An MRI machine needs to detect signals that oscillate at very high frequencies. It does so with an LC circuit containing a 15mH coil. To what value should the capacitance be set to detect a 450 MHz signal?

Answer:

B. [tex]8sin(6.2x-12t)[/tex]

Explanation:

The general equation of a wave is expressed as [tex]y = Asin(kx-\omega t)[/tex]

A is the amplitude of the wave

k is the wave number and it is expressed as [tex]k =\frac{2\pi}{\lambda}[/tex]

[tex]\omega[/tex] is the angular frequency expressed as [tex]\omega = 2\pi f[/tex]

[tex]\lambda[/tex] is the wavelength and f is the angular frequency

Given k = 6.2rad/m and [tex]\omega = 12rad/s[/tex]

On substituting this value into the general wave equation;

[tex]y = Asin(kx-\omega t)\\y = Asin(6.2x-12t)[/tex]

From the expression gotten, the only equation that could be the equation of the wave is [tex]y = 8sin(6.2x-12t)[/tex]

Answer:

The average velocity for this trip is 0 km/hr

Explanation:

We know that average velocity = total displacement/total time.

Now, its displacement is d = final position - initial position.

Since the  car starts and ends at its initial position at Hither, if we assume its initial position is 0 km, then its final position is also 0 km.

So, its displacement is d = 0 km - 0 km = 0 km.

Since the total time for the round trip is 2 hours, the average velocity is

total displacement/ total time = 0 km/2 hr = 0 km/hr.

So the average velocity for this trip is 0 km/hr  

Answer:

The number of turns of the wire needed is 243 turns

Explanation:

Given;

self inductance of the solenoid, L = 1.8 mH

cross sectional area of the inductor, A = 1.6 x 10⁻³ m²

length of the inductor, l = 0.066 m

The self inductance of long solenoid is given by;

L = μ₀n²Al

where;

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

n is number of turns per length

A is the area of the solenoid

l is length of the solenoid

[tex]n = \sqrt{\frac{L}{\mu_o Al} } \\\\n = \sqrt{\frac{1.8*10^{-3}}{(4\pi*10^{-7}) (1.6*10^{-3})(0.066)} } \\\\n = \sqrt{13562583.184} \\\\n = 3682.74 \ turns/m[/tex]

The number of turns is given by;

N = nL

N = (3682.74)(0.066)

N = 243 turns

Therefore, the number of turns of the wire needed is 243 turns

Explanation:

Dark Energy. Dark Energy is a hypothetical form of energy that exerts a negative, repulsive pressure, behaving like the opposite of gravity. It has been hypothesised to account for the observational properties of distant type Ia supernovae, which show the universe going through an accelerated period of expansion

Answer:

Tension, T = 0.556 N

Explanation:

It is given that,

Length of vocal cords, l = 22 mm = 0.022 m

Mass per unit length, [tex]\mu=0.0042\ kg/m[/tex]

We need to find the tension is required in the vocal cords in order to produce a tone of middle C of frequency 261.62 Hz. The frequency in terms if tension is given by :

[tex]f=\dfrac{1}{2l}\sqrt{\dfrac{T}{\mu}}[/tex]

T = tension in the vocal cords

[tex]f^2=\dfrac{1}{4l^2}\times \dfrac{T}{\mu}\\\\T=4l^2\mu f^2\\\\T=4\times (0.022)^2\times 0.0042 \times (261.62 )^2\\\\T=0.556\ N[/tex]

So, the tension in the vocal cords is 0.556 N.

Answer:

733m/s

Explanation:

Assuming that Just after impact:

given that at lowest point Is

T2 + V2 = T3 + V3

1 /2(4 + 0.002) (vB)²2 + 0 = 0 + (4 + 0.002)(9.81)(1.25)(1 -cos 6°)

(vB)2 = 0.3665

m>s For the system of bullet and block: ( S+ ) Σmv1 = Σmv2 0.002(vB)1 = (4 + 0.002)(0.3665) (vB)1 = 733 m/s

Answer:

Inductance of a coil(L) = 0.44 H (Approx)

Explanation:

Given:

coil produces emf = 2.40 V

Old current = -27 mA

New current = 33 mA

Time taken = 11 mS

Find:

Inductance of a coil(L)

Computation:

Inductance of a coil(L) = -emf / [Δi / Δt]

Inductance of a coil(L) = -2.4 / [(-33 - 27) / 11]

Inductance of a coil(L) = -2.4 / [-5.4545]

Inductance of a coil(L) = 0.44 H (Approx)

Answer:

The voltage across the resistor is zero, and the voltage across the capacitor is equal to the terminal voltage of the battery.

Explanation:

This is because when a capacitor is charged no current or voltage flows through it so it will have a voltage equal to the terminal voltage of the battery

Answer:

68.585m/sec , 779.1 N

Explanation:

To feel weightless, centripetal acceleration must equal g (9.8m/sec^2). The accelerations then cancel.

From centripetal motion.

F =( mv^2)/2

But since we are dealing with weightlessness

r = 480m

g = 9.8m/s^2

M also cancels, so forget M.

V^2 = Fr

V = √ Fr

V =√ (9.8 x 480) = 4704

= 68.585m/sec.

b) Centripetal acceleration = (v^2/2r) = (68.585^2/960) = 4704/960

= 4.9m/sec^2.

Weight (force) = (mass x acceleration) = 159kg x (g - 4.9)

159kg × ( 9.8-4.9)

159kg × 4.9

= 779.1N

A) The speed of the scooter at which the driver will feel weightlessness is;

v = 68.586 m/s

B) The apparent weight of both the driver and the scooter at the top of the hill is;

F_net = 779.1 N

We are given;

Mass; m = 159 kg

Radius; r = 480 m

A) Since it's motion about a circular hill, it means we are dealing with centripetal force.

Formula for centripetal force is given as;

F = mv²/r

Now, we want to find the speed of the scooter if the driver feels weightlessness.

This means that the centripetal force would be equal to the gravitational force.

Thus;

mg = mv²/r

m will cancel out to give;

v²/r = g

v² = gr

v = √(gr)

v = √(9.8 × 480)

v = √4704

v = 68.586 m/s

B) Now, he is travelling with speed of;

v = 68.586 m/s

And the radius is 2r

Let's first find the centripetal acceleration from the formula; α = v²/r

Thus; α = 4704/(2 × 480)

α = 4.9 m/s²

Now, since he has encountered a hill with a radius of 2r up the slope, it means that the apparent weight will now be;

F_app = m(g - α)

F_net = 159(9.8 - 4.9)

F_net = 779.1 N

Read more at; https://brainly.com/question/9017432

Answer:

Motor unit is made up of motor neurons. Group of Motor Units work together to coordinate contraction of single muscle. When an individual needs to carry several boxes down stairs then his brain gives signal to neurons who innervates a group of skeletal muscle. When neurons receive signal they stimulate all muscle fibers in that particular motor unit.

Explanation:

Motor unit is made up of motor neurons. Group of Motor Units work together to coordinate contraction of single muscle. When an individual needs to carry several boxes down stairs then his brain gives signal to neurons who innervates a group of skeletal muscle. When neurons receive signal they stimulate all muscle fibers in that particular motor unit.

Q: An appliance with a 20 Ω resistor has a power rating of 15.0 W. Find the maximum current which can flow safely through the appliance g

Answer:

0.866 A

Explanation:

From the question,

P = I²R............................. Equation 1

Where P = power, I = maximum current, R = Resistance.

Make I the subject of the equation

I = √(P/R).................... Equation 2

Given: P = 15 W, R = 20 Ω

Substitute these values into equation 2

I = √(15/20)

I = √(0.75)

I = 0.866 A

Hence the maximum current that can flow safely through the appliance = 0.866 A

Answer:

a) h = 13,205.4 m

b)  r_f = 2.12 106 m

c)        e% = 0.68%

Explanation:

a) This is an exercise we are asked to use energy conservation,

Starting point. On the surface of Mimas

        Em₀ = K = ½ m v²

Final point. Where the ball stops

       [tex]Em_{f}[/tex] = U = m g h

        Em₀ = Em_{f}

        ½ m v² = m g h

         h = ½ v² / g

let's calculate

         h = ½ 41² / 0.0636

         h = 13,205.4 m

b) For this part we are asked to use the law of universal gravitation, write the energy

starting point. Satellite surface

           Em₀ = K + U = ½ m v² - GmM / r_o

final point. Where the ball stops

            [tex]Em_{f}[/tex]= U = - G mM / r_f

          Em₀ = Em_{f}

          ½ m v² - G m M / r_o = - G mM / r_f

In this case all distances are measured from the center of the satellite

         1 / rf = 1 / GM (-½ v² + G M / r_o)

let's calculate

         1 / rf = 1 / (6.67 10⁻¹¹ 3.75 10¹⁹) (- ½ 41 2 + 6.67 10⁻¹¹ 3.75 10¹⁹ / 1.98 105)

         1 / r_f = 3,998 10⁻¹¹(-840.5 + 12.63 10³)

          1 / r_f = 4,714 10⁻⁷

          r_f = 1 / 4,715 10⁻⁷

          r_f = 2.12 106 m

to measure this distance from the satellite surface

          r_f ’= r_f - r_o

          r_f ’= 2.12 106 - 1.98 105

         r_f ’= 1,922 106 m

c) the percentage difference is

          e% = 13 205.4 / 1,922 106 100

          e% = 0.68%

The estimate of part a is a little low

The image is missing, so i have attached it.

Answer:

The force exerted on the large block by the small block = 8.4 N

Explanation:

From the image attached, the mass of the small block = 2M while the mass of the large block = 3M

Also,Force on small block = F and force on large block = 2F

Equilibrium of forces on the left gives;

2F - N = 3Ma

Thus,

Ma = (2F - N)/3 - - - - eq1

Also, on right hand side, Equilibrium of forces gives;

N - F = 2Ma

Ma = (N - F)/2 - - - - eq2

Equating eq(1) and eq(2) gives us;

(2F - N)/3 = (N - F)/2

Where N is the force exerted on the large block by the small block.

Making N the subject gives;

4F - 2N = 3N - 3F

5N = 7F

N = 7F/5

We are given F = 6N

Thus;

N = 7(6)/5

N = 8.4 N

Answer: D) 1 and 2 tie, then 3, then 4.

Explanation: Gravitational Force is one of the 4 fundamental forces of nature (the others being eletromagnetic, weak force and strong force) and is explained by Newton's Law of Universal Gravitation, in which, every massive particle attracts every other massive particle.

The way to calculate gravitational force is:

[tex]F_{G} = \frac{GMm}{r^{2}}[/tex]

G is Universal Gravitational Constant and it is constant anywhere in the universe.

M and m are mass of each object;

r is distance between the objects;

The formula shows that gravitational force acts at an inverse square law, i.e., if objects are 2 distances apart, Force between them will decrease to one quarter of it was.

So, analysing the question, a particle inside an uniform spherical shell not at the center and at the center will have equal forces.

Outside at a distance 2r, force will be less than at a distance r.

Then the order is 1=2 > 3 > 4

Answer:

2

Explanation:

since the second object was in it stationary, it velocity is 0 m/s

Answer:

100 degrees Celsius

Explanation:

Water starts to boil at 100 degrees celcius or 212 degrees fahrenheit.

At 100 degrees Celsius water begin to boil and turns to steam.

The melting point for water is 0 degrees C (32 degrees F). The boiling point of water varies with atmospheric pressure. At lower pressure or higher altitudes, the boiling point is lower. At sea level, pure water boils at 212 °F (100°C).

If the temperature is much above 212°F, the water will boil. That means that it won't just evaporate from the surface but will form vapor bubbles, which then grow, inside the liquid itself. If the water has very few dust flecks etc.

Learn more about a boiling point here https://brainly.com/question/40140

#SPJ2

Answer:

The volume is [tex]V_a = 1.510 *10^{-5} m^3[/tex]

Explanation:

From the question we are told that

     The depth below the see is  [tex]d_1 = 30.0 \ m[/tex]

     The density of the sea is  [tex]\rho_s = 1025 \ kg /m^3[/tex]

      The temperature at this level is [tex]T_d = 5.00 ^oC = 278 \ K[/tex]

      The volume of the air bubble at this depth is  [tex]V_d = 0.95 \ cm^3 = 0.95 *0^{-6}\ m[/tex]

     The temperature at the surface is  [tex]T_a = 20^oC =293\ K[/tex]

Generally the pressure at the given depth is mathematically evaluated as  

        [tex]P_d = P_o + \rho_s * g * d[/tex]

Where [tex]P_o[/tex] is the atmospheric pressure with a constant value

        [tex]P_o = 1.013 *10^{5} \ Pa[/tex]

substituting values

       [tex]P_d = 1.013 * 10^{5} * + (1025 * 9.8 * 30 )[/tex]

        [tex]P_d = 4.02650 * 10^{5} \ Pa[/tex]

According to the combined gas law  

          [tex]\frac{P_a * V_a }{T_a } = \frac{P_d * V_d }{T_d }[/tex]

=>      [tex]V_a = \frac{4.026650 *10^{5} * 0.95 *10^{-6} * 293 }{278 * 1.013*10^{5} }[/tex]

=>     [tex]V_a = 1.510 *10^{-5} m^3[/tex]

I bel.ieve the answer is 279Ghz

The required value of pressure-variation amplitude of the given sound wave is 11.84 Pa.

Given data:

The speed of sound in air is, v = 340 m/s.

The density of air is, [tex]\rho = 1.2 \;\rm kg/m^{3}[/tex].

The frequency of sound wave is, f = 330 Hz.

The displacement amplitude of sound wave is, [tex]A = 14 \;\rm \mu m= 14 \times 10^{-6} \;\rm m[/tex].

The standard expression for the pressure variation amplitude for the sound wave propagating in air medium is,

[tex]\Delta P= B \times A \times K[/tex]

Here,

B is the Bulk Modulus and its value is, [tex]B = \rho \times v^{2}[/tex].

K is the wave form constant and its value is, [tex]K = \dfrac{2 \pi f}{v}[/tex].

Solving as,

[tex]\Delta P= (\rho \times v^{2}) \times A \times \dfrac{2 \pi f}{v}\\\\\Delta P= (\rho \times v) \times A \times (2 \pi f)\\\\\Delta P= (1.2 \times 340) \times (14 \times 10^{-6}) \times (2 \pi \times 330)\\\\\Delta P= 11.84 \;\rm Pa[/tex]

Thus, we can conclude that the required value of pressure-variation amplitude of the given sound wave is 11.84 Pa.

Learn more about the pressure-variation amplitude here:

https://brainly.com/question/13091615

Answer:

-72.0°C

Explanation:

PV = nRT

Since n, number of moles, is constant:

PV / T = PV / T

(4.65×10⁶ Pa) V / (21 + 273.15) K = (1.06×10⁶ Pa) (3V) / T

T = 201.16 K

T = -72.0°C

Answer:

The fraction of light that escapes the water surface as the water moves deeper into the water will decrease.

Explanation:

The speed of light in water is small compared to the speed of light in air, and a larger part of the light energy is absorbed in water than in air. When the bulb is immersed in water, some of the light energy is absorbed by the mass of water. When the light bulb is further moved deeper into the water, the fraction of light that escapes decreases, because more mass of water is made available to absorb more of the light energy from the bulb.

Answer:

The speed of the ball relative to the ground if the ball is thrown forward is 58.1 m/s

Explanation:

Given;

speed of the ball thrown inside boxcar, [tex]V_B[/tex] = 23.2 m/s

speed of the boxcar moving along the tracks, [tex]V_T[/tex] = 34.9 m/s

Determine the speed of the ball relative to the ground if the ball is thrown forward.

If the ball is thrown forward, the speed of the ball relative to the ground will be sum of the ball's speed plus speed of the boxcar.

[tex]V_{relative \ speed} = V_B + V_T\\\\V_{relative \ speed} = 23.2 + 34.9\\\\V_{relative \ speed} = 58.1 \ m/s[/tex]

Therefore,  the speed of the ball relative to the ground if the ball is thrown forward is 58.1 m/s.

Answer:

408N at 89.89°

Explanation:

This problem requires that we resolve the force vectors into

x- and y

-componentsOnce this is done, we can add the components easily, as the one 2-dimensional problem will be two 1-dimensional problems.

Finally, we will convert the resultant force into standard form and find the equilibrant.

Resolve into components:

F1x =F1cos 180°= 232(−1)=−232N

F1y=F1sin180°=0N

F2x=F2cos(−140°)=194(−0.766)=−148.6N

F1y=F1sin(−140°)=232(−0.643)=−149.17N

Note the change of the angle used to give the direction of

F2. Standard angles (rotation from thex

-axis; counterclockwise is +) should be used to avoid sign errors in the results.

Now, we add the components:

Fx=F1x+F2x=−380.6N

Fy=F1y+F1y=−148.17N

Technically, this is the resultant force. However, it should be changed back into standard form. Here's how:

F=√(Fx)2(Fy)2=√(−380.6)^2(−148.17)^2=408N

θ=tan−1(−148.17−380.6)

=89.89°

Answer:

1.8 x 10^-8A

Explanation:

Using the equation for current:

I= Q/t

current = (9X10^-12)/ (0.50X 10^-3)

= 1.8^-8A

Answer:

case 1 of physics is the answer

Answer:

Infrared telescope and camera

Explanation:

An infrared telescope uses infrared light to detect celestial bodies. The infrared radiation is one of the known forms of electromagnetic radiation. Infrared radiation is given off by a body possessing some form of heat. All bodies above the absolute zero temperature in the universe radiates some form of heat, which can then be detected by an infrared telescope, and infrared radiation can be used to study or look into a system that is void of detectable visible light.

Stars are celestial bodies that are constantly radiating heat. In order to see a clearer picture of the these bodies, Infrared images is better used, since they are able to penetrate the surrounding clouds of dust, and have located many more stellar components than any other types of telescope, especially in dusty regions of star clusters like the Trapezium cluster.

Answer:

0

Explanation:

On a graph, if there is plot of time vs velocity, then area of velocity plot gives the displacement.

also we can see area of plot is velocity* time which is equal to formula of displacement.

area for this plot is velocity * time

Thus,

from

t =0 to t = 0.2

v = 20

t = 0.2 - 0 = 0.2

thus, displacement till 0.2 seconds = 20*0.2 = 4 Km

____________________________________________________

from

t =0 to t = 0.4

v = 0

t = 0.4 - 0.2 = 0.2

thus, displacement from  0.2 seconds to 0.4 seconds = 0*0.2 = 0 Km

____________________________________________________

from

t =0.4 to t = 0.6

v = -20

t = 0.6 - 0.4 = 0.2

thus, displacement from  0.4 seconds to 0.6 seconds = -20*0.2 = -4 Km

Thus, total displacement = 4+0 -4 = 0

Thus, net displacement made by car is 0.

Answer:

A) V_rms = 29 V

B) Vav = 0 V

Explanation:

A) We are told that;

V = V_o cos ωt

voltage amplitude; V = V_o = 41.0V

Now, the formula for the root-mean-square potential difference Vrms is given as;

V_rms = V/√2

Thus plugging in relevant values, we have;

V_rms = 41/√2

V_rms = 29 V

B) Due to the fact that the voltage is sinusoidal from the given V = V_o cos ωt, we can say that the average potential difference Vav between the two terminals of the power supply would be zero.

Thus; Vav = 0 V

A. The root-mean-square potential difference ([tex]V_{rms}[/tex]) is equal to 28.99 Volts.

B. For this voltage with a sinusoidal waveform (sine wave), the average potential difference ([tex]V_{ave}[/tex]) between the two terminals of the power supply is equal to zero (0).

Given the following data:

The voltage across the terminals of an alternating current (AC) power supply varies directly with time according to the equation:

[tex]V_0 = V_0cos(t)[/tex]

A. To find the root-mean-square potential difference ([tex]V_{rms}[/tex]):

Mathematically, root-mean-square for voltage in an alternating current (AC) power supply (circuit) is given by the formula:

[tex]V_{rms} = \frac{V}{\sqrt{2} }[/tex]

Substituting the given parameter into the formula, we have;

[tex]V_{rms} = \frac{41}{\sqrt{2} }\\\\V_{rms} = \frac{41}{1.4142 }\\\\V_{rms} = 28.99\; Volts[/tex]

B. To find the average potential difference ([tex]V_{ave}[/tex]) between the two terminals of the power supply:

For this voltage with a sinusoidal waveform (sine wave), the average potential difference ([tex]V_{ave}[/tex]) between the two terminals of the power supply is equal to zero (0).

Read more: https://brainly.com/question/15121836

Answer:

F= 3.56e22N

Explanation:

Using the force of radiation acting on the earth which is

force = radiation pressure x area = (intensity/c)xpi R^2

force = 1370W/m^2 x pi x( 6.37x10^6m)^2/3x10^8m/s

force = 5.82x10^8 N

But the sun's gravitational attraction means the magnitude of the solar gravitational force on earth: If that's the case, the answer is approx 10^22 N:

F=GMm/r^2

G=6.67x10^(-11)=6.67e-11

M=mass sun = 2x10^30kg=2e30

m=mass earth = 6x10^24kg

r=earth sun distance = 1.5x10^11m

F=(6.6e-11)(2e30)(6e24)/(1.5e11)^2 =

F= 3.56e22N

Answer:

2.8

Explanation:

Using p = m/v; (old density)

p' = m/v (new density)

=m/0.350 V

p'/p = (m/0.350V)/(m/v) = 1/0.350 = 2.86