The magnitude of the magnetic flux through the surface of a circular plate is 6.80 10-5 T · m2 when it is placed in a region of uniform magnetic field that is oriented at 43.0° to the vertical. The radius of the plate is 8.50 cm. Determine the strength of the magnetic field. mT A circular plate of radius r is lying flat. A field of arrows labeled vector B rising up and to the right pass through the plate.

Answer:

12.5 rad/s²

Explanation:

Angular Acceleration: This can be defined as the ratio of linear acceleration and radius. The S.I unit is rad/s²

From the question,

a = αr................... Equation 1

Where a = linear acceleration, α = angular acceleration, r = radius.

But,

a = (v-u)/t.............. Equation 2

Where v = final velocity, u = initial velocity, t = time.

Substitute equation 2 into equation 1

(v-u)/t = αr

make α the subject of the equation

α = (v-u)/tr................. Equation 3

Given: v = 30 m/s, u = 0 m/s, t = 6 s, r = 0.4 m

Substitute into equation 3

α = (30-0)/(0.4×6)

α = 30/2.4

α = 12.5 rad/s²

Answer:

141178.8

Explanation:

use : density x velocity²

1.2 x 343² = 141178.8 pa

Answer:

[tex]v_i = 1.44\frac{m}{s}[/tex]

Explanation:

The computation of the initial velocity of the fly is shown below:-

But before that we need to do the following calculations

For 4.22 seconds

[tex]\bar v = \frac{-5.80 m}{4.22 s}[/tex]

[tex]= -1.37\frac{m}{s}[/tex]

For uniform acceleration

[tex]\bar v = \frac{v_i +v_f}{2}[/tex]

[tex]= v_i + v_f[/tex]

[tex]= -2.74\frac{m}{s}[/tex]

With initial and final velocities

[tex]= -1.33\frac{m}{s^2}[/tex]

[tex]= \frac{v_i +v_f}{4.22s}[/tex]

[tex]= -v_i + v_f[/tex]

[tex]= -5.61\frac{m}{s}[/tex]

So, the initial velocity is

[tex]v_i = 1.44\frac{m}{s}[/tex]

We simply applied the above steps to reach at the final solution i.e initial velocity

Answer:

(a)    f = 0.58Hz

(b)    vmax = 0.364m/s

(c)    amax = 1.32m/s^2

(d)    E = 0.1J

(e)    [tex]x(t)=0.1m\ cos(2\pi(0.58s^{-1})t)[/tex]

Explanation:

(a) The frequency of the oscillation, in a spring-mass system, is calulated by using the following formula:

[tex]f=\frac{1}{2\pi}\sqrt{\frac{k}{m}}[/tex]          (1)

k: spring constant = 20.0N/m

m: mass = 1.5kg

you replace the values of m and k for getting f:

[tex]f=\frac{1}{2\pi}\sqrt{\frac{20.0N/m}{1.5kg}}=0.58s^{-1}=0.58Hz[/tex]

The frequency of the oscillation is 0.58Hz

(b) The maximum speed is given by:

[tex]v_{max}=\omega A=2\pi f A[/tex]     (2)

A: amplitude of the oscillations = 10.0cm = 0.10m

[tex]v_{max}=2\pi (0.58s^{-1})(0.10m)=0.364\frac{m}{s}[/tex]

The maximum speed of the mass is 0.364 m/s.

The maximum speed occurs when the mass passes trough the equilibrium point of the oscillation.

(c) The maximum acceleration is given by:

[tex]a_{max}=\omega^2A=(2\pi f)^2 A[/tex]

[tex]a_{max}=(2\pi (0.58s^{-1}))(0.10m)=1.32\frac{m}{s^2}[/tex]

The maximum acceleration is 1.32 m/s^2

The maximum acceleration occurs where the elastic force is a maximum, that is, where the mass is at the maximum distance from the equilibrium point, that is, the acceleration.

(d) The total energy of the system is:

[tex]E=\frac{1}{2}kA^2=\frac{1}{2}(20.0N/m)(0.10m)^2=0.1J[/tex]

The total energy is 0.1J

(e) The displacement as a function of time is:

[tex]x(t)=Acos(\omega t)=Acos(2\pi ft)\\\\x(t)=0.1m\ cos(2\pi(0.58s^{-1})t)[/tex]

Answer:

[tex]\frac{50}{\pi }[/tex]Hz

Explanation:

In alternating current (AC) circuits, voltage (V) oscillates in a sine wave pattern and has a general equation as a function of time (t) as follows;

V(t) = V sin (ωt + Ф)            -----------------(i)

Where;

V = amplitude value of the voltage

ω = angular frequency = 2 π f        [f = cyclic frequency or simply, frequency]

Ф = phase difference between voltage and current.

Now,

From the question,

V(t) = 230 sin (100t)              ---------------(ii)

By comparing equations (i) and (ii) the following holds;

V = 230

ω = 100

Ф = 0

But;

ω = 2 π f = 100

2 π f = 100             [divide both sides by 2]

π f = 50

f = [tex]\frac{50}{\pi }[/tex]Hz

Therefore, the frequency of the voltage is [tex]\frac{50}{\pi }[/tex]Hz

Answer:

same direction = 80 (n)

opposite direction = 20 (n) going one direction

Explanation:

same direction means they are added to each other

and opposite means acting on eachother

Answer:

5

Explanation:

Answer:

STATIC,  STATIC

KINETIC friction is less than static friction

Explanation:

In this exercise you are asked to complete the sentences with the correct words.

STATIC friction prevents the relative movement of two surfaces in contact.

For moving surfaces the friction is STATIC is greater than the kinetic friction.

For the last two sentences I think they are misspelled, the correct thing is

KINETIC friction is less than static friction

Answer:

Explanation:

Given that

speed u=4*10^6 m/s

electric field E=4*10^3 N/c

distance b/w the plates d=2 cm

basing on the concept of the electrostatices

now we find the acceleration b/w the plates

acceleration a=qE/m=1.6*10^-19*4*10^3/9.1*10^-31=0.7*10^15 =7*10^14 m/s

now we find the horizantal distance travelled by electrons hit the plates

horizantal distance X=u[2y/a]^1/2

=4*10^6[2*2*10^-2/7*10^14]^1/2

=3*10^-2=3 cm

now we find the velocity f the electron strike the plate

v^2-(4*10^6)^2=2*7*10^14*2*10^-2

v^2=16*10^12+28*10^12

v^2=44*10^12

speed after hits =>V=6.6*10^6 m/s

Answer:

The speed of the rod is 1.383 m/s

Explanation:

Given;

length of the conducting rod, L = 31 cm = 0.31 m

induced emf on the rod, emf = 0.75V

magnetic field around the rod, B = 1.75 T

Apply the following Faraday's equation for electromagnetic induction in a moving rod to determine the speed of the rod.

emef = BLv

where;

B is the magnetic field

L is length of the rod

v is the speed of the rod

v = emf / BL

v = (0.75) / (1.75 x 0.31)

v = 1.383 m/s

Therefore, the speed of the rod is 1.383 m/s

Answer:

The rate at which energy is dissipated in the resistor is equal to the rate at which energy is stored in the inductor's magnetic field in 24.95 ms.

Explanation:

The energy stored in the inductor is given as

E₁ = ½LI²

The rate at which energy is stored in the inductor is

(dE₁/dt) = (d/dt) (½LI²)

Since L is a constant

(dE₁/dt) = ½L × 2I (dI/dt) = LI (dI/dt)

(dE₁/dt) = LI (dI/dt)

Rate of Energy dissipated in a resistor = Power = I²R

(dE₂/dt) = I²R

When the rate at which energy is dissipated in the resistor equal to the rate at which energy is stored in the inductor's magnetic field

(dE₁/dt) = (dE₂/dt)

OK (dI/dt) = I²R

L (dI/dt) = IR

Current in a this kind of series setup of inductor and resistor at any time, t, is given as

I = (V/R) (1 - e⁻ᵏᵗ)

k = (1/time constant) = (R/L)

(dI/dt) = (kV/R) e⁻ᵏᵗ = (RV/RL) e⁻ᵏᵗ = (V/L) e⁻ᵏᵗ

L (dI/dt) = IR

L [(V/L) e⁻ᵏᵗ] = R [(V/R) (1 - e⁻ᵏᵗ)

V e⁻ᵏᵗ = V (1 - e⁻ᵏᵗ)

e⁻ᵏᵗ = 1 - e⁻ᵏᵗ

2 e⁻ᵏᵗ = 1

e⁻ᵏᵗ = (1/2) = 0.5

e⁻ᵏᵗ = 0.5

In e⁻ᵏᵗ = In 0.5 = -0.69315

- kt = -0.69315

kt = 0.69315

k = (1/time constant)

Time constant = 36.0 ms = 0.036 s

k = (1/0.036) = 27.78

27.78t = 0.69315

t = (0.69315/27.78) = 0.02495 = 24.95 ms

Hope this Helps!!!

Answer:

The potential at the center of the sphere is -924 V

Explanation:

Given;

radius of the sphere, R = 0.22 m

electric field at the surface of the sphere, E = 4200 N/C

Since the electric field is directed towards the center of the sphere, the charge is negative.

The Potential is the same at every point in the sphere, and it is given as;

[tex]V = \frac{1}{4 \pi \epsilon_o} \frac{q}{R}[/tex] -------equation (1)

The electric field on the sphere is also given as;

[tex]E = \frac{1}{4 \pi \epsilon _o} \frac{|q|}{R^2}[/tex]

[tex]|q |= 4 \pi \epsilon _o} R^2E[/tex]

Substitute in the value of q in equation (1)

[tex]V = \frac{1}{4 \pi \epsilon_o} \frac{-(4 \pi \epsilon _o R^2E)}{R} \ \ \ \ q \ is \ negative\ because \ E \ is\ directed \ toward \ the \ center\\\\V = -RE\\\\V = -(0.22* 4200)\\\\V = -924 \ V[/tex]

Therefore, the potential at the center of the sphere is -924 V

Answer:

v(t) = s′(t) = −9sin(t)+9cos(t)

a(t) = v′(t) = −9cos(t) −9sin(t)

Explanation:

Given that

s = 9 cos(t) + 9 sin(t), t ≥ 0

Then acceleration and velocity is

v(t) = s′(t) = −9sin(t)+9cos(t)

a(t) = v′(t) = −9cos(t) −9sin(t)

Answer:

Muons reach the earth in great amount due to the relativistic time dilation from an earthly frame of reference.

Explanation:

Muons travel at exceedingly high speed; close to the speed of light. At this speed, relativistic effect starts to take effect. The effect of this is that, when viewed from an earthly reference frame, their short half life of about two-millionth of a second is dilated. The dilated time, due to relativistic effects on time for travelling at speed close to the speed of light, gives the muons an extended relative travel time before their complete decay. So in reality, the muon do not have enough half-life to survive the distance from their point of production high up in the atmosphere to sea level, but relativistic effect due to their near-light speed, dilates their half-life; enough for them to be found in sufficient amount at sea level.  

Answer:

[tex]\large \boxed{\text{3.3 cm}^{3}}[/tex]

Explanation:

Assume the stone consists of basalt, which has a density of 3.0 g/cm³.

[tex]\rho = \text{10 g}\times\dfrac{\text{1 cm}^{3}}{\text{3.0 g}} = \text{3.3 cm}^{3}\\\\\text{The volume of the stone is $\large \boxed{\textbf{3.3 cm}^{3}}$}[/tex]

Answer:

-1748*10^N/C

Explanation:

See attached file

Complete question:

A solid conducting sphere is placed in an external uniform electric field. With regard to the electric field on the sphere's interior, which statement is correct?

A. the interior field points in a direction parallel to the exterior field

B. There is no electric field on the interior of the conducting sphere.

C. The interior field points in a direction perpendicular to the exterior field.

D. the interior field points in a direction opposite to the exterior field.

Answer:

B. There is no electric field on the interior of the conducting sphere.

Explanation:

Conductors are said to have free charges that move around easily. When the conductor is now placed in a static electric field, the free charges react to attain electrostatic equilibrium (steady state).

Here, a solid conducting sphere is placed in an external uniform electric field. Until the lines of the electric field are perpendicular to the surface, the free charges will move around the spherical conductor, causing polarization. There would be no electric field in the interior of the spherical conductor because there would be movement of  free charges in the spherical conductor in response to any field until its neutralization.

Option B is correct.

There is no electric field on the interior of the conducting sphere.

Answer:

-   maximum displacement = 3.00nm

-   λ = 1.79m

-  f = 286.47 s^-1

Explanation:

You have the following equation for a sound wave:

[tex]s(x,t)=3.00nm\ cos(3.50m^{-1}x- 1,800s^{-1} t)[/tex]              (1)

The general form of the equation of a sound wave can be expressed as the following formula:

[tex]s(x,t)=Acos(kx-\omega t)[/tex]            (2)

A: amplitude of the wave = 3.00nm

k: wave number = 3.50m^-1

w: angular frequency = 1,800s^-1

- The maximum displacement of the wave is given by the amplitude of the wave, then you have:

maximum displacement = A = 3.00nm

- The wavelength is given by :

[tex]\lambda=\frac{2\pi}{k}=\frac{2\pi}{3.50m^{-1}}=1.79m[/tex]

The values for the wavelength is 1.79m

- The frequency is:

[tex]f=\frac{\omega}{2\pi}=\frac{1,800s^{-1}}{2\pi}=286.47s^{-1}[/tex]

The frequency is 286.47s-1

Answer:

It is calculated as Force × perpendicular distance.

Explanation:

Torque is a rotational force and twisting force that can cause an object to rotate in it's axis. This cause angular rotation.

The torque due to gravity on a body about its centre of mass is zero because the centre of mass is the that point of the body at which the force acts by the gravity that is mg.

But if the pivot point of a balance is not at the centre of mass of the balance, it will be FORCE × PERPENDICULAR DISTANCE because at that point, there is no centre in which the force act on a body by gravity. The distance and force will be use to calculate.

Answer:

A pie chart is a type of graph in which a circle is divided into sectors that each represents a proportion of the whole

Explanation:

pie charts are a useful way to organize data in order to see the size of components relative to the whole.

Answer:

Pls see attached file

Explanation:

Answer:

Q = 23.49 C

Explanation:

We have,

Electric current drawn by the air conditioner is 16.2 A

Time, t = 1.45 s

It is required to find the electric charge passes through the circuit during this period. We know that electric current is defined as the electric charge flowing per unit time. So,

[tex]I=\dfrac{q}{t}\\\\q=It\\\\q=16.2\times 1.45\\\\q=23.49\ C[/tex]

So, the charge of 23.49 C is passing through the circuit during this period.

Answer:

E = - dV/dx

Explanation:

Las superficies equipòtenciales son superficie donde el potencial eléctrico es constante por lo cual nos podemos desplazaren ella sin realizar nigun trabajo.

El campo electrico es el campo que existen algún punto en el espacio creado por alguna ddistribucion de carga.

De los antes expuesto las dos magnitudes están relacionadas

         E = - dV/dx

por lo cual el potenical es el gradiente del potencial eléctrico.

Como el campo eléctrico sobre un superficie equipotenciales constante, podemos colocar una punta de prueba con un potencial dado y seguir la linea que de una diferencia de potencial constar, lo cual permite visualizar las forma de cada linea equipotencial

Answer:

1/4 of its original value

Explanation:

Newton's law of universal gravitation states that when two bodies of masses M₁ and M₂ interact, the force of attraction (F) between these bodies is directly proportional to the product of their masses and inversely proportional to the square of the distance (r) between these bodies. i.e

F ∝ [tex]\frac{M_1 M_2}{r^2}[/tex]       ------------(i)

From the equation above, it can be deduced that;

F ∝ [tex]\frac{1}{r^2}[/tex]

=> F = G [tex]\frac{1}{r^2}[/tex]       -----------(ii)

Where;

G = constant of proportionality called the gravitational constant

Equation (ii) can be re-written as

Fr² =  G

=> F₁r₁² = F₂r₂²              -----------(iii)

Where;

F₁ and r₁ are the initial values of the force and distance respectively

F₂ and r₂ are the final values of the force and distance respectively

From the question, if the distance doubles i.e;

r₂ = 2r₁,

Then the final value of the gravitational force F₂ is calculated as follows;

Substitute the value of r₂ = 2r₁ into equation (iii) as follows;

F₁r₁² = F₂(2r₁)²

F₁r₁² = 4F₂r₁²          [Divide through by r₁²]

F₁ = 4F₂                 [Make F₂ subject of the formula]

F₂ = F₁ / 4              [Re-write this]

F₂ = [tex]\frac{1}{4} F_1[/tex]

Therefore the gravitational force will be 1/4 of its original value when the distance between the bodies doubles.

Answer:

for the first interference m = 1   y = 2,839 10-3 m

for the second interference m = 2   y = 5,678 10-3 m

Explanation:

The double slit interference phenomenon, for constructive interference is described by the expression

                d sin θ = m λ

where d is the separation between the slits, λ the wavelength and m an integer that corresponds to the interference we see.

In these experiments in general the observation screen is L >> d, let's use trigonometry to find the angles

           tan θ = y / L

with the angle it is small,

          tan θ = sin θ / cos θ = sin θ

we substitute

         sin θ = y / L

         d y / L = m λ

the distance between the central maximum and an interference line is

        y = m λ L / d

let's reduce the magnitudes to the SI system

     λ = 546 nm = 546 10⁻⁹ m

     d = 0.25 mm = 0.25 10⁻³ m

let's substitute the values

      y = m 546 10⁻⁹ 1.3 / 0.25 10⁻³

      y =  m 2,839 10⁻³

the explicit value for a line depends on the value of the integer m, for example

for the first interference m = 1

the distance from the central maximum to the first line is y = 2,839 10-3 m

for the second interference m = 2

the distance from the central maximum to the second line is y = 5,678 10-3 m

Answer:

Explanation:

In a conductor, electric current can flow freely, in an insulator it cannot.

Metals such as copper typify conductors, while most non-metallic solids are said to be good insulators, having extremely high resistance to the flow of charge through them.

Most atoms hold on to their electrons tightly and are insulators.

Answer:

Explanation:

v= u + at

v is final velocity , u is initial velocity . a is acceleration and t is time

Initial velocity u = 0 . Putting the given values in the equation

v = 0 + g sin 18 x 3.5

= 10.6 m /s

For a skateboarder who starts from the rest, the speed when he reaches the bottom of the ramp will be 10.6 m/s.

The term "velocity" refers to a vector measurement of the rate and direction of motion. Velocity is the rate of movement in a single direction, to put it simply. Velocity can be used to determine how fast a rocket is heading into space and how fast a car is moving north on a congested motorway.

There are several types of velocity :

The pace at which a person's velocity changes is known as acceleration. This implies that an object is accelerating if its velocity is rising or falling. An object that is accelerating won't have a steady change in location every second like an item moving at a constant speed does.

According to the question, the given values are :

Time, t = 3.50 sec

Initial Velocity, u = 0 m/s

Use equation of motion :

v = u+at

v = 0+ g sin 18 × 3.5

v = 10.6 m/s.

So, the final velocity will be 10.6 m/s.

To get more information about Velocity and Acceleration :

https://brainly.com/question/14683118

#SPJ2

Complete Question:

A 0.50-kg ball that is tied to the end of a 1.5-m light cord is revolved in a horizontal plane, with the cord making a 30° angle with the vertical.

(a) Determine the ball’s speed. (b) If, instead, the ball is revolved so that its

speed is 3.7 m/s, what angle does the cord make with the vertical?

(Check attached image for the diagram.)

Answer:

(a) The ball’s speed, v = 2.06 m/s

(b) The angle the cord makes with the vertical is 50.40⁰

Explanation:

If the ball is revolved in a horizontal plane, it will form a circular trajectory,

the radius of the circle, R = Lsinθ

where;

L is length of the string

The force acting on the ball is given as;

F = mgtanθ

This above is also equal to centripetal force;

[tex]mgTan \theta = \frac{mv^2}{R} \\\\Recall, R = Lsin \theta\\\\mgTan \theta = \frac{mv^2}{Lsin \theta}\\\\v^2 = glTan \theta sin \theta\\\\v = \sqrt{glTan \theta sin \theta} \\\\v = \sqrt{(9.8)(1.5)(Tan30)(sin30)} \\\\v = 2.06 \ m/s[/tex]

(b) when the speed is 3.7 m/s

[tex]v = \sqrt{glTan \theta sin \theta} \ \ \ ;square \ both \ sides\\\\v^2 = glTan \theta sin \theta\\\\v^2 = gl(\frac{sin \theta}{cos \theta}) sin \theta\\\\v^2 = \frac{gl*sin^2 \theta}{cos \theta} \\\\v^2 = \frac{gl*(1- cos^2 \theta)}{cos \theta}\\\\gl*(1- cos^2 \theta) = v^2cos \theta\\\\(9.8*1.5)(1- cos^2 \theta) = (3.7^2)cos \theta\\\\14.7 - 14.7cos^2 \theta = 13.69cos \theta\\\\14.7cos^2 \theta + 13.69cos \theta - 14.7 = 0 \ \ \ ; this \ is \ quadratic \ equation\\\\[/tex]

[tex]Cos\theta = \frac{13.69\sqrt{13.69^2 -(-4*14.7*14.7)} }{14.7} \\\\Cos \theta = 0.6374\\\\\theta = Cos^{-1}(0.6374)\\\\\theta = 50.40 ^o[/tex]

Therefore, the angle the cord makes with the vertical is 50.40⁰

Answer:

Explanation:

given:

radius (r) = 1.88 km

velocity (v) = 136.3 km/hr

required:

banking angle ∡ ?

first:

convert 1.88 km to m = 1.88km * 1000m / 1km

r = 1880 m

convert velocity v = 136.3 km/hr to m/s = 136.3 km/hr * (1000 m/ 3600s)

v = 37.86 m/s

now.. calculate the angle

Ф = inv tan (v² / r * g)            we know that gravity = 9.8 m/s²

Ф = inv tan (37.86² / (1880 * 9.8))

Ф = 4.4°