A factory has a machine which bends wire at a rate of 9 unit(s) of curvature per second. How long does it take to bend a straight wire into a circle of radius 2

Answer:

Explanation:

The magnetic field produced is expressed using the formula

[tex]B = \frac{\mu_0NI}{L}[/tex]

B is the magnetic field = 0.30T

I is the current produced in the coil = 4.5A

[tex]\mu_0[/tex] is the magnetic permittivity in vacuum = 1.26*10^-6Tm/A

L is the length of the solenoid = 32 cm = 0.32 m

N is the number of turns in the solenoid.

Making N the subject of the formula from the equation above;

[tex]B = \frac{\mu_0NI}{L}\\\\BL = \mu_0NI\\\\Dividing\ both\ sides \ by \ \mu_0I\\\\\frac{BL}{\mu_0I} =\frac{\mu_oNI}{\mu_0I} \\\\[/tex]

[tex]N = \frac{BL}{\mu_0I}[/tex]

Substituting the give values to get N;

[tex]N = \frac{0.3*0.32}{1.26*10^{-6} * 4.5}\\\\N = \frac{0.096}{0.00000567} \\\\N = 16,931.21[/tex]

The number of turns the solenoid must have is approximately 16,931 turns

Answer:

The work done by both Joel and Jerry is equal to 0 J.

Explanation:

The work done on a body by an external agency is the product of the force applied on the body and the distance through which the body moves. Therefore,

W = F.d

where,

W = Work Done on the Body

F = Force Applied on the Body

d = displacement covered by the body

In the given case of both Joel and Jerry, they are unable to move the car. It means that the displacement covered by the car is zero. Hence,

W = F(0)

W = 0 J (For both Joel and Jerry)

Answer:

The magnitude of the magnetic field will act in a direction towards me.

Explanation:

When a charged particle enters a magnetic field, it is deflected. The direction of travel of the particle is deflected, but the kinetic energy of the particle is not affected. The force experienced by a charged particle as it enters a magnetic field that acts perpendicular to the path of the velocity of the particle, will produce a force that is perpendicular to both the direction of travel of the particle and the direction of the magnetic field. In this case, the proton moves in the y-direction, the magnetic field is in the x-direction, therefore the force experienced by the particle will be towards me.

Answer:

The product of the object's weight and the horizontal distance between the two positions.

Explanation:

Work is the product of force and the distance through which this force is moved. The distance moved can be vertical, or horizontal. For two bodies located the same distance from the center of the earth, the work done will be the product of the weight of the product and the horizontal distance between the two positions. If the vertical work is needed, then the work is zero, since there is no height gradient between them.

Answer:

Explanation:

Average power done by the torque is expressed as the ratio of the workdone by the toque to time.

Power = Workdone by torque/time

Workdone by the torque = [tex]\tau \theta[/tex] = [tex]I\alpha * \theta[/tex]

I is the rotational inertia = 16kgm²

[tex]\theta = angular\ displacement[/tex]

[tex]\theta = 2 rev = 12.56 rad[/tex]

[tex]\alpha \ is \ the\ angular\ acceleration[/tex]

To get the angular acceleration, we will use the formula;

[tex]\alpha = \frac{\omega_f^2- \omega_i^2}{2\theta}[/tex]

[tex]\alpha = \frac{9.0^2- 7.0^2}{2(12.54)}\\\alpha = 1.28\ rad/s^{2}[/tex]

Workdone by the torque = 16 * 1.28 * 12.56

Workdone by the torque = 257.23 Joules

Average power done by the torque = Workdone by torque/time

=  257.23/2.0

= 128.61 Watts

Explanation:

We have

A simple pendulum is observed to swing through 71 complete oscillations in a time period of 1.80 min.

The frequency of a pendulum is equal to the no of oscillation per unit time. so,

[tex]f=\dfrac{N}{t}\\\\f=\dfrac{71}{1.8\times 60}\\\\f=0.65\ Hz[/tex]

Tim period is reciprocal of frequency. So,

[tex]T=\dfrac{1}{0.65}\\\\T=1.53\ s[/tex]

The time period of a pendulum is given by :

[tex]T=2\pi \sqrt{\dfrac{l}{g}}[/tex]

l is length of pendulum

[tex]l=\dfrac{T^2g}{4\pi ^2}\\\\l=\dfrac{T^2g}{4\pi ^2}\\\\l=\dfrac{(1.53)^2\times 9.8}{4\pi ^2}\\\\l=0.58\ m[/tex]

So, the period and length of the pendulum are 1.53 s and 0.58 m respectively.

Answer:

I2 = 3.076 A

Explanation:

In order to calculate the current in the second loop, you take into account that the magnitude of the magnetic field at the center of the ring is given by the following formula:

[tex]B=\frac{\mu_oI}{2R}[/tex]        (1)

I: current in the wire

R: radius of the wire

μo: magnetic permeability of vacuum = 4π*10^-7 T/A

In the case of the two wires with opposite currents and different radius, but in the same plane, you have that the magnitude of the magnetic field at the center of the rings is:

[tex]B_T=\frac{\mu_oI_1}{2R_1}-\frac{\mu_oI_2}{2R_2}[/tex]         (2)

I1: current of the first ring = 8A

R1: radius of the first ring = 0.078m

I2: current of the second ring = ?

R2: radius of the first second = 0.03m

To find the values of the current of the second ring, which makes the magnitude of the magnetic field equal to zero, you solve the equation (2) for I2:

[tex]\frac{\mu_oI_2}{2R_2}=\frac{\mu_oI_1}{2R_1}\\\\I_2=I_1\frac{R_2}{R_1}=(8A)\frac{0.03m}{0.078m}=3.076A[/tex]

The current of the second ring is 3.076A and makes that the magntiude of the total magnetic field generated for both rings is equal to zero.

Answer:

the answer is option A = photoelectric effect

Explanation:

If the threshold frequency of a metal is lower than the energy of X-rays, then photoelectric effect will happen.

Answer:

(a) 0.31

(b) 0.245

Explanation:

(a)

F' = μ'mg.................... Equation 1

Where F' = Horizontal Force required to set the block in motion, μ' = coefficient of static friction, m = mass of the block, g = acceleration due to gravity.

make μ' the subject of the equation above

μ' = F'/mg............. Equation 2

Given: F' = 75 N, m = 25 kg

constant: g = 9.8 m/s²

Substitute these values into equation 2

μ' = 75/(25×9.8)

μ' = 75/245

μ' = 0.31.

(b) Similarly,

F = μmg.................. Equation 3

Where F = Horizontal force that is required to keep the block moving with constant speed, μ = coefficient of kinetic friction.

make μ the subject of the equation

μ = F/mg.............. Equation 4

Given: F = 60 N, m = 25 kg, g = 9.8 m/s²

Substitute these values into equation 4

μ  = 60/(25×9.8)

μ = 60/245

μ = 0.245

Answer:

  I = 0.2934 I₀

Explanation:

The expression that governs the transmission of polarization is

         I = I₀ cos² θ

Let's apply this to our case, when the unpolarized light enters the first polarized, the polarized light that comes out has the intensity of

        I₁ = I₀ / 2

this is the light that enters the second polarizer

        I = I₁ cos² θ  

we substitute

        I = I₀ / 2 cos² 40

        I = I₀ 0.2934

        I = 0.2934 I₀

Answer:A

Explanation:

Explanation:

Given that,

Gravitational force = 600 N

Frictional force = 25 N

Pulled by the Force = 250 N

We know that,

The gravitational force in downward and normal force act in upward. the frictional force in left side and the box pulled by the force to the right side.

The balance equation is along y-axis

The box will not move in y-axis therefore, the net force in the y-axis will be zero.

Hence, The net force in the y-direction will be zero.

Answer:

Doppler Radar gathers information about precipitation by sending out pulses of ___Radio wave___ energy

Answer:

The number of turns of the solenoid is 3536 turns

Explanation:

Given;

magnetic field of the solenoid, B = 0.1 T

current in the solenoid, I = 1.8 A

length of the solenoid, L = 8cm = 0.08m

The magnetic field near the center of the solenoid is given by;

B = μ₀nI

Where;

μ₀ is permeability of free space = 4π x 10⁻⁷ m/A

n is number of turns per length

I is the current in the coil

The number of turns per length is calculated as;

n = B / μ₀I

n = (0.1 ) / (4π x 10⁻⁷ x 1.8)

n = 44203.95 turns/m

The number of turns is calculated as;

N = nL

N = (44203.95)(0.08)

N = 3536 turns

Therefore, the number of turns of the solenoid is 3536 turns

Answer:

The additional force is  [tex]F_3 = 120 \ N[/tex]

Explanation:

From the question we are told that

      The horizontal force in one direction is  [tex]F_i = 480 \ N[/tex]

       The horizontal force in the opposite direction is  [tex]F_f = -600 \ N[/tex]

The negative sign shows that it is acting in the opposite direction

Generally for the box to remain stationary the net force on it must be equal to zero  that is  

        [tex]F_1 + F_2 +F_3 = 0[/tex]

Where [tex]F_3[/tex] is the additional force required  

    So

          [tex]F_3 = -F_1 - F_2[/tex]

substituting values

         [tex]F_3 = -480 - [-600][/tex]

        [tex]F_3 = -480 + 600[/tex]

       [tex]F_3 = 120 \ N[/tex]

Answer:

the electric field is pointing horizontal direction and in south direction

Explanation:

In an electromagnetic wave, the magnetic field and electrical field are perpendicular to each other and these are perpendicular to the direction of the waves.

Answer:

 The magnitude of the electric force is  [tex]F_e = 0.00098 \ N[/tex]

Explanation:

From the question we are told that

    The  mass of the paper is  [tex]m= 100 mg = 100 *10^{-6} \ kg[/tex]

    The  position is  [tex]d = 8.0\ mm = 0.008 \ m[/tex]

Generally the magnitude of the  electric force at the point of equilibrium between the electric force and the gravitational force is  mathematically represented as  

         [tex]F_e = F_g = mg[/tex]

Where  [tex]F_g[/tex] is gravitational force

   substituting values

         [tex]F_e = 100 *10^{-6} * 9.8[/tex]

         [tex]F_e = 0.00098 \ N[/tex]

Now generally the gravitational force acts downward (negative y axis ) hence the reason the electric force is same magnitude but opposite in direction (upward  + y - axis  )

Answer:

1.99*10-4sec

Explanation:

Signal propagation speed=0.82∗2.46∗108m/s

d=2000 m

Tp=20000/0.82∗2.46∗108 sec

ContentionPeriod=2Tp=2∗20000/0.82∗2.46∗10^8

= 1.99* 10^-4seconds

Answer:

A. b) Directed towards center

B. [tex]v = 7.854\ m/s[/tex]

C. [tex]a_c = 12.337\ m/s^2[/tex]

D. [tex]w = 1.57\ rad/s[/tex]

Explanation:

The "force" that they feel pressing their backs against the wall is because the reaction to the  centripetal acceleration .

A.

This acceleration has its direction towards the center of the circle. (option b)

B.

Their linear speed can be calculated with the equation:

[tex]v = (\theta/t)*r[/tex]

Where [tex]\theta[/tex] is the total angular position moved in radians ([tex]1\ rev = 2\pi\ radians[/tex]), 't' is the time elapsed for the angular position moved and 'r' is the radius. So we have that:

[tex]v = (2\pi/4)*5 = 7.854\ m/s[/tex]

C.

The centripetal acceleration is given by the equation:

[tex]a_c = v^2/r[/tex]

[tex]a_c = 7.854^2/5[/tex]

[tex]a_c = 12.337\ m/s^2[/tex]

D.

Their angular speed is given by the equation:

[tex]w = \theta/t = 2\pi/4 = \pi/2 = 1.57 \ rad/s[/tex]

Answer:

Explanation:

F ×1 = 0.5×0.145×47×47

F = 160.15 N

Answer:

The distance from the pivot point that the small child will sit in order to maintain the balance is 1.8 m

Explanation:

Given;

mass of the bigger child, M = 30 kg

mass of the smaller child, m = 20 kg

distance between the two children, d = 3 m

This information can be represented diagrammatically;

                                    3m

         |<------------------------------------------------>|

----------------------------------------------------------------------------

         ↓             x            Δ            3-x           ↓

         20kg                                                 30kg

x is the distance from the pivot point that the small child will sit in order to maintain the balance

Take moment about the pivot;

Clockwise moment = anticlockwise moment

30(3-x) = 20x

90 -30x = 20x

90 = 20x + 30x

90 = 50x

x = 90 / 50

x = 1.8 m

Therefore, the distance from the pivot point that the small child will sit in order to maintain the balance is 1.8 m

The distance from the pivot point which the small child must sit in order to maintain the balance is 1.8 meters.

Given the following data:

To determine what distance from the pivot point is the small child sitting in order to maintain the balance, we would take moment about a pivot:

Note: The distance of the child from the pivot is equal to [tex]3-n[/tex]

For moment:

Clockwise moment = anticlockwise moment

[tex]30(3-n) = 20n\\\\90-30n=20n\\\\90=20+30n\\\\90=50n\\\\n=\frac{90}{50}[/tex]

n = 1.8 meters

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Answer:

Explanation:

For the problem, we should have same reynolds number

ρvd/mu = constant

1000×1×10⁻³×0.3×10⁻³/1.002×10⁻³ = 1400×0.5×d/600

d = 25.66 cm

Answer:

Explanation:

Hope this helped,

Kavitha

Answer:

a. the bottom medium

Explanation:

it has the least index of refraction and hence most rarer.

Answer:

Explanation:

A )

electric field E = V / d where V is potential difference between plates separated by distance d .

putting the given values

E = 370 / .040  V / m

= 9250 V / m

B )

Force on charged particle of charge q in electric field E

F = q E

F = 2.4 x 10⁻⁹ x 9250

= 22200 x 10⁻⁹

= 222 x 10⁻⁷ N .

C ) since field is uniform , force will be constant

work done by electric field putting up this force

= force x displacement

= 222 x 10⁻⁷  x 40 x 10⁻³

= 888 x 10⁻⁹ J

D )

change in potential energy

= q ( V₁ - V₂ )

= 2.40 X 10⁻⁹ x 370

= 888 x 10⁻⁹ J .

(a) The magnitude of electric field in the region between the plates is 9,250 V/m.

(b) The magnitude of the force the field exerts on a particle with the given charge is 2.22 x 10⁻⁵ N.

(c) The work done by the field on the particle as it moves from the higher potential plate to the lower is [tex]8.88 \times 10^{-7} \ J[/tex].

(d) the change of the potential energy is [tex]8.88 \times 10^{-7} \ J[/tex].

The given parameters;

(a) The magnitude of electric field in the region between the plates is calculated as;

[tex]E = \frac{V}{d} \\\\E = \frac{370 }{40 \times 10^{-3} } \\\\E = 9,250 \ V/m[/tex]

(b) The magnitude of the force the field exerts on a particle with the given charge is calculated as follows;

F = Eq

F = 9,250 x 2.4 x 10⁻⁹

F = 2.22 x 10⁻⁵ N

(c) The work done by the field on the particle as it moves from the higher potential plate to the lower is calculated as follows;

[tex]W = Fd\\\\W = 2.22 \times 10^{-5} \times 40\times 10^{-3} \\\\W =8.88 \times 10^{-7} \ J[/tex]

(d) the change of the potential energy is calculated as;

[tex]\Delta U = q \Delta V\\\\\Delta U = q(V_1 - V_2)\\\\\\Delta U = 2.4 \times 10^{-9}(370)\\\\\Delta U = 8.88 \times 10^{-7} \ J[/tex]

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Complete Question

The diagram for this question is showed on the first uploaded image (reference homework solutions )

Answer:

The  velocity at the bottom is  [tex]v = 11.76 \ m/ s[/tex]

Explanation:

From the question we are told that

   The  total distance traveled is  [tex]d = 1.2 \ m[/tex]

    The mass of the block is  [tex]m_b = 0.3 \ kg[/tex]

      The  height of the block from the ground is h =  0.60 m  

According the law of  energy  

   [tex]PE = KE[/tex]

Where  PE  is the potential energy which is mathematically represented as

      [tex]PE = m * g * h[/tex]

substituting values

     [tex]PE = 3 * 9.8 * 0.60[/tex]

      [tex]PE = 17.64 \ J[/tex]

So

   KE  is the kinetic energy at the bottom which is mathematically represented as

          [tex]KE = \frac{1}{2} * m v^2[/tex]

So

      [tex]\frac{1}{2} * m* v ^2 = PE[/tex]

substituting values  

  =>    [tex]\frac{1}{2} * 3 * v ^2 = 17.64[/tex]

=>       [tex]v = \sqrt{ \frac{ 17.64}{ 0.5 * 3 } }[/tex]

=>    [tex]v = 11.76 \ m/ s[/tex]

Answer:

T = 2.06h

Explanation:

In order to calculate the time that the Apollo takes to complete an orbit around the moon, you use the following formula, which is one of the Kepler's law:

[tex]T=\frac{2\pi r^{3/2}}{\sqrt{GM_m}}[/tex]         (1)

T: time for a complete orbit = ?

r: radius of the orbit

G: Cavendish's constant = 6.674*10^-11 m^3.kg^-1.s^-2

Mm: mass of the moon = 7.34*10^22 kg

The radius of the orbit is equal to the radius of the moon plus the distance from the surface to the Apollo:

[tex]r=R_m+160km\\\\[/tex]

Rm: radius of the moon = 1737.1 km

[tex]r=1737.1km+160km=1897.1km=1897.1*10^3 m[/tex]

Then, you replace all values of the parameters in the equation (1):

[tex]T=\frac{2\pi (1897.1*10^3m)^{3/2}}{\sqrt{(6.674*10^{-11}m^3/kgs^2)(7.34*10^22kg)}}\\\\T=7417.78s[/tex]

In hours you obtain:

[tex]T=7417.78s*\frac{1h}{3600s}=2.06h[/tex]

The time that the Apollo takes to complete an orbit around the moon is 2.06h

Answer:

Here, "v" is the velocity of electron and "V" is the potential.

Answer:

(a) P = 103064 Pa = 103.064 KPa

(b) P = 102476 Pa = 102.476 KPa

Explanation:

(a)

First we need to find the gauge pressure:

Gauge Pressure = Pg = (density)(g)(h)

Pg = (1200 kg/m³)(9.8 m/s²)(0.15 m)

Pg = 1764 Pa

So, the absolute Pressure is:

Absolute Pressure = P = Atmospheric Pressure + Pg

P = 1.013 x 10⁵ Pa + 1764 Pa

P = 103064 Pa = 103.064 KPa

(b)

First we need to find the gauge pressure:

Gauge Pressure = Pg = (density)(g)(h)

Pg = (1200 kg/m³)(9.8 m/s²)(0.1 m)

Pg = 1176 Pa

So, the absolute Pressure is:

Absolute Pressure = P = Atmospheric Pressure + Pg

P = 1.013 x 10⁵ Pa + 1176 Pa

P = 102476 Pa = 102.476 KPa

The absolute pressure in the bulb is approximately 1.031 x 10⁵ Pa when h = 0.15 m and 1.025 x 10⁵ Pa when h = 0.10 m.

Absolute pressure is the total pressure exerted by a fluid, including both the pressure from the fluid itself and the atmospheric pressure. It is the sum of the gauge pressure, which is the pressure above atmospheric pressure, and the atmospheric pressure. Absolute pressure is measured relative to a complete vacuum, where the pressure is zero.

In fluid mechanics, absolute pressure is important for determining the forces and behaviors of fluids in various systems. It is commonly expressed in units such as pascals (Pa), atmospheres (atm), pounds per square inch (psi), or torr.

The absolute pressure in the bulb can be calculated using the following formula:

P = P₀ + ρgh

where:

P is the absolute pressure in the bulb,

P₀ is the atmospheric pressure (1.013 x 10⁵ Pa),

ρ is the density of the sauce (1200 kg/m³),

g is the acceleration due to gravity (9.8 m/s²), and

h is the height of the sauce in the tube.

(a) When h = 0.15 m:

P = 1.013 x 10⁵ Pa + (1200 kg/m³) x (9.8 m/s²) x (0.15 m)

P ≈ 1.013 x 10⁵ Pa + 1764 Pa

P ≈ 1.031 x 10⁵ Pa

(b) When h = 0.10 m:

P = 1.013 x 10⁵ Pa + (1200 kg/m³) x (9.8 m/s²) x (0.10 m)

P ≈ 1.013 x 10⁵ Pa + 1176 Pa

P ≈ 1.025 x 10⁵ Pa

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Answer:

Explanation:

according to resultant of two parallel forces,

Fpivot = Fobject + Fbricks

so that, the net force is zero