A leaf spring in an off-road truck with a spring constant k of 87.6 kN/m (87,600 N/m) is compressed a distance of 6.2 cm (0.062 m) from its original unstretched position. What is the increase in potential energy of the spring (in kJ)?

Answer:

Explanation:

Given that a coil has a turns of

N = 110 turns

And the flux is given as function of t

ΦB = 9.75 ✕ 10^-3 sin(ωt),

Given that, at an instant the angular velocity is 8.70 ✕ 10² rev/min

ω = 8.70 ✕ 10² rev/min

Converting this to rad/sec

1 rev = 2πrad

Then,

ω = 8.7 × 10² × 2π / 60

ω = 91.11 rad/s

Now, we want to find the induced EMF as a function of time

EMF is given as

ε = —NdΦB/dt

ΦB = 9.75 ✕ 10^-3 sin(ωt),

dΦB/dt = 9.75 × 10^-3•ω Cos(ωt)

So,

ε = —NdΦB/dt

ε = —110 × 9.75 × 10^-3•ω Cos(ωt)

Since ω = 91.11 rad/s

ε = —110 × 9.75 × 10^-3 ×91.11 Cos(91.11t)

ε = —97.71 Cos(91.11t)

The EMF as a function of time is

ε = —97.71 Cos(91.11t)

Extra

The maximum EMF will be when Cos(91.11t) = -1

Then, maximum emf = 97.71V

Answer:

1) μ = 1.33 10⁻³ kg / m , F = - 14,256 ,  2) v= 103.53 m/s, 3)  f = 138.04 Hz , 4)  1, 25, 50, 76, 101   , 5) A = 0.00869 m , 6)  # _position = (# _account-1) (1.5m / 100 accounts)

Explanation:

1) Linear density is the mass per unit length

     μ = m / L

     μ = 2 1 10⁻³ / 1,5

     μ = 1.33 10⁻³ kg / m

this is the density when the chain is stretched, which is when the pulse occurs

we can find the tension with

     F = - k (x₁-x₀)

where k is the spring constant

     F = - 28.8 (1.5 -1.005)

     F = - 14.256 N

the negative sign indicates that the force is restorative

2) the pulse speed is

      v = √ T /μ

      v = √ 14,256 / 1,33 10⁻³

      v = 103.53 m / s

3) If standing waves are formed with fixed points at the ends and 4 antinodes, the wavelength is

          2 λ = L

            λ = L / 2

wave speed is related to frequency and wavelength

           v = λ f

            f = v / λ

            f = v 2 / L

            f = 103.53 2 / 1.5

            f = 138.04 Hz

4) The marbles are numbered, the marbles that remain motionless are

   the first (1) and the last (101)

Let's look for the distance to each node, for this we must observe that in each wavelength there is a node at the beginning, one in the center and one at the end, therefore the nodes are in

         #_node = m λ / 2 = m L / 4

        #_node     position (m)

         1                  1.5 / 4 = 0.375

         2             2 1.5 / 4 = 0.75

         3             3 1.5 / 4 = 1,125

Since there are 101 marbles in the initial length, this number does not change with increasing length, so there is 101 marble in 1.5 m. Let's find with a direct proportion rule the number of marbles at these points with nodes

        #_canica = 0.375 m (101 marble / 1.5 m) 0.375 67.33

        # _canica = 25

        #_canica = 0.75 67.33

        #_canica = 50

        # _canica = 1,125 67.33

        #canica = 75.7 = 76

in short the number of the fixed marbles is

      1, 25, 50, 76, 101 canic

5) The movement of the account is oscillatory at this point, which is why it is described by

          y = A cos wt

          [tex]v_{y}[/tex]= -A w sin wt

the speed is maximum for when the breast is worth ±1

          v_{y} = Aw

           A = v_{y} / w

angular velocity related to frequency

         w = 2π f

          A = v_{y} / 2πf

          A = 7.54 / (2π 138.04)

          A = 0.00869 m

6) for the position of each account we can use a direct proportion rule

      in total there are 100 accounts distributed in the 1.50 m distance, the #_account is in the # _position. Note that it starts to be numbered 1, so this number must be subtracted from the index of the amount

       # _position = (# _account-1) (1.5m / 100 accounts)

#_canic position(m)

   1          0

   2         0.015

   3         0.045

   4         0.06

7) the wave has a constant velocity, but every wave is oscillated perpendicular to this velocity, with an oscillatory movement described by the expression

         y = Acos wt

the maximum speed is

         [tex]v_{y}[/tex] = -Aw sin wt

speed is maximum when the sine is ±1

         v_{y} = A w

to calculate the amplitude of the count we use that for a standing wave

         y = 2Asin kx

          y / A = 2 sin (2π /λ x)

the wavelength is

 λ = 0.75 m

the position is

x (30) = 29 1.5 / 100 = 0.435  m

          y (30) A = 2 sin (2pi 0.435 / 0.75)

          y (30) / A = 0.96 m

Answer:

A) speed = 3144287.425 m/s

B) period = 8.57x10^-8 s

C) KE = 3.302x10^-14 J

D) potential difference = 103187.5 V

Explanation:

Detailed explanation and calculation is shown in the image below.

Answer:

Please see the attached picture for the answer.

Explanation:

Final answer:

Einstein's Gedanken experiments reveal the constant speed of light and challenge intuitive notions of time and simultaneity in special relativity. In Albert's reference frame and an outside observer's frame, light beams travel at the same speed, but the perception of simultaneity can differ due to relativistic effects.

Explanation:

Gedanken Experiments and Einstein's Theory of Relativity

Albert Einstein used Gedanken's experiments to explore the implications of relativity on the concepts of time and simultaneity. These thought experiments challenged intuitive notions by demonstrating how the speed of light remains constant in all frames of reference, a cornerstone of special relativity. Let's address the student's questions based on this principle:

Part A: In both Albert's frame of reference and your frame of reference, the beams of light travel at the same speed since the speed of light is constant regardless of the observer's motion relative to the source.

Part B: Albert sees both beams of light strike the ends of the freight car simultaneously. However, due to relativistic effects, a stationary observer might see the light traveling in the direction of the freight car's motion strike first.

Part C: Both in Albert's and your frame of reference, the light strikes the ceiling and floor simultaneously because there is no relative motion along the direction of the light beams' propagation.

Part D: In Albert's frame of reference, both lasers strike him simultaneously. For a stationary observer, depending on the direction of the freight car's motion, one assassin may seem to fire before the other due to relativistic effects.

Einstein's ingenious analytical methods demonstrated through Gedanken experiments, led to the conclusion that many seemingly obvious predictions must be reconsidered when dealing with the postulates of relativity, which have been confirmed through meticulous experimentation.

Answer:

Their final velocity is 0.122m/s

Explanation:

Using the law of conservation of momentum which states that the sum of momentum of bodies before collision is equal to the sum of their momentum after collision. The bodies move with a common velocity after collision.

Momentum = mass × velocity

BEFORE COLLISION

momentum of the first train

= 1.5×10^5 × 0.3

= 0.45×10^5kgm/s

Momentum of second train

= 1.1×10^5 × (-0.12) (velocity is negative since the body is moving towards the left)

= -0.132 × 10^5kgm/s

AFTER COLLISION

Momentum of both bodies is given as:

(1.5×10^5+1.1×10^5)V

= 2.6×10^5V

V is their common velocity

According to the law:

0.45×10^5+(-0.132×10^5) =2.6×10^5V

0.45×10^5 - 0.132×10^5 = 2.6×10^5V

0.318×10^5 = 2.6×10^5V

0.318 = 2.6V

V = 0.318/2.6

V = 0.122m/s

B. The Earth radiates an amount of energy into space equal to the amount it receives.

Part of the solar energy is reflected by the Earth into space, this is known as albedo. The other part of the energy radiated by the Earth in the form of infrared radiation, is absorbed by the greenhouse gases, which cause most of this infrared radiation to be emitted into space. Therefore, the net flow of energy is zero.

Answer:

1) 883 kgm2

2) 532 kgm2

3) 2.99 rad/s

4) 944 J

5) 6.87 m/s2

6) 1.8 rad/s

Explanation:

1)Suppose the spinning platform disk is solid with a uniform distributed mass. Then its moments of inertia is:

[tex]I_d = m_dR^2/2 = 183*2.31^2/2 = 488 kgm^2[/tex]

If we treat the person as a point mass, then the total moment of inertia of the system about the center of the disk when the person stands on the rim of the disk:

[tex]I_{rim} = I_d + m_pR^2 = 488 + 74*2.31^2 = 883 kgm^2[/tex]

2) Similarly, he total moment of inertia of the system about the center of the disk when the person stands at the final location 2/3 of the way toward the center of the disk (1/3 of the radius from the center):

[tex]I_{R/3} = I_d + m_p(R/3)^2 = 488 + 74*(2.31/3)^2 = 532 kgm^2[/tex]

3) Since there's no external force, we can apply the law of momentum conservation to calculate the angular velocity at R/3 from the center:

[tex]I_{rim}\omega_{rim} = I_{R/3}\omega_{R/3}[/tex]

[tex]\omega_{R/3} = \frac{I_{rim}\omega_{rim}}{I_{R/3}}[/tex]

[tex]\omega_{R/3} = \frac{883*1.8}{532} = 2.99 rad/s[/tex]

4)Kinetic energy before:

[tex]E_{rim} = I_{rim}\omega_{rim}^2/2 = 883*1.8^2/2 = 1430 J[/tex]

Kinetic energy after:

[tex]E_{R/3} = I_{R/3}\omega_{R/3}^2/2 = 532*2.99^2/2 = 2374 J[/tex]

So the change in kinetic energy is: 2374 - 1430 = 944 J

5) [tex]a_c = \omega_{R/3}^2(R/3) = 2.99^2*(2.31/3) = 6.87 m/s^2[/tex]

6) If the person now walks back to the rim of the disk, then his final angular speed would be back to the original, which is 1.8 rad/s due to conservation of angular momentum.

The ventriloquist uses the perceptual principle known as the McGurk Effect to create the illusion that words are coming from their dummy's mouth. This involves syncing their speech with the movements of the dummy's mouth and mastering aspects of speech production. We perceive the words to be coming from the dummy due to the combined audiovisual cues.

A ventriloquist convinces us that words are coming from their dummy's mouth by making use of the perceptual principle known as the McGurk Effect. This audiovisual speech perception demonstrates that we don't just hear speech but also 'see' it. The ventriloquist creates the illusion by carefully syncing the opening and closing of the dummy's mouth with their own speech. This overlaid speech and vision information persuades us to perceive the sound as coming from the dummy.

Human speech itself is produced by shaping the cavity formed by the throat and mouth, the vibration of vocal cords, and using the tongue to adjust the fundamental frequency and combination of those sounds. Thus, excellent ventriloquists master these aspects of speech production without visibly moving their own mouth or lips, reinforcing the illusion.

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Answer:

Explanation:

the picture attached shows the whole explanation

Answer:

hii bro.... from India. ....i am from Bilaspur cg

Find the screenshots in the attachment for complete solution. Follow the sequence

The catapult can generate 216,900,000 J of work during a single stroke, which is significantly more energy than the 142,222,500 J required to accelerate the aircraft.

To calculate the work done during the expansion of the steam in the catapult, we can use the first law of thermodynamics, which is the energy balance equation for a closed system:

ΔU = Q - W

Where:

ΔU is the change in internal energy of the system.

Q is the heat added to the system.

W is the work done by the system.

In this case, the steam in the catapult is the system, and we want to find the work done (W) during the expansion.

We can calculate the change in internal energy (ΔU) using the following equation:

ΔU = m * (u_final - u_initial)

Where:

m is the mass of the steam.

u_final is the specific internal energy of the steam at the final state.

u_initial is the specific internal energy of the steam at the initial state.

Given that the steam expands from 15 MPa and 450°C to 0.4 MPa, we need to find the specific internal energies at these two states. You'll typically need steam tables or thermodynamic software for precise values, but I'll provide approximate values for illustration:

For the initial state (15 MPa and 450°C), the specific internal energy might be approximately u_initial = 3270 kJ/kg.

For the final state (0.4 MPa), the specific internal energy might be approximately u_final = 2480 kJ/kg.

The mass (m) of the steam is given as 270 kg.

Now, calculate the change in internal energy:

ΔU = 270 kg * (2480 kJ/kg - 3270 kJ/kg)

ΔU = -216,900 kJ

The negative sign indicates a decrease in internal energy during the expansion.

Now, let's calculate the work done (W). Since this is an expansion, the work done by the system is positive:

W = -ΔU

W = -(-216,900 kJ)

W = 216,900 kJ

Now, let's compare this to the energy required to accelerate a 30,000 kg aircraft from rest to 350 km per hour. To calculate this energy, we can use the kinetic energy formula:

KE = 0.5 * m * v^2

Where:

KE is the kinetic energy.

m is the mass of the aircraft.

v is the velocity.

Converting 350 km per hour to m/s:

350 km/h * (1000 m/km) / (3600 s/h) ≈ 97.22 m/s

Now, calculate the kinetic energy:

KE = 0.5 * 30,000 kg * (97.22 m/s)^2

KE ≈ 142,222,500 J (joules)

So, the energy required to accelerate the aircraft is approximately 142,222,500 joules.

Comparing the work done by the catapult (216,900 kJ or 216,900,000 J) to the energy required to accelerate the aircraft (142,222,500 J), we can see that the catapult generates significantly more energy during a single stroke than is required to accelerate the aircraft. The catapult can generate much more work due to the expansion of steam, making it suitable for launching an aircraft.

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Answer:

B) A person on the moving Earth observing the light from a distant star

Explanation:

The aberration of starlight is a phenomenon in Astronomy used to describe the 'seeming' or apparent movement of a star around its true position. This seeming' or apparent movement of a star is caused by and dependent on the velocity of the observer. The movement of the observer relative to the star creates the notion that the star is moving. However, in reality, the star is static.  The star is not moving, what is really moving is the observer; this movement of the observer is what makes it seem that the star was moving. It is not an optical illusion, although, the effect seems close enough.

For example, in the analogy given:

A car moving in the rain or under the rainfall

The car is the one moving in the same way that the Earth is the one revolving. The rainfall drops vertically in the same way that the starlight is static. The movement of the car relative to the rainfall is what makes it seem that the rain is falling 'diagonally'. The same visual analogy is observe when a person on the moving Earth observing the light from a distant star

Hence, the correct option is B

Answer:

a) = 6.23eV

b) = 0eV

c) = 6.23V

d) = 304.12nm

Explanation:

λ = 199nm

E = 4.08eV = Φ

hf = K(max) + Φ

Φ = work function of the target material

hf = photon energy

K(max) = k.e of the metal

K(max) = [(6.626*10⁻³⁴) * (3.0*10⁸)] / 199*10⁻⁹

K(max) = 9.99*10⁻¹⁹J

1.602*10⁻¹⁹J = 1eV

9.99*10⁻¹⁹ = 6.23eV

K(max) = 6.23eV

b). The slowest moving electron has a kinetic energy of zero

c). The stopping potential is the potential difference required to stop the fastest electron.

eV = K(max)

V = K(max) / e

V = 6.23eV / e

V = 6.23V

d)

The cut- off wavelength occurs when the maximum K.E is zero.

Φ = hc / λ

λ₀ = hc / Φ

λ₀ = (6.626*10⁻³⁴ * 3.0*10⁸) / (4.08 * 1.602*10⁻¹⁹)

λ₀ = 1.9878*10⁻²⁵ / 6.5361*10⁻¹⁹

λ₀ = 3.04*10⁻⁷m

λ₀ = 304.12nm

Answer:

The circuit breaker will trip because the current drawn is in excess of its capacity

Explanation:

The 20 A circuit breaker is designed to not carry current in excess of its capacity.

Total power demand on power strip = 900 + 990 + 650 = 2540 w

Let us assume a standard American voltage outlet of 120 V

Recall that electric power is

P = I x V

Where I is current, and

V = voltage.

For the 2540 W power drawn, the current I is

I = P/V = 2540/120 = 21.16 A

This is 1.16 A in excess of its capacity.

Answer:

[tex]E=3.5(8.98*10^{6}x-2.69*10^{15}t)[/tex]

[tex]B=1.17*10^{-8}(8.98*10^{6}x-2.69*10^{15}t)[/tex]

Explanation:

The electric field equation of a electromagnetic wave is given by:

[tex]E=E_{max}(kx-\omega t)[/tex] (1)

We know that the wave length is λ = 700 nm and the peak electric field magnitude of 3.5 V/m, this value is correspond a E(max).

By definition:

[tex]k=\frac{2\pi}{\lambda}[/tex]            

[tex]k=8.98*10^{6} [rad/m][/tex]      

And the relation between λ and f is:                

[tex]c=\lambda f[/tex]

[tex]f=\frac{c}{\lambda}[/tex]

[tex]f=\frac{3*10^{8}}{700*10^{-9}}[/tex]

[tex]f=4.28*10^{14}[/tex]

The angular frequency equation is:

[tex]\omega=2\pi f[/tex]

[tex]\omega=2\pi*4.28*10^{14}[/tex]

[tex]\omega=2.69*10^{15} [rad/s][/tex]

Therefore, the E equation, suing (1), will be:

[tex]E=3.5(8.98*10^{6}x-2.69*10^{15}t)[/tex] (2)

For the magnetic field we have the next equation:

[tex]B=B_{max}(kx-\omega t)[/tex] (3)

It is the same as E. Here we just need to find B(max).

We can use this equation:

[tex]E_{max}=cB_{max}[/tex]

[tex]B_{max}=\frac{E_{max}}{c}=\frac{3.5}{3*10^{8}}[/tex]

[tex]B_{max}=1.17*10^{-8}T[/tex]

Putting this in (3), finally we will have:

[tex]B=1.17*10^{-8}(8.98*10^{6}x-2.69*10^{15}t)[/tex] (4)

I hope it helps you!

Final answer:

To find the equations of the fields for an electromagnetic wave in the red spectrum with given parameters, calculate the frequency using the speed of light and wavelength, then apply it to the sinusoidal equations representing the electric and magnetic fields.

Explanation:

To determine the equations for the electric and magnetic fields (E and B, respectively) of an electromagnetic wave in the visible red spectrum with a wavelength (λ) of 700 nm and a peak electric field magnitude (Ē) of 3.5 V/m, we first need to calculate the frequency (f) of the wave.

Since the speed of light (c) is approximately 3 × 108 m/s, the frequency can be calculated by using the relationship c = f × λ. After finding the frequency, we can then write down the equation for the electric field E(x, t). Assuming that the wave is propagating in the +x direction and that the electric field oscillates in the y-direction, with no initial phase change, the equation for the electric field is:

E(x, t) = Ē × sin(2π(ft - x/λ))

To find the associated magnetic field B, we use the fact that the magnitudes of E and B are related by the speed of light c, such that B = E/c. Since electromagnetic waves have their electric and magnetic fields perpendicular to each other, if E is in the y-direction, B will be in the z-direction. The equation for the magnetic field is:

B(x, t) = B × sin(2π(ft - x/λ))

Where B is the peak magnetic field strength.

Answer:

2.9 m/s

Explanation:

The speed of the two-block system center of mass will not be changed by the collision, since it is an internal force. The only force acting upon the two-block system, then, will be gravity. We can calculate the effects of gravity upon the speed of the blocks along the slope by taking the sine of the angle of the slope (37°) and multiplying it by the magnitude of Fg in the vertical direction. sin(37°)*(3.92 N) = 2.36 N. This force acts upon the system and accelerates it down the slope, which can be modeled with the equation 2.36 N = (0.40 kg)*a. Solving for a, we find that gravity accelerates the block at 5.9 m/s2 along the slope of the block. Using this figure, we can find the speed of the system with the equation v = v0 + at. Initial velocity of the system is zero, as both blocks are moving towards each other at equal speed, so v = (5.9 m/s2)*(0.50 s). Velocity of the system after 0.50 seconds = 2.9 m/s.

The center-of-mass of an isolated two-block system moving towards each other at the same speed remains the same before the collision; therefore, the center-of-mass velocity is also 0.35 m/s just before the blocks collide.

In this scenario, we are dealing with the principle of conservation of momentum in an isolated system. In two-dimensional collisions involving identical masses moving toward each other at the same speed, the center-of-mass velocity does not change due to the collision.

To find the speed of the two-block system's center of mass, we can use the formula for center-of-mass velocity, that is the weighted average of the individual velocities. Since the blocks have identical mass, the center-of-mass velocity is just the average of their individual velocities. Given both blocks are moving toward each other at a speed of 0.35 m/s, the speed of the center-of-mass of the system before the blocks collide is also 0.35 m/s.

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The Earth is slightly flatter at the poles, making the correct answer option C. It is an oblate spheroid with a denser core made primarily of iron and nickel.

The correct answer to the question, 'The earth is:', is C: slightly flatter at the poles. This is because the Earth's shape is an oblate spheroid, meaning it's somewhat squished at the poles and bulges a bit at the equator due to its rotation. The Earth's equatorial radius is greater than its polar radius, which results in this slight flattening at the poles. Also, the Earth's core is composed predominantly of iron and nickel, making it very dense.

While it is true that the Earth is not a perfect sphere, it is also not thinner at the equator as option B suggests. Option D mentions that Earth is made of mostly carbon and iron, which is incorrect; the Earth is composed primarily of iron, oxygen, silicon, and other elements, but not mostly carbon.

Answer:

Option B and Option D are true

Explanation:

We are given;

Number of atoms in block A = 800

Energy content in block A = 20 quanta

Number of atoms in block B = 200

Energy content in block B = 80 quanta

The energy of a system which is an extensive quantity,depends on the mass or number of moles of the system. However, at equilibrium, the energy density of the two copper blocks will be equal. That is, each atom of Cu in the two blocks will, on average, have the same energy. Because block A has 4 times more atoms than block B, it will have 4 times more quanta of energy. Thus, option B is therefore true while option A is false.

Temperature is a measure of the average kinetic energy of the atoms in a material. Now, if each atom in blocks A and B have the same average energy, then the temperatures of blocks A and B will be equal at equilibrium. Thus, option D is true.

Entropy of a system is an extensive quantity that depends on the the mass or number of atoms in the system. Because block A is bigger than block B, it will have higher entropy. However, that the specific entropy (the entropy per mole or per unit mass) is an intensive quantity -- it is independent of the size of a system. The molar entropy of blocks A and B are equal at equilibrium. Thus option C is false.

For the given condition in the paragraph, the statements (a) and (c) are false. And the statements given in option (b) and (d) are true.

Given data:

Number of atoms in Block A is, 800 atoms.

Initial amount of energy in Block A is, 20 quanta.

Number of atoms in Block B is, 200 atoms.

Initial amount of energy in Block B is, 80 quanta.

We will use the concept of Energy to relate it with the temperature, to solve the given problem. Also, there is some glance about the equilibrium condition as discussed:

Thus, we conclude that for the given condition, the statements (a) and (c) are false. And the statements given in option (b) and (d) are true.

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Answer:

31,360J

Explanation:

Gravitation potential energy (gpe) is calculated from the formula mgh.

That implies, gpe = mgh

Therefore substituting the values of m and h as given in the question, knowing in mine that the acceleration due to gravity( g) is 9.8 N/kg, will give 31,360J

Never forget to put your SI units, because even if your answer is numerical correct, it will be incorrect because it represents no physical quantity.

The gravitational potential energy of the skier at the top of the slope, calculated using the formula PE = mgh, is 31,360 joules.

To find the gravitational potential energy of the skier, we use the formula PE = mgh, where PE is the potential energy, m is the mass, g is the acceleration because of gravity, and h is the height. The acceleration because gravity is 9.8 m/s².

So, we substitute these values into the formula:

PE = (80 kg) × (9.8 m/s²) × (40 m) = 31,360 joules.

Therefore, the gravitational potential energy of the skier before she skips down the slope is 31,360 joules.

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Answer:

l = l0 ( 1 - u^2/v^2) ^0.5

Explanation:

This is the equation of lenght contraction of special relativity

Answer:

a) 351351.35m/s

b) 1.044*10^{-8}kg/C

Explanation:

a) Electric force and magnetic force over the charge must have the same magnitude. From there we can compute the seep of the charge.

[tex]F_E=F_B\\\\qE=qvB\\\\v=\frac{E}{B}=\frac{1.95*10^{5}V/m}{0.555T}=351351.35\frac{m}{s}[/tex]

b) the mass-charge ratio is given by:

[tex]\frac{m}{q}=\frac{rB}{v}=\frac{(6.61*10^{-3}m)(0.555T)}{351351.35m/s}=1.044*10^{-8}\frac{kg}{C}[/tex]

hope this helps!!

Answer:

10

Explanation:

v=f×lander

20=f2

f=10

The potential at x = 1.0 m in the given uniform electric field, with the given parameters, would be 400 V.

The subject question pertains to the concept of electric potential in a uniform electric field. The potential difference, V, in an uniform electric field is given by the equation V = Ed, where E is the field strength and d is the distance. Given an electric field strength, E, of 650 N/C and a potential, V, at x = 3.0 m of 1 700 V, we seek the potential at x = 1.0m. Since the electric field is uniform, we know that the change in potential is linear with distance. Because the distance decreases by 2 meters (from x = 3.0 m to x = 1.0 m), the potential will decrease by E*2, which is 650 N/C * 2 m = 1300 V. So, the potential at x = 1.0 m is 1 700 V - 1 300 V = 400 V.

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To find the electric potential at x = 1.0 m in a uniform electric field directed along the x-axis, subtract the potential difference due to the field over the distance moved from the initial potential; the answer is 400 V.

The question is asking to calculate the electric potential at a certain point given a uniform electric field and an initial electric potential at a different point. To find the potential at x = 1.0 m, we can use the relationship between electric field (E), electric potential (V), and distance (d), with the following formula: V = V_0 - E * d, where V is the potential at the point of interest, V_0 is the initial potential, E is the electric field strength, and d is the distance between the points.

Gor the given electric field of 650 N/C directed parallel to the positive x-axis, and with the potential at x = 3.0 m being 1700 V, the potential difference \\Delta V caused by moving from x = 3.0 m to x = 1.0 m can be calculated by multiplying the electric field strength by the distance over which the field is applied, which is 2.0 m (3.0 m - 1.0 m). Hence, \\Delta V = E * d = 650 N/C * 2.0 m = 1300 V.

Therefore, the potential at x = 1.0 m is V = 1700 V - 1300 V = 400 V.

Answer:

B(2 pi r) = uo i = uo (J pi r^2)

Magnetic field, B = μo Jr/2

Explanation:

The magnitude of the magnetic field inside the wire at a distance r1 < R inside the wire is;

B = ½μ_o × Jr

We want to find the magnitude of the magnetic field inside the wire at a distance r1 < R.

The formula for Magnetic field at a distance r located inside a conductor of radius R is given by Ampere's circuital law as;

B × 2πr = μ_o × Jπr²

Where;

B is magnitude of magnetic field

μ_o is a constant known as magnetic permeability

J is current density

Thus;

B × 2πr = μ_o × Jπr²

πr will cancel out from both sides to give;

2B = μ_o × Jr

B = ½μ_o × Jr

Thus, in conclusion them magnitude of the magnetic field is ½μ_o × Jr

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Answer:

3.6 N

Explanation:

E=F/q

so

F=qxE

F= 9x10^-5x4x10^4

F= 3.6 N

Answer:

Explanation:

For pendulum , time period is

T = 2π √ l / g

T² = 4π² l/ g

l = / g T² / 4π²

= 9.8 x 5² / 4π²

= 6.21 m

Angular impulse = Torque x time

= 30 x 6.21 x .3 = increase in angular momentum

30 x 6.21 x .3 = I ω ; I is moment of inertia and ω is angular velocity .

I ω = 55.89

I = 1/3 m l²

= 1/3 x 5 x 6.21²

= 64.27

Angular kinetic energy = 1/2 I ω²

= 1/2(I ω)²/ I

= .5x 55.89²/ 64.27

= 24.30 J

Due to it , the centre of mass of pendulum increases by height h so that

h = l/2 ( 1 - cos θ )

1/2 I ω² = mg l/2 ( 1 - cos θ)

24.3 = 5 x 9.8 x 3.1 ( 1 - cos θ)

( 1 - cos θ) = .16

cos θ = .84

θ  = 33 degree.

The length of the pendulum is about 6.25m and the maximum angle of displacement would occur when the pendulum is kicked with the maximum force of 30N.

The length of a pendulum is determined by the formula T=2π√(L/g). Given that the period T is 5.0 seconds and g (acceleration due to gravity) is 9.8 m/s², we can rearrange the equation to solve for L (length), resulting in L = (T² * g) / (4π²) = (5.0)² * 9.8 / (4π²) ≈ 6.25m. This regard to the maximum angle of displacement, when a pendulum is in simple harmonic motion, which is typically for displacements less than 15 degrees, the displacement is directly proportional to its force. Therefore, the maximum angle would occur when the force is the greatest, in this case, when the student kicks the pendulum with a force of 30 N.

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Answer:

Explanation:

Given that,

Number of turns

N = 43 turns

Dimensions of rectangle

Length L = 10cm = 0.1m

Width W = 5cm = 0.05

Then, area of rectangle

A = L×W = 0.1 × 0.05 = 0.005m²

Initial magnetic field

Bi = 0T

Final magnetic field

Bf = 0.5T

The displacement time

∆t = 0.431s

Induce emf ε?

EMF is given as

ε = —NdΦ/dt

Where magnetic flux

Φ = BA

Note A is constant

Then,

ε = —NdΦ/dt = —Nd(BA)/dt

ε = —N•A•dB/dt

ε = —N•A•(∆B/∆t)

ε = —N•A•(Bf - Bi) / (∆t)

ε = —43 × 0.005 × (0.5 - 0) /0.431

ε = —43 × 0.005 × 0.5 /0.431

ε = —0.249 V

The average induced EMF is 0.249V

Answer:

(a) 17634.24 Ω

(b) 0.0068 A

Explanation:

(a)

The formula for inductive inductance is given as

X' = 2πFL................... Equation 1

Where X' = inductive reactance, F = frequency, L = inductance

Given: F = 60 Hz, L = 46.8 H, π = 3.14

Substitute into equation 1

X' = 2(3.14)(60)(46.8)

X' = 17634.24 Ω

(b)

From Ohm's law,

Vrms = X'Irms

Where Vrms = Rms Voltage, Irms = rms Current.

make Irms the subject of the equation

Irms = Vrms/X'...................... Equation 2

Given: Vrms = 120 V, X' = 17634.24 Ω

Substitute into equation 2

Irms = 120/17634.24

Irms = 0.0068 A

Answer:

0.83 ω

Explanation:

mass of flywheel, m = M

initial angular velocity of the flywheel, ω = ωo

mass of another flywheel, m' = M/5

radius of both the flywheels = R

let the final angular velocity of the system is ω'

Moment of inertia of the first flywheel , I = 0.5 MR²

Moment of inertia of the second flywheel, I' = 0.5 x M/5 x R² = 0.1 MR²

use the conservation of angular momentum as no external torque is applied on the system.

I x ω = ( I + I') x ω'

0.5 x MR² x ωo = (0.5 MR² + 0.1 MR²) x ω'

0.5 x MR² x ωo = 0.6 MR² x ω'

ω' = 0.83 ω

Thus, the final angular velocity of the system of flywheels is 0.83 ω.