A radar installation operates at 9000 MHz with an antenna (dish) that is 15 meters across. Determine the maximum distance (in kilometers) for which this system can distinguish two aircraft 100 meters apart.

Answers

Answer 1

Answer:

R = 36.885 km

Explanation:

In order to distinguish the two planes we must use the Rayleigh criterion that establishes two distinguishable objects if in their diffraction the central maximum of one coincides with the first minimum of the other

The diffraction equation for slits is

            a sin θ = m λ

the first minimum occurs for m = 1

             sin θ = λ a

as the diffraction experiments the angles are very small, we approximate

             sin θ = θ

 

             θ = λ / a

This expression is for a slit, in the case of circular objects, when solving the system in polar coordinates, a numerical constant appears, leaving the expression of the form

            θ = 1.22 λ / a

In this problem they give us the frequency, let's find the wavelength with the relation

           c = λ f

           λ = c / f

           θ = 1.22 c/ f a

since they ask us for the distance between the planes, we can use the definition of radians

          θ = s / R

if we assume that the distance is large, we can approximate the arc to the horizontal distance

          s = x

       

we substitute

             x / R = 1.22 c / fa

             R = x f a / 1.22c

Let's reduce the magnitudes to the SI system

            f = 9000 MHz = 9 109 Hz

            a = 15 m

           x = 100 m

let's calculate

            R = 100 10⁹ 15 / (1.22 3 108)

            R = 3.6885 10⁴ m

let's reduce to km

            R = 3.6885 10¹ km

            R = 36.885 km


Related Questions

A stereo speaker produces a pure "G" tone, with a frequency of 392 Hz. What is the period T of the sound wave produced by the speaker?

Answers

Answer:

The  period is [tex]T = 0.00255 \ s[/tex]

Explanation:

From the question we are told that

  The  frequency is  [tex]f = 392 \ Hz[/tex]

Generally the period is mathematically represented as  

           [tex]T = \frac{1}{f}[/tex]

=>       [tex]T = \frac{1}{ 392}[/tex]

=>       [tex]T = 0.00255 \ s[/tex]

A particle undergoes damped harmonic motion. The spring constant is 100 N/m, the damping constant is 8.0 x 10-3 kg.m/s, and the mass is 0.050 kg. If the particle starts at its maximum displacement, x = 1.5 m, at time t = 0. What is the amplitude of the motion at t = 5.0 s?

Answers

Answer:

The amplitude [tex]A(5) = 1 \ m[/tex]

Explanation:

From the question we are told that

     The  spring constant is  [tex]k = 100 \ N/m[/tex]

      The  damping constant is  [tex]b = 8.0 *10^{-3} \ kg \cdot m/s[/tex]

       The mass is  [tex]m = 0.050 \ kg[/tex]

       The  maximum displacement is [tex]A_o = 1.5 \ m \ at t = 0[/tex]

       The  time  considered is  t =  5.0 s

Generally the displacement(Amplitude) of damped harmonic motion is mathematically represented as

           [tex]A(t) = A_o * e ^{ - \frac{b * t}{2 * m} }[/tex]

substituting values

         [tex]A(5) = 1.5 * e ^{ - \frac{ 8.0 *10^{-3} * 5}{2 * 0.050} }[/tex]

         [tex]A(5) = 1 \ m[/tex]

       

The advantage of a hydraulic lever is A : it transforms a small force acting over a large distance into a large force acting over a small distance. B : it transforms a small force acting over a small distance into a large force acting over a large distance. C : it allows you to exert a larger force with less work. D : it transforms a large force acting over a large distance into a small force acting over a small distance. E : it transforms a large force acting over a small distance into a small force acting over a large distance.

Answers

Answer:

A) it transforms a small force acting over a large distance into a large force acting over a small distance.

Explanation:

The hydraulic lever works based on Pascal's law of transmission of pressure through a fluid. In the hydraulic lever, the pressure transmitted is the same.

Pressure transmitted P = F/A

where F is the force applied

and A is the area over which the force is applied.

This pressure can be manipulated on the input end as a small force applied over a small area, and then be transmitted to the output end as a large force over a large area.

F/A = f/a

where the left side of the equation is for the output, and the right side is for the input.

The volume of the displaced fluid will be the same on both ends of the hydraulic lever. Since we know that

volume V = (area A) x (distance d)

this means that the the piston on the input smaller area of the hydraulic lever will travel a greater distance, while the piston on the larger output area of the lever will travel a small distance.

From all these, we can see that the advantage of a hydraulic lever is that it transforms a small force acting over a large distance into a large force acting over a small distance.

A 1.25-kg ball begins rolling from rest with constant angular acceleration down a hill. If it takes 3.60 s for it to make the first complete revolution, how long will it take to make the next complete revolution?

Answers

Answer:

The time taken is  [tex]\Delta t = 1.5 \ s[/tex]

Explanation:

From the question we are told that

   The mass of the ball is  [tex]m = 1.25 \ kg[/tex]

    The time taken to make the first complete revolution is  t= 3.60 s

    The displacement of the first complete revolution is  [tex]\theta = 1 rev = 2 \pi \ radian[/tex]

Generally the displacement for one  complete revolution is mathematically represented as

       [tex]\theta = w_i t + \frac{1}{2} * \alpha * t^2[/tex]

Now given that the stone started from rest [tex]w_i = 0 \ rad / s[/tex]

     [tex]2 \pi =0 + 0.5* \alpha *(3.60)^2[/tex]

     [tex]\alpha = 0.9698 \ s[/tex]

Now the displacement for two  complete revolution is

         [tex]\theta_2 = 2 * 2\pi[/tex]

         [tex]\theta_2 = 4\pi[/tex]

Generally the displacement for two complete revolution is mathematically represented as  

     [tex]4 \pi = 0 + 0.5 * 0.9698 * t^2[/tex]

=>   [tex]t^2 = 25.9187[/tex]

=>   [tex]t= 5.1 \ s[/tex]

So

 The  time taken to complete the next oscillation is mathematically evaluated as

     [tex]\Delta t = t_2 - t[/tex]

substituting values

      [tex]\Delta t = 5.1 - 3.60[/tex]

     [tex]\Delta t = 1.5 \ s[/tex]

           

 

The time for the ball to complete the next revolution is 1.5 s.

The given parameters;

mass of the ball, m = 1.25 kgtime of motion, t = 3.6 sone complete revolution, θ = 2π

The constant angular acceleration of the ball is calculated as follows;

[tex]\theta = \omega t \ + \ \frac{1}{2} \alpha t^2\\\\2\pi = 0 \ + \ 0.5(3.6)^2 \alpha\\\\2\pi = 6.48 \alpha \\\\\alpha = \frac{2 \pi }{6.48} \\\\\alpha = 0.97 \ rad/s^2[/tex]

The time to complete the next revolution is calculated as follows;

[tex]4\pi = 0 + \frac{1}{2} (0.97)t^2\\\\8\pi = 0.97t^2\\\\t^2 = \frac{8\pi }{0.97} \\\\t^2 = 25.91\\\\t = \sqrt{ 25.91} \\\\t = 5.1 \ s[/tex]

[tex]\Delta t = 5.1 \ s \ - \ 3.6 \ s \\\\\Delta t = 1.5 \ s[/tex]

Thus, the time for the ball to complete the next revolution is 1.5 s.

Learn more here:https://brainly.com/question/20738528

CAN SOMEONE HELP ME PLEASE ITS INTEGRATED SCIENCE AND I AM STUCK

Answers

Answer:

[tex]\huge \boxed{\mathrm{Option \ D}}[/tex]

Explanation:

Two forces are acting on the object.

Subtracting 2 N from both forces.

2 N → Object ← 5 N

- 2 N                 - 2N

0 N → Object ← 3 N

The force 3 N is pushing the object to the left side.

The mass of the object is 10 kg.

Applying formula for acceleration (Newton’s Second Law of Motion).

a = F/m

a = 3/10

a = 0.3

When you slosh the water back and forth in a tub at just the right frequency, the water alternately rises and falls at each end, remaining relatively calm at the center. Suppose the frequency to produce such a standing wave in a 55m wide tub is 0.80 Hz.

Required:
What is the speed of the water wave?

Answers

Answer:

The  speed of the water wave is [tex]v = 88 \ m/s[/tex]

Explanation:

From the question we are told that

      The  width of the tube is  [tex]L = 55 \ m[/tex]

     The fundamental  frequency is  [tex]f = 0.80 \ Hz[/tex]

Generally the fundamental frequency is mathematically represented as

      [tex]f = \frac{v}{2 * L }[/tex]

=>    [tex]v = f * 2 * L[/tex]

substituting values

       [tex]v = 0.8 * 2 * 55[/tex]

       [tex]v = 88 \ m/s[/tex]

The speed of the water wave will be 88 m/s.

Given information:

When you slosh the water back and forth in a tub at just the right frequency, the water alternately rises and falls at each end, remaining relatively calm at the center.

The frequency of the standing wave is [tex]f=0.8[/tex] Hz.

The width of the tub is [tex]w=55[/tex] m.

Let v be the speed of the standing wave.

The speed of the wave can be calculated as,

[tex]v=2wf\\v=2\times 55\times 0.8\\v=88\rm\; m/s[/tex]

Therefore, the speed of the water wave will be 88 m/s.

For more details, refer to the link:

https://brainly.com/question/1967686

The magnetic field of a plane-polarized electromagnetic wave moving in the z-direction is given by in SI units. What is the frequency of the wave

Answers

Complete Question    

The magnetic field of a plane-polarized electromagnetic wave moving in the z-direction is given by

[tex]B=1.2* 10^{-6} sin [2\pi[(\frac{z}{240} ) - ( \frac{t * 10^7}{8} ) ] ][/tex]    in SI units.

Answer:

The  value  is  [tex]f = 1.98918*10^{5}\ Hz[/tex]

Explanation:

From the question we are told that

   The magnetic field is    [tex]B=1.2* 10^{-6} sin [2\pi[(\frac{z}{240} ) - ( \frac{t * 10^7}{8} ) ] ][/tex]

 This above  equation can be modeled as

       [tex]B=1.2* 10^{-6} sin [2\pi[(\frac{z}{240} ) - ( \frac{t * 10^7}{8} ) ] ] \equiv A sin ( kz -wt )[/tex]

So  

       [tex]w = \frac{10^7}{8}[/tex]

Generally the frequency is mathematically represented as

       [tex]f = \frac{w}{2 \pi}[/tex]

=>    [tex]f = \frac{ \frac{10^7}{8} }{2 \pi}[/tex]

=>    [tex]f = 1.98918*10^{5}\ Hz[/tex]

"Determine the magnitude of the net force of gravity acting on the Moon during an eclipse when it is directly between Earth and the Sun."

Answers

Answer:

Net force = 2.3686 × 10^(20) N

Explanation:

To solve this, we have to find the force of the earth acting on the moon and the force of the sun acting on the moon and find the difference.

Now, from standards;

Mass of earth;M_e = 5.98 × 10^(24) kg

Mass of moon;M_m = 7.36 × 10^(22) kg

Mass of sun;M_s = 1.99 × 10^(30) kg

Distance between the sun and earth;d_se = 1.5 × 10^(11) m

Distance between moon and earth;d_em = 3.84 × 10^(8) m

Distance between sun and moon;d_sm = (1.5 × 10^(11)) - (3.84 × 10^(8)) = 1496.96 × 10^(8) m

Gravitational constant;G = 6.67 × 10^(-11) Nm²/kg²

Now formula for gravitational force between the earth and the moon is;

F_em = (G × M_e × M_m)/(d_em)²

Plugging in relevant values, we have;

F_em = (6.67 × 10^(-11) × 5.98 × 10^(24) × 7.36 × 10^(22))/(3.84 × 10^(8))²

F_em = 1.9909 × 10^(20) N

Similarly, formula for gravitational force between the sun and moon is;

F_sm = (G × M_s × M_m)/(d_sm)²

Plugging in relevant values, we have;

F_se = (6.67 × 10^(-11) × 1.99 × 10^(30) ×

7.36 × 10^(22))/(1496.96 × 10^(8))²

F_se = 4.3595 × 10^(20) N

Thus, net force = F_se - F_em

Net force = (4.3595 × 10^(20) N) - (1.9909 × 10^(20) N) = 2.3686 × 10^(20) N

An archer practicing with an arrow bow shoots an arrow straight up two times. The first time the initial speed is vi and second

time he increases the initial sped to 4v. How would you compare the maximum height in the second trial to that in the first trial?

Answers

Answer:

The maximum height reached in the second trial is 16times the maximum height reached in the first trial.

Explanation:

The following data were obtained from the question:

First trial

Initial speed (u) = v

Final speed (v) = 0

Second trial

Initial speed (u) = 4v

Final speed (v) = 0

Next, we shall obtain the expression for the maximum height reached in each case.

This is illustrated below:

First trial:

Initial speed (u) = v

Final speed (v) = 0

Acceleration due to gravity (g) = 9.8 m/s²

Height (h₁) =.?

v² = u² – 2gh₁ (going against gravity)

0 = (v)² – 2 × 9.8 × h₁

0 = v² – 19.6 × h₁

Rearrange

19.6 × h₁ = v²

Divide both side by 19.6

h₁ = v²/19.6

Second trial

Initial speed (u) = 4v

Final speed (v) = 0

Acceleration due to gravity (g) = 9.8 m/s²

Height (h₂) =.?

v² = u² – 2gh₂ (going against gravity)

0 = (4v)² – 2 × 9.8 × h₂

0 = 16v² – 19.6 × h₂

Rearrange

19.6 × h₂ =16v²

Divide both side by 19.6

h₂ = 16v²/19.6

Now, we shall determine the ratio of the maximum height reached in the second trial to that of the first trial.

This is illustrated below:

Second trial:

h₂ = 16v²/19.6

First trial:

h₁ = v²/19.6

Second trial : First trial

h₂ : h₁

h₂ / h₁ = 16v²/19.6 ÷ v²/19.6

h₂ / h₁ = 16v²/19.6 × 19.6/v²

h₂ / h₁ = 16

h₂ = 16 × h₁

From the above illustrations, we can see that the maximum height reached in the second trial is 16times the maximum height reached in the first trial.

A string is stretched and fixed at both ends, 200 cm apart. If the density of the string is 0.015 g/cm, and its tension is 600 N, what is the wavelength (in cm) of the first harmonic?

Answers

Answer:

200cm

Explanation:

Answer:

100cm

Explanation:

Using

F= ( N/2L)(√T/u)

F1 will now be (0.5*2)( √600/0.015)

=> L( wavelength)= 200/2cm = 100cm

What is temperature?
O A. The force exerted on an area
B. A measure of mass per unit volume
O C. The net energy transferred between two objects
OD. A measure of the movement of atoms or molecules within an
object​

Answers

Answer:

The net energy transferred between two objects

Explanation:

The physical property of matter that expresses hot or cold is called temperature. It demonstrates the thermal energy. A thermometer is used to measure temperature. It defines the rate to which the chemical reaction occurs. It tells about the thermal radiation emitted from an object.

The correct option that defines temperature is option C.

Answer:

A measure of the movement of atoms or molecules within an object

Explanation:

Process of elimination

Matter's resistance to a change in motion is called

Answers

Answer:

Inertia! I hope this helps!

Answer:

inertia

Explanation

Inertia.

A laboratory electromagnet produces a magnetic field of magnitude 1.38 T. A proton moves through this field with a speed of 5.86 times 10^6 m/s.

a. Find the magnitude of the maximum magnetic force that could be exerted on the proton.
b. What is the magnitude of the maximum acceleration of the proton?
c. Would the field exert the same magnetic force on an electron moving through the field with the same speed? (Assume that the electron is moving in the direction as the proton.)

1. Yes
2. No

Answers

.Answer;

Using Fmax=qVB

F=(1.6*10^-19 C)(5.860*10^6 m/s)(1.38 T)

ANS=1.29*10^-12 N

2. Using Amax=Fmax/ m

Amax =(1.29*10^-12 N) / (1.67*10^-27 kg)

ANS=1.93*10^15 m/s^2*

3. No, the acceleration wouldn't be the same. Since The magnitude of the electron is equal to that of the proton, but the direction would be in the opposite direction and also Since an electron has a smaller mass than a proton

The block moves up an incline with constant speed. What is the total work WtotalWtotalW_total done on the block by all forces as the block moves a distance LLL

Answers

Answer:

External force    W₁ = F L

Friction force    W₂ = - fr L

weight component   W₃ = - mg sin θ L

Y Axis   Force      W=0

Explanation:

When the block rises up the plane with constant velocity, it implies that the sum of the forces is zero.

For these exercises it is indicated to create a reference system with the x axis parallel to the plane and the y axis perpendicular

let's write the equations of translational equilibrium in given exercise

X axis

        F - fr -Wₓ = 0

        F = fr + Wₓ

the components of the weight can be found using trigonometry

         Wₓ = W sin θ

         [tex]W_{y}[/tex] = W cos θ

let's look for the work of these three forces

          W = F x cos θ

External force

          W₁ = F L

since the displacement and the force have the same direction

Friction force

          W₂ = - fr L

since the friction force is in the opposite direction to the displacement

For the weight component

          W₃ = - mg sin θ L

because the weight component is contrary to displacement

Y Axis  

          N- Wy = 0

in this case the forces are perpendicular to the displacement, the angle is 90º and the cosine 90 = 0

therefore work is worth zero

PLEASE HELP FAST The object distance for a convex lens is 15.0 cm, and the image distance is 5.0 cm. The height of the object is 9.0 cm. What is the height of the image?

Answers

Answer:

The image height is 3.0 cm

Explanation:

Given;

object distance, [tex]d_o[/tex] = 15.0 cm

image distance, [tex]d_i[/tex] = 5.0 cm

height of the object, [tex]h_o[/tex] = 9.0 cm

height of the image, [tex]h_i[/tex] = ?

Apply lens equation;

[tex]\frac{h_i}{h_o} = -\frac{d_i}{d_o}\\\\ h_i = h_o(-\frac{d_i}{d_o})\\\\h_i = -9(\frac{5}{15} )\\\\h_i = -3 \ cm[/tex]

Therefore, the image height is 3.0 cm. The negative values for image height indicate that the image is an inverted image.

Thomas and Lilian are walking down the street to get to the corner store. They walk 5 blocks up the street and turn right by the stop sign. Once they turn at the stop sign they continue walking for 8 more blocks. They make a left, walk 2 blocks and cross the street to arrive at the corner store. While there they purchase a few snacks, sit at the curb, and then walk back home where they originally started. Thomas and Lilian are discussing their walk in reference to their overall displacement and distance. They seem to be in disagreement about their journey. Thomas says their overall displacement and distance are both zero, because they are back where they started. Lilian thinks their total distance and displacement are greater than zero.

Which person do you most agree with?
You are not expected to actually calculate in order to solve this problem.

Answers

Answer:

Thomas is correct that the zero displacements

Lilian is right that the distance is greater than zero.

Explanation:

In this problem we have to be clear about the difference between displacement and distance.

The displacement is a vector, that is, it has a modulation and direction, in this case we can draw a vector for the outward trip and another vector for the return trip, both will have the same magnitude, but their directions are opposite, so the resulting vector is zero.

The distance is a scalar and its value coincides with the modulus of the distance vector, in our case the distance is d for the outward journey and d for the return journey, so the total distance is 2d, which is different from zero.

The two students have some reason, but neither complete,

The displacement is zero because it is a vector and

the distance is different from zero (2d) because it is a scalar

 

Thomas is correct that the zero displacements

Lilian is right that the distance is greater than zero.

Therefore I agree with both, because each one has a 50% of the reason

An oil film (n = 1.48) of thickness 290 nm floating on water is illuminated with white light at normal incidence. What is the wavelength of the dominant color in the reflected light? A. Blue (470 nm) B. Green (541 nm) C. Violet (404 nm) D. Yellow (572 nm)

Answers

Answer:

The correct option is  D

Explanation:

From the question we are told that

   The  refractive index of oil film is [tex]k = 1.48[/tex]

   The  thickness is [tex]t = 290 \ nm = 290*10^{-9} \ m[/tex]

   

Generally for constructive interference

      [tex]2t = [m + \frac{1}{2} ]* \frac{\lambda}{k}[/tex]

For reflection of a bright fringe m =  1

 =>   [tex]2 * (290*10^{-9}) = [1 + \frac{1}{2} ]* \frac{\lambda}{1.48}[/tex]

=>     [tex]\lambda = 5.723 *10^{-7} \ m[/tex]

This wavelength fall in the range of a yellow light

How much heat is required to convert 5.0 kg of ice from a temperature of - 20 0C to water at a temperature of 205 0F

Answers

Answer:

Explanation:

To convert from °C to °F , the formula is

( F-32 ) / 9 = C / 5

F is reading fahrenheit scale and C is in centigrade scale .

F = 205 , C = ?

(205 - 32) / 9 = C / 5

C = 96°C approx .

Let us calculate the heat required .

Total heat required = heat required to heat up the ice at - 20 °C  to 0°C  + heat required to melt the ice + heat required to heat up the water at  0°C to

96°C.

=  5 x 2.04 x (20-0) +  5 x 336 + 5 x ( 96-0 ) x 4.2  kJ .

= 204 + 1680 + 2016

= 3900 kJ .

A plastic dowel has a Young's Modulus of 1.50 ✕ 1010 N/m2. Assume the dowel will break if more than 1.50 ✕ 108 N/m2 is exerted.
(a) What is the maximum force (in kN) that can be applied to the dowel assuming a diameter of 2.40 cm?
______Kn
(b) If a force of this magnitude is applied compressively, by how much (in mm) does the 26.0 cm long dowel shorten? (Enter the magnitude.)
mm

Answers

Answer:

a

   [tex]F = 67867.2 \ N[/tex]

b

  [tex]\Delta L = 2.6 \ mm[/tex]

Explanation:

From the question we are told that

      The Young modulus is  [tex]Y = 1.50 *10^{10} \ N/m^2[/tex]

      The stress is  [tex]\sigma = 1.50 *10^{8} \ N/m^2[/tex]

      The  diameter is  [tex]d = 2.40 \ cm = 0.024 \ m[/tex]

The radius is mathematically represented as

       [tex]r =\frac{d}{2} = \frac{0.024}{2} = 0.012 \ m[/tex]

The cross-sectional area is  mathematically evaluated as

        [tex]A = \pi r^2[/tex]

         [tex]A = 3.142 * (0.012)^2[/tex]

        [tex]A = 0.000452\ m^2[/tex]

Generally the stress is mathematically represented as

        [tex]\sigma = \frac{F}{A}[/tex]

=>     [tex]F = \sigma * A[/tex]

=>    [tex]F = 1.50 *10^{8} * 0.000452[/tex]

=>    [tex]F = 67867.2 \ N[/tex]

Considering part b

      The length is given as [tex]L = 26.0 \ cm = 0.26 \ m[/tex]

Generally Young modulus is mathematically represented as

           [tex]E = \frac{ \sigma}{ strain }[/tex]

Here strain is mathematically represented as

         [tex]strain = \frac{ \Delta L }{L}[/tex]

So    

       [tex]E = \frac{ \sigma}{\frac{\Delta L }{L} }[/tex]

        [tex]E = \frac{\sigma }{1} * \frac{ L}{\Delta L }[/tex]

=>     [tex]\Delta L = \frac{\sigma * L }{E}[/tex]

substituting values

       [tex]\Delta L = \frac{ 1.50*10^{8} * 0.26 }{ 1.50 *10^{10 }}[/tex]

       [tex]\Delta L = 0.0026[/tex]

Converting to mm

      [tex]\Delta L = 0.0026 *1000[/tex]

      [tex]\Delta L = 2.6 \ mm[/tex]

We can reasonably model a 75 W incandescent light bulb as a sphere 6.0 cm in diameter. Typically only about 5% of the energy goes to visible light; the rest goes largely to non-visible infrared radiation. (a) What is the visible light intensity at the surface of the bulb

Answers

Answer:

Visible light intensity at the surface of the bulb (I) = 331 W/m²

Explanation:

Given:

Energy = 75 W

Radius = 6 /2 = 3 cm = 3 × 10⁻² m

Energy goes to visible light = 5% = 0.05

Find:

Visible light intensity at the surface of the bulb (I)

Computation:

Visible light intensity at the surface of the bulb (I) = P / 4A

Visible light intensity at the surface of the bulb (I) = (0.05)(75) / 4π(3 × 10⁻²)²

Visible light intensity at the surface of the bulb (I) = 3.75 / 4π(9 × 10⁻⁴)

Visible light intensity at the surface of the bulb (I) = 331 W/m²

Does the moon light originate from the moon only

Answers

Answer:

No

Explanation:

Moon has no light of its own. It just shines because its surface reflects light from the sun and that's what we see.

:-)

A charge of 15 is moving with velocity of 6.2 x17 which makes an angle of 48 degrees with respect to the magnetic field. If the force on the particle is 4838 N, find the magnitude of the magnetic field.
a. 06.0T.
b. 08.0T.
c. 07.0T.
d. 05.0 T.

Answers

Complete question:

A charge of 15C is moving with velocity of 6.2 x 10³ m/s which makes an angle of 48 degrees with respect to the magnetic field. If the force on the particle is 4838 N, find the magnitude of the magnetic field.

a. 0.06 T

b. 0.08 T

c. 0.07 T

d. 0.05 T

Answer:

The magnitude of the magnetic field is 0.07 T.

Explanation:

Given;

magnitude of the charge, q = 15C

velocity of the charge, v = 6.2 x 10³ m/s

angle between the charge and the magnetic field, θ = 48°

the force on the particle, F = 4838 N

The magnitude of the magnetic field can be calculated by applying Lorentz force formula;

F = qvBsinθ

where;

B is the magnitude of the magnetic field

B = F / vqsinθ

B = (4838) / (6.2 x 10³ x 15 x sin48)

B = 0.07 T

Therefore, the magnitude of the magnetic field is 0.07 T.

A cylindrical container with a cross-sectional area of 66.2 cm2 holds a fluid of density 856 kg/m3 . At the bottom of the container the pressure is 119 kPa . Assume Pat = 101 kPa

A) What is the depth of the fuild?

B) Find the pressure at the bottom of the container after an additional 2.35×10−3 m3 of this fluid is added to the container. Assume that no fluid spills out of the container.

Answers

Answer:

A. h = 2.15 m

B. Pb' = 122 KPa

Explanation:

The computation is shown below:

a)  Let us assume the depth be h

As we know that

[tex]Pb - Pat = d \times g \times h \\\\ ( 119 - 101) \times 10^3 = 856 \times 9.8 \times h[/tex]

After solving this,  

h = 2.15 m

Therefore the depth of the fluid is 2.15 m

b)

Given that  

height of the extra fluid is

[tex]h' = \frac{2.35 \times 10^{-3}}{ area} \\\\ h' = \frac{2.35 \times 10^{-3}} { 66.2 \times 10^{-4}}[/tex]

h' = 0.355 m

Now let us assume the pressure at the bottom is Pb'

so, the equation would be

[tex]Pb' - Pat = d \times g \times (h + h')\\\\Pb' = 856 \times 9.8 \times ( 2.15 + 0.355) + 101000[/tex]

Pb' = 122 KPa

(A)  The depth of the fluid is 2.14 m.

(B)  The new pressure at the bottom of container is 121972 Pa.

Given data:

The cross-sectional area of the container is, [tex]A =66.2 \;\rm cm^{2}=66.2 \times 10^{-4} \;\rm m^{2}[/tex].

The density of fluid is, [tex]\rho = 856 \;\rm kg/m^{3}[/tex].

The container pressure at bottom is, [tex]P=119 \;\rm kPa=119 \times 10^{3} \;\rm Pa[/tex].

The atmospheric pressure is, [tex]P_{at}=101 \;\rm kPa=101 \times 10^{3}\;\rm Pa[/tex].

(A)

The given problem is based on the net pressure on the container, which is equal to the difference between the pressure at the bottom and the atmospheric pressure. Then the expression is,

[tex]P_{net} = P-P_{at}\\\\\rho \times g \times h= P-P_{at}[/tex]

Here, h is the depth of fluid.

Solving as,

[tex]856\times 9.8 \times h= (119-101) \times 10^{3}\\\\h=\dfrac{ (119-101) \times 10^{3}}{856\times 9.8}\\\\h= 2.14 \;\rm m[/tex]

Thus, the depth of the fluid is 2.14 m.

(B)

For an additional volume of [tex]2.35 \times 10^{-3} \;\rm m^{3}[/tex] to the liquid, the new depth is,

[tex]V=A \times h'\\\\h'=\dfrac{2.35 \times 10^{-3}}{66.2 \times 10^{-4}}\\\\h'=0.36 \;\rm m[/tex]

Now, calculate the new pressure at the bottom of the container as,

[tex]P'-P_{at}= \rho \times g \times (h+h')\\\\\P'-(101 \times 10^{3})= 856 \times 9.8 \times (2.14+0.36)\\\\P'=121972 \;\rm Pa[/tex]

Thus, we can conclude that the new pressure at the bottom of container is 121972 Pa.

Learn more about the atmospheric pressure here:

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A rectangular coil having N turns and measuring 15 cm by 25 cm is rotating in a uniform 1.6-T magnetic field with a frequency of 75 Hz. The rotation axis is perpendicular to the direction of the field. If the coil develops a sinusoidal emf of maximum value 56.9 V, what is the value of N?
A) 2
B) 4
C) 6
D) 8
E) 10

Answers

Answer:

A) 2

Explanation:

Given;

magnetic field of the coil, B = 1.6 T

frequency of the coil, f = 75 Hz

maximum emf developed in the coil, E = 56.9 V

area of the coil, A = 0.15 m x 0.25 m = 0.0375 m²

The maximum emf in the coil is given by;

E = NBAω

Where;

N is the number of turns

ω is the angular velocity = 2πf = 2 x 3.142 x 75 = 471.3 rad/s

N = E / BAω

N = 56.9 / (1.6 x 0.0375 x 471.3)

N = 2 turns

Therefore, the value of N is 2

A) 2

If one could transport a simple pendulum of constant length from the Earth's surface to the Moon's, where acceleration due to gravity is one-sixth (1/6) that on the Earth, by what factor would be the pendulum frequency be changed

Answers

Answer:

The frequency will change by a factor of 0.4

Explanation:

T = 2(pi)*sqrt(L/g)

Since g(moon) = (1/6)g(earth), the period would change by sqrt[1/(1/6)] = sqrt(6) ~ 2.5 times longer on the moon. Since the period & frequency are inverses, the frequency would be 1/2.5 or 0.4 times shorter on the moon.

If you wanted to make your own lenses for a telescope, what features of a lens do you think would affect the images that you can see

Answers

Answer:

Therefore the characteristics to be found are:

* the focal length must be large and the focal length of the eyepiece must be small

* The diameter of the objective lens should be as large as possible, to be able to collect small without need from light

* The system must be configured to the far sight tip,

Explanation:

The length of the telescope is

         L = f_ocular + f_objetive

the magnification of the telescope is

         m = - f_objective / f_ocular

These are the two equations that describe the behavior of the telescope. Therefore the characteristics to be found are:

* the focal length must be large and the focal length of the eyepiece must be small

* The diameter of the objective lens should be as large as possible, to be able to collect small without need from light

* The system must be configured to the far sight tip,

A lab technician uses laser light with a wavelength of 650 nmnm to test a diffraction grating. When the grating is 42.0 cmcm from the screen, the first-order maxima appear 6.09 cmcm from the center of the pattern. How many lines per millimeter does this grating have?

Answers

Answer:

221 lines per millimetre

Explanation:

We know that for a diffraction grating, dsinθ =mλ where d = spacing between grating, θ = angle to maximum, m = order of maximum and λ = wavelength of light.

Since the grating is 42.0 cm from the screen and its first order maximum (m = 1) is at 6.09 cm from the center of the pattern,

tanθ = 6.09 cm/42.0 cm = 0.145

From trig ratios, cot²θ + 1 = cosec²θ

cosecθ = √((1/tanθ)² + 1) = √((1/0.145)² + 1) = √48.562 = 6.969

sinθ = 1/cosecθ = 1/6.969 = 0.1435

Also, sinθ = mλ/d at the first-order maximum, m = 1. So

sinθ = (1)λ/d = λ/d

Equating both expressions we have  

0.1435 = λ/d

d = λ/0.1435

Now, λ = 650 nm = 650 × 10⁻⁹ m

d = 650 × 10⁻⁹ m/0.1435

d = 4529.62 × 10⁻⁹ m per line

d = 4.52962 × 10⁻⁶ m per line

d = 0.00452962 × 10⁻³ m per line

d = 0.00452962 mm per line

Since d = width of grating/number of lines of grating

Then number of lines per millimetre = 1/grating spacing

= 1/0.00452962

= 220.77 lines per millimetre

≅ 221 lines per millimetre since we can only have a whole number of lines.

A solenoid is designed to produce a magnetic field of 3.50×10^−2 T at its center. It has a radius of 1.80 cm and a length of 46.0 cm , and the wire can carry a maximum current of 13.0 A.

Required:
a. What minimum number of turns per unit length must the solenoid have?
b. What total length of wire is required?

Answers

Answer:

a. 2143 turns/m

b. 111.5 m

Explanation:

a. The minimum number of turns per unit length (N/L) can be found using the following equation:

[tex] B = \frac{\mu_{0}NI}{L} [/tex]

[tex] \frac{N}{L} = \frac{B}{\mu_{0}I} = \frac{3.50 \cdot 10^{-2} T}{4\pi \cdot 10^{-7} Tm/A*13.0 A} = 2143 turns/m [/tex]

Hence, the minimum number of turns per unit length is 2143 turns/m.

b. The total length of wire is the following:

[tex] N = 2143 turns/m*L = 2143 turns/m*46.0 \cdot 10^{-2} m = 986 turns [/tex]

Since each turn has length 2πr of wire, the total length is:

[tex] L_{T} = N*2\pi r = 986 turn*2*\pi*1.80 \cdot 10^{-2} m = 111.5 m [/tex]

Therefore, the total length of wire required is 111.5 m.

I hope it helps you!

The linear density rho in a rod 3 m long is 8/ x + 1 kg/m, where x is measured in meters from one end of the rod. Find the average density rhoave of the rod.

Answers

Answer:

The average density of the rod is 1.605 kg/m.

Explanation:

The average density of the rod is given by:

[tex] \rho = \frac{m}{l} [/tex]    

To find the average density we need to integrate the linear density from x₁ = 0 to x₂ = 3, as follows:

[tex] \int_{0}^{3} \frac{8}{3(x + 1)}dx [/tex]

[tex] \rho = \frac{8}{3} \int_{0}^{3} \frac{1}{(x + 1)}dx [/tex]   (1)

Using u = x+1  →  du = dx  → u₁= x₁+1 = 0+1 = 1 and u₂ = x₂+1 = 3+1 = 4

By entering the values above into (1), we have:

[tex] \rho = \frac{8}{3} \int_{0}^{3} \frac{1}{u}du [/tex]

[tex]\rho = \frac{8}{3}*log(u)|_{1}^{4} = \frac{8}{3}[log(4) - log(1)] = 1.605 kg/m[/tex]

Therefore, the average density of the rod is 1.605 kg/m.  

       

I hope it helps you!    

The average density of the rod is  [tex]1.605 \;\rm kg/m^{3}[/tex].

Given data:

The length of rod is, L = 3 m.

The linear density of rod is, [tex]\rho=\dfrac{8}{x+1} \;\rm kg/m[/tex].

To find the average density we need to integrate the linear density from x₁ = 0 to x₂ = 3,  The expression for the average density is given as,

[tex]\rho' = \int\limits^3_0 { \rho} \, dx\\\\\\\rho' = \int\limits^3_0 { \dfrac{m}{L}} \, dx\\\\\\\rho' = \int\limits^3_0 {\dfrac{8}{3(x+1)}} \, dx[/tex]............................................................(1)

Using u = x+1  

du = dx

u₁= x₁+1 = 0+1 = 1

and

u₂ = x₂+1 = 3+1 = 4

By entering the values above into (1), we have:

[tex]\rho' =\dfrac{8}{3} \int\limits^3_0 {\dfrac{1}{u}} \, du\\\\\\\rho' =\dfrac{8}{3} \times [log(u)]^{4}_{1}\\\\\\\rho' =\dfrac{8}{3} \times [log(4)-log(1)]\\\\\\\rho' =1.605 \;\rm kg/m^{3}[/tex]

Thus, we can conclude that the average density of the rod is  [tex]1.605 \;\rm kg/m^{3}[/tex].

Learn more about the average density here:

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A battery establishes a voltage V on a parallel-plate capacitor. After the battery is disconnected, the distance between the plates is doubled without loss of charge. Accordingly:_____.
a. stay same
b. increases
c. decreases
d. the capacitance decreases and the voltage between the plates increases.

Answers

Answer:

d.

Explanation:

Since, the capacitance( decreases )

therefore voltage between the plates(increases ).

Hence, option d is correct.

C =εA/d.

d is doubled, therefore  C decrease ( inverse relation).

D) The capacitance decreases and the voltage between the plates increases.

Battery

A battery establishes a voltage V on a parallel-plate capacitor. After the battery is disconnected, the distance between the plates is doubled without loss of charge. Accordingly, the capacitance decreases and the voltage between the plates increases.

The capacitance - (decreases)

The voltage between the plates- (increases ).

Thus, the correct answer is D.

Learn more about "Battery":

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