equation 1

at the point where the force equals the maximum friction force

in this case the block is still still so a = 0

           F = fr

           F = (μ  mg) cos θ

We can see that the quantities in parentheses with constants, so as the angle increases, the applied force must be less.

This is the force that balances the friction force, any force slightly greater than F initiates the movement.

Consequently, to overcome the out of friction we must increase the angle of the plane

the correct answer is to increase the angle of the plane

Explanation:

We know that,

[tex]v(wave \: speed) = f(frequency) \times \alpha (wavelength)[/tex]

frequency (f) = 1 / t (sec) = 8/60 = 0.13 Hz

V ( wave speed) = 0.13 * 120 = 16 m/sec

The speed of the given wave is equal to 15.96 m/s.

The frequency of the wave can be defined as the number of oscillations of a wave in one second. The frequency has S.I. units which can be expressed as per second or hertz (Hz).

The wavelength can be described as the distance between the two adjacent points in phase. Two crests or two troughs of a wave are separated by a distance is called wavelength.

The relationship between wavelength (λ), frequency (ν), and wave speed (V):

V = νλ

Given, the frequency of the wave, ν = 8 min⁻¹ = 0.133 s⁻¹

The wavelength of the wave, λ = 120 m

The speed of the waves can calculate from the above-mentioned relationship:

V = νλ = 120 × 0.133 = 15.96 m/s

Therefore, the speed of the wave is equal to 15.96 m/s.

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Answer:

5.465 × 10^10 revolutions

Explanation:

Formula for Magnetic Field = m. v/ q . r

M = mass of electron = mass of positron = 9.11 x 10^-31 kg,

radius of the positron = 5.03 mm

We convert to meters.

1000mm = 1m

5.03mm = xm

Cross multiply

x = 5.03/1000mm

x = 0.00503m

q = Electric charge = -1.6 x 10^-19 C

Magnetic field (B) = 0.85 T

Speed of the positron is unknown

0.85 = 9.11 x 10^-31 kg × v/ -1.6 x 10^-19 C × 0.00503

0.85 × 1.6 x 10^-19 C × 0.00503 = 9.11 x 10^-31 kg × v

v = 0.85 × -1.6 x 10^-19 C × 0.00503/9.11 x 10^-31 kg

v = 6.8408 ×10-22/ 9.11 x 10^-31 kg

v = 750911086.72m/s

Formula for complete revolutions =

Speed × time / Circumference

Time = 2.30s

Circumference of the circular path = 2πr

r =0.00503

Circumference = 2 × π × 0.00503

= 0.0316044221

Revolution = 750911086.72 × 2.30/0.0316044221

= 1727095499.5/0.0316044221

= 546541562294 revolutions

Approximately = 5.465 × 10^10 revolutions

Answer:

lateral splaying of echoes in the far field can be improved by Increasing the maximum number of transmit focal zones and optimize their location.

This question is incomplete, the complete question is;

A force of 193 pounds makes an angle of  79°14' with a second force. The resultant of the two forces makes an angle of 27°0' to the first force. Find the magnitudes of the second force and of the resultant.

Answer:

magnitudes of the second force (vector) is 110.84 lb

the resultant force force has a magnitude of 239.85 lb

Explanation:

Given that;

Magnitude of resultant vector R = ?

Direction of resultant vector α = 27°0'

Magnitude of vector p = 193

Magnitude of vector Q = ?

Angle between two vectors ∅ = 79°14'

Using the formula

tan∝ = [ Qsin∅ / P + Qcos∅]

tan27°0' = [ Qsin79°14' / 193 + Qcos79°14' )

we cross multiply

(193tan27°0') + (Qcos79°14'tan27°0' ) = Qsin79°14'

Q = 193tan27°0' / (sin79°14' - cos79°14'tan27°0')

Q = 110.84 lb

Therefore magnitudes of the second force (vector) is 110.84 lb

Now

R = √( p² + Q² + 2PQcos∅ )

R = √( 193² + 110.84² + ( 2 × 193 × 110.84 × cos79°14'))

R = 239.85 lb

Therefore the resultant force force has a magnitude of 239.85 lb

Answer:

your question answer is 22°

Answer:

The question is not complete, here is the other part.

Assume that n = 1.36.

Express your answer to three significant figures and include the appropriate units.

λ = 707.2nm

Explanation:

n = 1.36

t = 130

2 n t= (m+1/2) λ

To solve for λ.

λ = 2 n t ÷ m+1/2

λ = 2 × 1.36 × 130 ÷ m +1/2

λ =

If m= 0

λ= 353.6 ÷ 0+ 1/2

λ = 353.6 × 2

= 707.2nm

Answer:

The percentage change in resistance of the wire is 69%.

Explanation:

Resistance of a wire can be determined by,

R = (ρl) ÷ A

Where R is its resistance, l is the length of the wire, A its cross sectional area and ρ its resistivity.

When the wire is stretched, its length and area changes but its volume and resistivity remains constant.

[tex]l_{o}[/tex] = 1.3l, and [tex]A_{o}[/tex] = [tex]\frac{A}{1.3}[/tex]

So that;

[tex]R_{o}[/tex] = (ρ[tex]l_{o}[/tex]) ÷ [tex]A_{o}[/tex] = (ρ × 1.3l) ÷ ([tex]\frac{A}{1.3}[/tex])

    = (1.3lρ) ÷ ([tex]\frac{A}{1.3}[/tex])

    = [tex](1.3)^{2}[/tex] × [(ρl) ÷ A]

   = 1.69R               (∵ R = (ρl) ÷ A)

[tex]R_{o}[/tex] = 1.69R

Where [tex]R_{o}[/tex] is the new resistance, [tex]l_{o}[/tex] is the new length, and [tex]A_{o}[/tex] is the new area after stretching the wire.

The change in resistance of the wire = [tex]R_{o}[/tex] - R

                                      = 1.69R  - 1R

                                      = 0.69R

The percentage change in resistance = [tex]\frac{0.69R}{R}[/tex] × 100

                                                               = 0.69 × 100

                                                              = 69%

The percentage change in resistance of the wire is 69%.

Answer:

p = -q  

he distance is equal to the current distance, so the distance does not change

Explanation:

For this exercise we can solve it using the equation of the constructor

            1 / f = 1 / p + 1 / q

where f is the focal length, p the distance to the object and q the distance to the image

For a flat surface the radius is at infinity, therefore 1 / f = 0, which implies

          1 / p = - 1 / q

           p = -q

Therefore the distance is equal to the current distance, so the distance does not change

Answer:

b

Explanation:

Answer

123.5 x 10 ^-3 radian

Explanation:

Given the Width of slit a = 1 x 10⁻³ / 200

a = 5x 10⁻⁶ m .

angle at which first order peak is formed

= λ / a (where λ is wavelength and a is width of slit)

given λ = 617.3 x 10⁻⁹ m

a = 5 x 10⁻⁶

θ = 617.3 x 10⁻⁹ / 5 x 10⁻⁶

= 123.5x 10⁻³ radian .

first order peak is formed at an angle of 123.5 x 10⁻³ radian .

Explanation:

Answer:use the formular distance over time i.e distance/time. Make sure to convert the distance from metres to kilometers and time from minutes to hours .

Explanation:

The average speed of the car is 31,680 meters per hour.

To calculate the average speed of the car, you need to divide the total distance traveled by the time it took to travel that distance.

Given:

Time taken (t) = 10 minutes = 10 minutes × (1 hour / 60 minutes) = 10/60 hours = 1/6 hours

Distance traveled (d) = 5,280 meters

Average Speed (v) = Distance (d) / Time (t)

Average Speed (v) = 5280 meters / (1/6) hours

To simplify, when you divide by a fraction, it's equivalent to multiplying by its reciprocal:

Average Speed (v) = 5280 meters × (6/1) hours

Average Speed (v) = 31,680 meters per hour

Hence, the average speed of the car is 31,680 meters per hour.

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Answer:

A. 0.0374C

B. 0.012F

C. 18 ohms

Explanation:

See attached file

Answer:

The charge is  [tex]Q = 2.177 *10^{-9} \ C[/tex]

Explanation:

From the question we are told that

     The electric potential is  [tex]V = 25.0 \ kV = 25.0 *10^{3}\ V[/tex]

     The  mass of the drop is  [tex]m = 0.168 \ m g = 0.168 *10^{-3} \ g = 0.168 *10^{-6}\ kg[/tex]

      The  speed is  [tex]v = 18.8 \ m/s[/tex]

Generally the charge on the paint drop due to the electric potential which will give it the speed stated in the question  is mathematically represented as

       [tex]Q = \frac{m v^2 }{ 2 * V }[/tex]

Substituting values

      [tex]Q = \frac{0.168 *10^{-6} (18)^2 }{ 2 * 25*10^3 }[/tex]

       [tex]Q = 2.177 *10^{-9} \ C[/tex]

Answer:

Explanation:

In the given case for destructive interference , the condition is,

path difference = (2n+1)λ /2  where n is an integer and λ is wavelength

2 μ d = (2n+1)λ /2

Putting λ = 653 nm

for minimum thickness n = 0

2 μ d = 653 / 2 nm

= 326.5 nm

For constructive interference the condition is

2 μ d = n λ₁

326.5 nm = n λ₁

λ₁ = 326.5 / n  

For n = 1

λ₁ = 326.5 nm ,

or , 326.5nm .

Longest wavelength possible is 326.5

Answer:

Atoms are the particles that all matter is made from. When two or more kinds of atoms combine, they form pure elements

The answer is option A

Answer:

its molecues

Explanation:

Answer:

α = π/3

β = π/6

Explanation:

Use arc length equation to find the sum of the angles.

s = rθ

π/20 m = (0.1 m) (α + β)

π/2 = α + β

Draw a free body diagram for each sphere.  Both spheres have three forces acting on them:

Weight force mg pulling down,

Normal force N pushing perpendicular to the surface,

and tension force T pulling tangential to the surface.

Sum of forces on A in the tangential direction:

∑F = ma

T − m₁g sin α = 0

T = m₁g sin α

Sum of forces on B in the tangential direction:

∑F = ma

T − m₂g sin β = 0

T = m₂g sin β

Substituting:

m₁g sin α = m₂g sin β

m₁ sin α = m₂ sin β

(1 kg) sin α = (√3 kg) sin (π/2 − α)

1 sin α = √3 cos α

tan α = √3

α = π/3

β = π/6

Answer:

The peak output voltage of this generator is 314.2 V.

Explanation:

Given;

the number of turns of the coil, N = 1000 turns

area of the coil, A = 0.001 m²

angular frequency of the coil, f = 100 cycles/seconds

magnitude of the magnetic field, B = 0.5 T

The peak output voltage of this generator is given by;

E = NBAω

Where;

ω is the angular velocity = 2πf

E = NBA(2πf)

E = 1000 x 0.5 x 0.001(2 x π x 100)

E = 314.2 V

Therefore, the peak output voltage of this generator is 314.2 V.

Answer:

B. 1.6 x 10⁻³ m

Explanation:

The magnetic field at the center of the loop is given by;

[tex]B = \frac{\mu_o I }{2R}[/tex]

Where;

μ₀ is the permeability of free space

I is the current in the loop

R is the radius of the circular loop

B is the magnetic field

Given;

diameter of the loop = 1cm

radius of the loop, r = 0.5 cm = 0.005 m

magnetic field, B = 2.5mT = 2.5 x 10⁻³ T

The current in the loop is calculated as;

[tex]I = \frac{2BR}{\mu_o} \\\\I = \frac{2*2.5*10^{-3}*0.005}{4\pi*10^{-7}} \\\\I = 19.89 \ A[/tex]

The magnetic at a distance from the long straight wire is calculated as;

[tex]B = \frac{\mu_o I}{2\pi d}[/tex]

where;

d is the distance from the wire;

[tex]d = \frac{\mu_o I}{2\pi B} \\\\d = \frac{4\pi *10^{-7} * 19.89}{2\pi *2.5*10^{-3}} \\\\d = 1.6 *10^{-3} \ m[/tex]

Therefore, the distance from the wire where the magnetic field is 2.5 mT is 1.6 x 10⁻³ m.

B. 1.6 x 10⁻³ m

This question involves the concepts of the magnetic field due to a loop and a  current-carrying wire and current.

A long straight wire carrying the same current as the loop of wire has a magnetic field of 2.5 mT at a distance of b "B. 1.5 x 10⁻³ m".

The magnetic field at the center of a loop of wire is given by the following formula:

[tex]B=\frac{\mu_o I}{2r}[/tex]

where,

B = Magnetic Field = 2.5 mT = 2.5 x 10⁻³ T

μ₀ = permeability of free space = 4π x 10⁻⁷ N/A²

I = current = ?

r = radius = diameter/2 = 1 cm/2 = 0.5 cm = 0.005 m

Therefore,

[tex]I = \frac{(2.5\ x\ 10^{-3}\ T)(2)(0.005\ m)}{4\pi\ x\ 10^{-7}\ N/A^2}[/tex]

I = 19.9 A

Now, the magnetic field at a distance from the straight wire is given by the following formula:

[tex]B=\frac{\mu_o I}{2\pi R}[/tex]

where,

R = distance from wire = ?

Therefore,

[tex]R = \frac{(4\pi \ x \ 10^{-7}\ N/A^2)(19.9\ A)}{2\pi(2.5\ x\ 10^{-3}\ T)}[/tex]

R = 1.6 x 10⁻³ m

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Answer:

The number of windings is 1.

Explanation:

The radius of the solenoid = 8.0 cm = 0.08 m

Length of the solenoid = 45.0 cm = 0.45 m

number of turn = ?

circumference of each winding = 2πr = 2 x 3.142 x 0.08 = 0.503 m

The number of windings = (Length of the solenoid)/(circumference of each winding)

==> 0.45/0.503 = 0.89 ≅ 1

Answer:

Explanation:

The direction of propagation of electromagnetic wave

is given by the direction of vector E x B where E is electrical field , B is magnetic field .

Given Electric field  = E i because it is along x axis

Magnetic field = Bj because it is along y axis

E x B = Ei x Bj

= EB k .

so direction of E  x B is along k direction or z  - axis so wave is propagating along z - axis .

The direction of motion of electromagnetic wave will be +z-direction.

Electromagnetic waves are waves that consist of the electric field and magnetic field.

The electric and magnetic fields are perpendicular to each other and the wave propagates in the direction perpendicular to both the fields.

Now, the direction of wave motion can be estimated by taking the cross-product of directional unit vectors of the electric and magnetic fields.

The electric field is in the +y direction and the magnetic field is in the +x-direction.

So, the direction of the wave will be,

[tex]i\times j=k[/tex]

Therefore, the direction of motion of electromagnetic wave will be +z-direction.

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Answer:

a)  q = 7.5 10⁻² C , b) 190 J , c)  I₀ = 50 A , d) 1.5 mC

Explanation:

The expression for capacitance is

            C = q / DV

            q = C DV

let's reduce the magnitudes to the SI system

            ΔV = 5 kV = 5000 V

            C = 15 μF = 15 10⁻⁶ F

              t = 90 μs = 90 10⁻⁶ s

            q = 15 10⁻⁶ 5000

            q = 7.5 10⁻² C

b) the energy in a capacitor is

             U = ½ C ΔV²

             U = ½ 15 10⁻⁶ 5000²

             U = 1,875 10² J

answer  190 J

c) At the moment the discharge begins, all the current is available and it decreases with time,

whereby

                V = I R

in the first instant I = Io

                I₀ = V / R

                I₀ = 5000/100

                I₀ = 50 A

but this is for a very short time

answer 50 A

d) The definition of current is

            i = dq / dt

in this case they give us the total current and the total time, so we can find the total charge

            i = q / t

            q = i t

            q = 17 90 10⁻⁶

            q = 1.53 10⁻³ C

answer is 1.5 mC

Answer:static friction and kinetic friction in a system always act in the same direction as each other and n the opposite direction of the applie force . Is the correct answer

Explanation:

Static friction and kinetic friction in a system always act in the same direction as each other and in the opposite direction of the applied force. The correct option is B.

Friction is the force that prevents one hard material from scooting or rolling over the other.

Frictional forces, such as the locomotion required to walk without dropping, are advantageous, but they also create a significant amount of resistance to motion.

We can control cars because of friction between the tires and the road: more precisely, because there are three types of friction: rolling friction, starting friction, and sliding friction.

Friction reduces the speed of moving objects and can even stop them from moving. The friction between the objects generates heat. As a result, energy is wasted in the machines. Friction will cause wear and tear on the machine parts.

In a system, static and kinetic friction always act in the same direction and in the opposite direction of the applied force.

Thus, the correct option is B.

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Answer:

Its traveling in the +x direction

Explanation:

The E-field is in the +y-direction, and the B-field is in the +z-direction, so it must be moving along the +x-direction, since the E-field, B-field and the direction of moving are all at right angles to each other.

The electromagnetic wave is travelling in the +x direction.

Electromagnetic waves are waves formed as a result of vibrations between an electric field and a magnetic field.

Given that:

Ey = E0 sin(kx - ωt)

Hence the electric field is moving in the +y direction.

Also, Bz = B0 sin(kx - ωt)

Hence the magnetic field is moving in the +z direction

Electric fields and magnetic fields (E and B) in an EM wave are perpendicular to each other and are also perpendicular to the direction of propagation of the wave.

Therefore the direction of the wave is travelling in the +x direction.

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The answer is 3. Observation

Explanation:

The sentence "The popcorn kernels popped twice as fast as the last batch" is the result of observing or measuring the time popcorn kernels require to pop. In this context, the sentence best matches the word "observation" which the term used in the Scientific method to refer to statements that are the result of studying a phenomenon, either through the senses such as sight or through precise instruments that allow scientists to understand numerically variables such as time, speed, temperature, etc.

Answer:

Explanation:

volume of water being lifted

= π r² h , where r is radius of cylinder and h is height of cylinder

= 3.14 x5² x 10

= 785 m³

mass of water = 785 x 10³ kg

mass of this much of water is lifted so that its centre of mass is lifted by height

10 / 2 = 5m .

So work done = mgh , m is mass of water , h is displacement of centre of mass and g is acceleration due to gravity

= 785 x 10³ x 9.8 x 5

= 38.465 x 10⁶ J  

Answer:

Time, [tex]t=1.07\times 10^{-23}\ s[/tex]

Explanation:

Given that,

When a high-energy proton or pion traveling near the speed of light collides with a nucleus, it may travel [tex]3.2\times 10^{-15}\ m[/tex] before interacting.

Let t is the time interval required for the strong interaction to occur. It will move with the speed of light. So,

[tex]t=\dfrac{d}{c}\\\\t=\dfrac{3.2\times 10^{-15}}{3\times 10^8}\\\\t=1.07\times 10^{-23}\ s[/tex]

So, the time interval is [tex]1.07\times 10^{-23}\ s[/tex]