The electic field inside a spherical volume of radius a is given by: vector E = p_0 r^2 / 4 epsilon r cap Find an expression for the charge density inside the spherical volume that gives rise to this electric field.

Answer:

1124.8 Volt

Explanation:

N = 200, Diameter = 0.18 m, Radius, r = 0.09 m, f = 3250 rpm = 54.17 rps

B = 0.65 T

the peak value of induced emf is given by

e0 = N x B x A x ω

e0 = 200 x 0.65 x 3.14 x 0.09 x 0.09 x 2 x 3.14 x 54.17

e0 = 1124.8 Volt

The peak voltage of the generator can be calculated using Faraday's law of electromagnetic induction, taking into consideration the number of turns in the coil, the strength of the magnetic field, the area of the coil, and the speed at which the coil is rotating. In this case, it's 1100 volts.

The subject of this question is a practical application of Faraday's law of electromagnetic induction, which is a topic typically covered in high school or college-level physics. We can find the peak voltage of a rotating generator using the formula for Induced electromotive force (emf), also known as voltage, in a rotating coil, which is given by ε_max = NBAω. Here, N is the number of turns in the coil, B is the magnetic field strength, A is the area of the coil, and ω is the angular velocity.

Let's calculate each parameter. The area A of the coil can be calculated using the formula for the area A = πr^2, where r is the radius of the coil. Given the diameter d=0.18 m, we get r = d/2 = 0.09 m, which gives A = π * (0.09 m)^2 = 0.025 m^2. The angular velocity ω in rad/s is calculated using the relation ω = 2πf, where f is the frequency in Hz. Given the frequency in rpm (revolutions per minute), we convert it to Hz by dividing by 60, hence f = 3250/60 = 54.16 Hz. Then ω = 2π * 54.16 Hz = 340.53 rad/s. Now, we can substitute the values into the emf equation: ε_max = (200 turns) * (0.65 T) * (0.025 m^2) * (340.53 rad/s) = 1100 volts. Hence, the peak voltage of the generator is 1100 volts.

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To find the speed of the 3,000-kg car before the collision, use the principle of conservation of momentum. Calculate the total momentum of the combined cars after the collision based on the mass and speed. Apply the principle of conservation of momentum again to determine the initial speed of the 3,000-kg car.

To find the speed of the 3,000-kg car before the collision, we can use the principle of conservation of momentum. In this case, the momentum before the collision is equal to the momentum after the collision. So, we can equate the momentum of the 2,000-kg car moving east to the momentum of the combined cars moving at an angle of 48.0° north of east.

Using trigonometry, we can determine the components of the velocity of the cars after the collision. The horizontal component will be the speed of the cars moving east, and the vertical component will be the speed of the cars moving north. From the given information, we can calculate the total momentum after the collision based on the mass and speed of the combined cars.

Finally, we can use the principle of conservation of momentum again to determine the speed of the 3,000-kg car before the collision. Rearranging the equation and substituting the known values, we can solve for the initial speed of the 3,000-kg car.

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The speed of the 3,000-kg car before the collision is 7.93 m/s.

To find the speed of the 3,000-kg car before the collision, we can use the principle of conservation of momentum. Before the collision, the 2,000-kg car is moving east at 10.0 m/s and the 3,000-kg car is moving north. After the collision, the two cars stick together and move as a unit. Using the given information, we can set up an equation

(2,000 kg)(10.0 m/s) + (3,000 kg)(v) = (5,000 kg)(5.98 m/s

Solving for v, we find that the speed of the 3,000-kg car before the collision is 7.93 m/s.

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Answer:

The minimum number of 100 Ω resistors that i need to design an effective resistor with 275Ω resistance are 8 resistors.

Explanation:

(2 Resistors of 100Ω in parallel) in series with (4 resistors of 100Ω in parallel) in series with 2 resistors of 100Ω.

2 resistors in parallel of 100Ω = 50Ω

+

4 resistors in parallel of 100Ω = 25Ω

+

2 resistors in series of 100 2Ω = 200Ω

=

275Ω

Answer:

4L

Explanation:

mass of pendulum = M, length of pendulum, L1 = L,

acceleration due to gravity = g, Amplitude = A

Use the formula for the time period for simple pendulum

[tex]T = 2\pi \sqrt{\frac{L}{g}}[/tex]     ..... (11)

Let the new length be L2 for which the time period is 2T.

[tex]2T = 2\pi \sqrt{\frac{L_{2}}{g}}[/tex]          ..... (2)

Divide equation (2) by equation (1)

[tex]\frac{2T}{T} = \sqrt{\frac{L_{2}}{L}}[/tex]

So, L2 = 4 L

Thus, the length of the pendulum is 4 L.

Answer:

Work done by firefighter = 13456.57 J

Explanation:

Here work done is equal to potential energy gained by him.

Potential energy, PE = mgh, where m is the mass, g is acceleration due to gravity value and h is the height.

Mass, m = 64.4 kg

Acceleration due to gravity, g = 9.8 m/s²

Height, h = 21.3 m

Substituting

Potential energy, PE = mgh = 64.4 x 9.81 x 21.3 = 13456.57 J

Work done by firefighter = 13456.57 J

Answer:

4.9 m/s²

Explanation:

F = reading of the elevator while running = 594 N

W = weight of person and elevator together when at stop = 396 N

m = mass of person and elevator together

a = acceleration of elevator

Weight of the person is given as

W = mg

inserting the values

396 = m (9.8)

m = 40.4 kg

Force equation for the motion of the elevator is given as

F - W = ma

Inserting the values

594 - 396 = (40.4) a

a = 4.9 m/s²

Answer: Addition polymerization & Condensation polymerization

Answer:

mathy math

Explanation:

do you eat at baskin-robbins?

btw, answer is probably 78 (6-9)x 67,587r Xy

Answer: Real image

Explanation:

converging lens will only produce a real image if the object is located beyond the focal point (i.e., more than one focal length away).

(a) [tex]1.50\cdot 10^{-6}J[/tex]

According to the work-energy theorem, the work done by the electric force is equal to the kinetic energy gained by the particle, so we can write:

[tex]W=K_f - K_i[/tex]

where

W is the work done by the electric force

[tex]K_f[/tex] is the final kinetic energy of the particle

[tex]K_i[/tex] is the initial kinetic energy of the particle

Since the particle starts from rest, [tex]K_i = 0[/tex]. Moreover,

[tex]K_f = 1.50\cdot 10^{-6}J[/tex]

Therefore, the work done by the electric force is

[tex]W=K_f = 1.50\cdot 10^{-6}J[/tex]

(b) -333.3 V

According to the law of conservation of energy, the gain in kinetic energy of the particle must correspond to a loss in electric potential energy, so we can write:

[tex]\Delta K = -\Delta U[/tex]

Where

[tex]\Delta K = 1.50\cdot 10^{-6} J[/tex] is the gain in kinetic energy

[tex]\Delta U[/tex] is the loss in electric potential energy

So we have

[tex]\Delta U = - \Delta K = -1.50\cdot 10^{-6}J[/tex]

The loss in electric potential energy can be rewritten as

[tex]\Delta U = q \Delta V[/tex]

where

[tex]q=+4.50 nC = 4.5\cdot 10^{-9} C[/tex] is the charge of the particle

[tex]\Delta V[/tex] is the change in electric potential over the distance the charge has moved

Solving for [tex]\Delta V[/tex],

[tex]\Delta V= \frac{\Delta U}{q}=\frac{-1.50\cdot 10^{-6}}{4.5\cdot 10^{-9}}=-333.3 V[/tex]

(c) 4166 V/m

The magnitude of the electric field is given by

[tex]E=\frac{|\Delta V|}{d}[/tex]

where

[tex]|\Delta V|[/tex] is the magnitude of the change in electric potential

d is the distance through which the charge has moved

Since we have

[tex]|\Delta V|=333.3 V\\d = 8.00 cm = 0.08 m[/tex]

The magnitude of the electric field is

[tex]E=\frac{333.3}{0.08}=4166 V/m[/tex]

(d) [tex]-1.50\cdot 10^{-6}J[/tex]

The change in electric potential energy of the charge  has already been calculated in part (b), and it is

[tex]\Delta U = -1.50\cdot 10^{-6}J[/tex]

Answer:

R = 0.27 ohm

i = 11.25 A

Explanation:

Resistance of a given cylindrical rod is

[tex]R = \rho \frac{L}{A}[/tex]

here we know that

[tex]\rho = \frac{1}{3 \times 10^4} = 3.33 \times 10^{-5} ohm-m[/tex]

Now we have

[tex]R = (3.33 \times 10^{-5})\times \frac{4 \times 10^{-3}}{0.5 \times 10^{-6}}[/tex]

[tex]R = 0.27 ohm[/tex]

now we know by ohm's law

[tex]\Delta V = i R[/tex]

[tex]14 - 11 = i ( 0.27)[/tex]

[tex]i = 11.25 A[/tex]

Answer:

15.6 m

Explanation:

d = diameter of the wheel = 43 cm = 0.43 m

r = radius of the wheel = (0.5) d = (0.5) (0.43) = 0.215 m

w₀ = initial angular velocity = 86 rpm = 9.01 rad/s

v₀ = initial linear speed = r w₀ = (0.215) (9.01) = 1.94 m/s

w = final angular velocity = 362 rpm = 37.91 rad/s

v = final linear speed = r w = (0.215) (37.91) = 8.15 m/s

t = time taken = 3.1 s

Using the equation

v = v₀ + at

8.15 = 1.94 + a (3.1)

a = 2 m/s²

d = distance traveled by a point at the edge of the wheel

Using the equation

d =  v₀ t + (0.5) at²

d =  (1.94) (3.1) + (0.5) (2) (3.1)²

d = 15.6 m

The problem requires the understanding of simple harmonic motion in physics. The position of an oscillating mass attached to a spring can be calculated using the SHM formulas and given parameters: weight of the mass, stretch of the spring, and acceleration due to gravity. The amplitude, spring constant, angular frequency, and phase constant are figured out before plugging them into the positional formula.

This question involves the concept of simple harmonic motion (SHM) in Physics. In this scenario, a mass attached to a spring and released from a certain position will oscillate in SHM. The position of the mass at specific times (t = π/12, π/8, π/6, π/4, and 9π/32 s) can be calculated using the SHM formulas.

Since the mass is released from 6 inches (or 0.5 feet) below the equilibrium position, this value represents the amplitude (A) of the oscillation. Additionally, we know that the spring constant (k) can be found from the weight of the mass and the stretch of the spring. This gives us k = W/d = 20 lbs / 0.5 ft = 40 lbs/ft.

The angular frequency (ω) of the oscillation can be derived from ω = sqrt(k/m), where m is the mass of the object. Using the information provided (considering g = 32 ft/s2), we find m = W/g = 20 lbs / 32 ft/ s2 = 0.625 slugs. Hence, ω = sqrt(40 lbs/ft / 0.625 slugs) = 8 rad/s.

Finally, using the formula for the position in a SHM (x = A*cos(ω*t + φ), where φ is the phase constant), and knowing that the mass was initially released from rest, we can determine that φ = 0. As a result, the position at the specified times can be calculated by substituting the corresponding values into the relation.

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To find the position of the mass at different times, use the equation for simple harmonic motion (SHM) and calculate the angular frequency. Then plug in the values and use the equation x = A * cos(ωt + φ) to find the positions.

The position x of the mass at different times can be found using the equation for simple harmonic motion (SHM):

x = A * cos(ωt + φ)

where x is the position, A is the amplitude, ω is the angular frequency, t is the time, and φ is the phase constant.

In this case, the amplitude A is 6 inches and the angular frequency ω can be found using the formula ω = sqrt(k/m), where k is the spring constant and m is the mass. The spring constant k can be found using the formula k = (g * m)/A, where g is the acceleration due to gravity.

By plugging in the values and calculating ω, you can then find the positions x at the given times using the equation x = A * cos(ωt + φ).

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Answer:

Energy density = 0.0831 J/m³

Explanation:

Energy density of a capacitor is given by the expression

        [tex]u=\frac{1}{2}\epsilon E^2[/tex]

We have electric field ,

              [tex]E=\frac{V}{d}=\frac{480}{3.5\times 10^{-3}}=1.37\times 10^5V/m[/tex]

Here there is no dielectric

So energy density,

         [tex]u=\frac{1}{2}\epsilon_0 E^2=\frac{1}{2}\times 8.85\times 10^{-12} \times (1.37\times 10^5)^2=8.31\times 10^{-2}=0.0831 J/m^3[/tex]

Energy density = 0.0831 J/m³  

Answer:

the impedance of the circuit is 25.7 ohms.

Explanation:

It is given that,

Voltage, V = 50 volts

Frequency, f = 60 Hz

Resistance, R = 25 ohms

Capacitive resistance, [tex]X_C=18\ ohms[/tex]

Inductive resistance, [tex]X_L=24\ ohms[/tex]

We need to find the impedance of the circuit. It is given by :

[tex]Z=\sqrt{R^2+(X_L-X_C)^2}[/tex]

[tex]Z=\sqrt{25^2+(24-18)^2}[/tex]

Z = 25.7 ohms

So, the impedance of the circuit is 25.7 ohms. Hence, this is the required solution.

Explanation:

It is given that,

Radius of earth, r = 6371 km

An earth satellite moves in a circular orbit above the Earth's surface, d = 561 km

So, radius of satellite, R = 6371 km + 561 km = 6932 × 10³ m

Time taken, t = 95.68 min = 5740.8 sec

(a) Speed of the satellite is given by :

[tex]v=\dfrac{d}{t}[/tex]

d = distance covered

For circular path, d = 2πR

[tex]v=\dfrac{2\pi \times 6932\times 10^3\ m}{5740.8\ sec}[/tex]

v = 7586.92 m/s

(b) Centripetal acceleration is given by :

[tex]a=\dfrac{v^2}{R}[/tex]

[tex]a=\dfrac{(7586.92\ m/s)^2}{6932\times 10^3\ m}[/tex]

[tex]a=8.3\ m/s^2[/tex]

Hence, this is the required solution.

a) The speed of the satellite is approximately 7584.38 m/s  

b) The magnitude of the centripetal acceleration is approximately 8.29 m/s².

To solve this problem, we will calculate both the speed and the magnitude of the centripetal acceleration of the satellite.

(a) Speed of the Satellite

First, we need to determine the radius of the satellite's orbit. The radius of the Earth is R = 6378 km. Since the satellite orbits 561 km above the surface, the radius of the orbit (r) is:

[tex]r = 6378 km + 561 km = 6939 km = 6939000 m[/tex]

The period (T) of the satellite is 95.68 minutes, which we convert to seconds:

[tex]T = 95.68 min \times 60 s/min = 5740.8 s[/tex]

Using the formula for the speed (v) of an object in circular motion:

[tex]v = 2\pi r/T[/tex]

We can plug in the values:

[tex]v = 2\pi \times 6939000 m / 5740.8 s = 7584.38 m/s[/tex]

(b) Magnitude of the Centripetal Acceleration

The centripetal acceleration (ac) is given by:

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

Substituting the values we have:

[tex]a_c = (7584.38 m/s)^2 / 6939000 m = 8.29 m/s^2[/tex]

Answer:0.4061 L

Explanation:

let initial volume of gas be [tex]V_1[/tex]=1 L

[tex]\gamma[/tex] =1.3

initial temprature[tex]\left ( T_1\right )[/tex]=273k

Now if gas is compressed adiabatically to half of its initial volume then

[tex]V_2[/tex]=0.5L

Using adiabatic relation

[tex]TV^{\gamma -1}[/tex]=constant

[tex]T_1V_1^{\gamma -1}[/tex]=[tex]T_2V_2^{\gamma -1}[/tex]

[tex]273\times \left ( \frac{1}{0.5}\right )^\left ( {\gamma -1}\right )[/tex]=[tex]T_2[/tex]

[tex]T_2[/tex]=273[tex]\times \left ( 2\right )^\left ( 0.3\right )[/tex]

[tex]T_2[/tex]=336.1k

Now the is cooled at constant pressure i.e.

[tex]\frac{V_2}{T_2}[/tex]=[tex]\frac{V_3}{T_3}[/tex]

[tex]\frac{0.5}{336.1}[/tex]=[tex]\frac{V_3}{273}[/tex]

[tex]\frac{0.5}{336.1}[/tex]=[tex]\frac{V_3}{273}[/tex]

[tex]V_3[/tex]=0.406 L

The final volume of the gas after it is cooled to 273 K at constant pressure, following an adiabatic compression to half its initial volume, will remain at 0.5 L.

The question involves an adiabatic compression of a gas followed by cooling at constant pressure. To find the final volume after the gas is cooled to 273 K at constant pressure, we can use the ideal gas law before and after the compression, considering that for adiabatic processes, PVγ is constant (where P is pressure, V is volume, and γ is the adiabatic index). After the adiabatic compression, we have a new volume of 0.5 L and a new pressure. We then cool the gas at this new pressure back to the original temperature of 273 K. By the ideal gas law (PV = nRT), at constant temperature and number of moles (n), the final volume (Vf) will be equal to the initial volume (Vi) because the pressure has remained constant after the compression step.

Therefore, even after cooling, the final volume will remain at 0.5 L because pressure does not change during the cooling process at constant pressure.

Answer:

[tex]v_B = 52.4 m/s[/tex]

Explanation:

For unbanked road the maximum friction force will provide centripetal force to the car.

So here we will have

[tex]F_c = \frac{mv^2}{R}[/tex]

Since we know that centripetal force here is due to friction force

[tex]F_c = F_f[/tex]

[tex]\mu mg = \frac{mv^2}{R}[/tex]

now for two cars we will have

[tex]\mu_A m_A g = \frac{m_A v_A^2}{R}[/tex]

also we have

[tex]\mu_B m_B g = \frac{m_B v_B^2}{R}[/tex]

now by division of two equations

[tex]\frac{\mu_A}{\mu_B} = \frac{v_A^2}{v_B^2}[/tex]

[tex]\frac{0.169}{0.826} = \frac{23.7^2}{v_B^2}[/tex]

so we will have

[tex]v_B = 52.4 m/s[/tex]

Final answer:

The maximum speed at which car B can negotiate the curve is approximately 52.4 m/s, assuming the same curve and conditions as for car A.

Explanation:

To determine the maximum speed at which car B can negotiate the curve, we need to use the relationship between the coefficient of static friction and the maximum speed a car can maintain without slipping on a curve.

The centripetal force required to keep a car moving in a circle of radius r is provided by the frictional force, which is the product of the coefficient of static friction μ and the normal force N, which for a flat curve is equal to the weight of the car.

Since car A, with a coefficient of static friction of 0.169, can negotiate the curve at a speed of 23.7 m/s, we can use proportionality to find the speed for car B, as the friction forces are proportional to the coefficients of static friction of their respective tires:

VB = VA ∙ √(μB / μA)

Substituting the given values:

VB = 23.7 m/s ∙ √(0.826 / 0.169)

VB = 23.7 m/s ∙ √(4.89) ≈ 23.7 m/s ∙ 2.21

VB ≈ 52.4 m/s

Therefore, the maximum speed at which car B can negotiate the curve is approximately 52.4 m/s, assuming the same curve and conditions as for car A.

Answer:

0.567 Weber

Explanation:

side, a = 0.31 m, B = 5.9 T

Area, A = (0.31)^2 = 0.0961 m^2

Magnetic flux, ∅ = B x A

∅ = 5.9 x 0.0961 = 0.567 Weber

Answer:

Q = 30.07 kJ/sec

Explanation:

GIVEN DATA:

temperature of steam = 40 degree celcius

mass flow rate = 63 kg/h

from saturated water tables,

from temperature 40 °, enthalpy of evaporation[tex]h_f[/tex] value is 2406 kj/kg

rate of heat transfer (Q) can be determine by using following relation

[tex]Q = \dot{m} h_f[/tex]

putting all value to get Q value

Q = 45 *2406

Q = 108270 kJ/h

[tex]Q = 108270 *\frac{1}{3600} kJ/s[/tex]

Q = 30.07 kJ/sec

Explanation:

According to the water table, the value of enthalpy of evaporation at a temperature of [tex]40^{o}C[/tex] is 2406.0 kJ/kg.

Hence, we will calculate the rate of heat transfer by using the formula as follows.

               Q = [tex]m \times h_{fg}[/tex]

where,  m = mass

           [tex]h_{fg}[/tex] = enthalpy of evaporation

Putting the given values into the above formula as follows.

              Q = [tex]m \times h_{fg}[/tex]

                  = [tex]63 kg/h \times 2406.0 kJ/kg[/tex]

                  = 151578 kJ/h

or,              = [tex]151578 \times \frac{1}{3600} kJ/s[/tex]

                  = 42.105 kW

Thus, we can conclude that rate of heat transfer from the steam to the cooling water flowing through the pipe is 42.105 kW.

Answer:

From  the given information we can infer that the field is not conservative.

Explanation:

For a conservative field the work done on an object in moving it from a position given by co-ordinates [tex](x_{1},y_{1},z_{1})[/tex] to another position with co-ordinates [tex](x_{2},y_{2},z_{2})[/tex]  shall be independent of the path we take in between to reach our final position (by definition of a conservative field). But in the given case since the initial and the final position of both the curves [tex]C_{1},C_{2}[/tex] coincide but the work done along both the paths is different thus we conclude that the field is not conservative.

Answer:

108.37°C

Explanation:

P₁ = Initial pressure = 101 kPa

V₁ = Initial volume = 530 m³

T₁ = Initial temperature = 10°C = 10+273.15 =283.15 K

P₂ = Final pressure = 101 kPa (because it is open to atmosphere)

V₂ = Final volume = 530 m³

P₁V₁ = n₁RT₁

⇒101×530 = n₁RT₁

⇒53530 J = n₁RT₁

P₂V₂ = n₂RT₂

⇒53530 J = n₂RT₂

[tex]\frac{m_1}{m_2}=\frac{\rho V_1}{\rho V_1-170}\\\Rightarrow \frac{m_1}{m_2}=\frac{1.244\times 530}{1.244\times 530-170}=1.347\\\Rightarrow \frac{m_1}{m_2}=1.347\\\Rightarrow \frac{n_1}{n_2}=1.347[/tex]

Dividing the first two equations we get

[tex]1=\frac{n_1}{n_2}\frac{T_1}{T_2}\\\Rightarrow 1=1.347\frac{283.15}{T_2}\\\Rightarrow T_2=1.347\times 283.15= 381.52\ K[/tex]

∴Temperature must the air in the balloon be warmed before the balloon will lift off is 381.25-273.15 = 108.37°C

To lift off, the air in the balloon must be warmed to a temperature of approximately 916.93 K.

To calculate the temperature to which the air in the balloon must be warmed before it lifts off, we can use the ideal gas law equation: PV = nRT.

The volume of the balloon is given as 530 m3, the pressure is atmospheric pressure (101 kPa), and the mass is 170 kg (which can be converted to moles using the molar mass of air). We can rearrange the equation to solve for temperature:

T = PV/(nR)

Substituting the values, we have:

T = (101,000 Pa) × (530 m3) / (n × 8.31 J/mol·K)

Where n is the number of moles of air. To find the number of moles, we can use the density of air at 10.0°C (1.244 kg/m3):

n = mass / molar mass = 170 kg / (1.244 kg/m3  × 530 m3)

Substituting this value for n and solving for T:

T = (101,000 Pa) × (530 m3) / ((170 kg / (1.244 kg/m3 × 530 m3)) × 8.31 J/mol·K)

Calculating, we find T ≈ 916.93 K.

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Answer:

it is concept that considered all matter in universe homogeneous and it is acceptable on large scale.

Explanation:

The cosmological principle is the concept that, when recognized on a large basis, the visual allocation of matter and energy is homogeneous and isotropic, since the forces are expected to act homogeneously across the universe and should therefore not produce any observed errors in the wide-scale. This eliminates any uncertainty about irregularities in the characteristics of matter and even includes the development of this matter since its creation during the Big Bang.

Final answer:

The cosmological principle states that the universe at any given time is the same everywhere on a large scale. This principle is crucial for understanding and studying the universe, as it allows us to make assumptions about its properties based on what we observe locally. It is a fundamental concept in cosmology.

Explanation:

The cosmological principle is the assumption that, on a large scale, the universe at any given time is the same everywhere, meaning it is isotropic and homogeneous. This principle is the starting assumption for nearly all theories that describe the entire universe. It implies that the universe is about the same everywhere, apart from changes with time, and that the part we can see around us is representative of the whole.

Answer:

a)4.36*10^-12W/m^2

b)L=6.39dB

c)ξ=5.73×10⁻¹¹m

Explanation:

Take speed of sound in air as 344m/s and density of air 1.2kg/m3 .

a)

[tex]I=\frac{P^2}{2pv}[/tex]

where

P=pressure

p=density of air

v=velocity

[tex]I=\frac{6*10^-5^2}{2*1.2*344} = 4.36*10^-12[/tex] W/m^2

b)

Sound intensity level in dB is defined as:  

L = 10∙log₁₀(I/I₀)  

with  

I₀ = 1.0×10⁻¹² W/m²  

Hence;  

L = 10∙log₁₀( 4.36x10^-12 W/m² / 1.0×10⁻¹² W/m²) = 6.39dB

c)

Displacement is given by :  

ξ = p/(Z∙ω) = p/(Z∙2∙π∙f)  

where  

Z = 416.9 N∙s/m³ = 416.9 Pa∙s/m

f frequency and ω angular frequency of the sound wave.  

So the amplitude of this sound wave is:  

ξ = 6×10⁻⁵Pa / (416.9 Pa∙s/m ∙ 2∙π∙ 400s⁻¹) = 5.73×10⁻¹¹m

To calculate the intensity and sound intensity level of a sound wave with a frequency of 400 Hz and a pressure amplitude of 6.0 * 10^(-10) Pa, use the given formulas. The intensity is 1.5 * 10^(-16) W/m², the sound intensity level is -60 dB, and the displacement amplitude is 5.3 * 10^(-9) m.

To calculate the intensity and sound intensity level of a sound wave with a frequency of 400 Hz and a pressure amplitude of 6.0 * 10^(-10) Pa, we can use the formulas:

(a) Intensity (I) = (Pressure Amplitude)^2 / (2 * Z)

(b) Sound Intensity Level (SIL) = 10 * log10(I / Io)

(c) Displacement Amplitude = Pressure Amplitude / (2 * π * f * v)

Using the given values, we can calculate:

(a) Intensity = (6.0 * 10^(-10))^2 / (2 * (1.21 * 10^(-3))) = 1.5 * 10^(-16) W/m²

(b) Sound Intensity Level = 10 * log10((1.5 * 10^(-16)) / (10^(-12))) = -60 dB

(c) Displacement Amplitude = (6.0 * 10^(-10)) / (2 * π * 400 * 343) = 5.3 * 10^(-9) m

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Answer:

47.86 m

Explanation:

Consider the motion along the vertical direction and assume the motion in downward direction as negative

y = vertical displacement = - 0.025 m

a = acceleration = - 9.8 m/s²

t = time taken to strike the target below the center

[tex]v_{oy}[/tex] = initial velocity along the vertical direction = 0 m/s

Using the kinematics equation

y = [tex]v_{oy}[/tex] t + (0.5) a t²

Inserting the values

- 0.025 = (0) t + (0.5) (- 9.8) t²

t = 0.0714 sec

Consider the motion along the horizontal direction

x = horizontal displacement = horizontal distance between the end of the rifle and the bull's-eye

v₀ = velocity along the horizontal direction = 670 m/s

Since there is no acceleration along the horizontal direction, we have

x = v₀ t

inserting the values

x = (670) (0.0714)

x = 47.86 m

The horizontal distance between the end of the rifle and the bull's-eye is approximately 47.9 meters.

To solve this problem, we need to determine the horizontal distance from the rifle to the bull's-eye based on the given data.

Understand the Problem: The bullet is fired horizontally with a muzzle speed of 670 m/s and hits the target 0.025 m below the center due to gravity.

Use Kinematics: Gravity affects the vertical motion, and the horizontal motion is constant because there's no acceleration horizontally in the given conditions.

Calculate the Time it Takes for the Bullet to Drop 0.025 m:

The vertical distance (y) the bullet drops can be calculated using the equation of motion under gravity:

[tex]y = \frac{1}{2} g t^2[/tex]

Where:

Rearranging for [tex]t[/tex]:

[tex]t = \sqrt{\frac{2y}{g}} = \sqrt{\frac{2 \times 0.025}{9.8}} \approx 0.0714 \text{ seconds}[/tex]

Calculate the Horizontal Distance (x):

Now that we have the time [tex]t[/tex], we can find the horizontal distance using the constant horizontal velocity.

[tex]x = v \cdot t[/tex]

Where:

[tex]x = 670 \times 0.0714 \approx 47.9 \text{ meters}[/tex]

Answer:

Frequency, f = 7.57 Hz

Explanation:

It is given that,

Capacitance, [tex]C=3\ \mu F=3\times 10^{-6}\ F[/tex]

Capacitive reactance, [tex]X_C=7\ k\Omega=7\times 10^3\ \Omega[/tex]

We need to find the frequency. The capacitive reactance of the capacitor is given by :

[tex]X_C=\dfrac{1}{2\pi fC}[/tex]

f is the frequency

[tex]f=\dfrac{1}{2\pi CX_C}[/tex]

[tex]f=\dfrac{1}{2\pi \times 3\times 10^{-6}\ F\times 7\times 10^3\ \Omega}[/tex]

f = 7.57 Hz

Hence, this is the required solution.

Answer:

Wavelength of the ball is [tex]\lambda=1.05\times 10^{-34}\ m[/tex]

Explanation:

It is given that,

Mass of the ball, m = 0.2 kg

It strikes the Earth after being dropped from a building of 50 m tall, h = 50 m

In this time, the potential energy is converted to kinetic energy. On applying the conservation of energy as :

[tex]\dfrac{1}{2}mv^2=mgh[/tex]

[tex]v=\sqrt{2gh}[/tex].............(1)

The De-broglie wavelength of the ball is given by :

[tex]\lambda=\dfrac{h}{mv}[/tex]

[tex]\lambda=\dfrac{h}{m\sqrt{2gh}}[/tex]

[tex]\lambda=\dfrac{6.63\times 10^{-34}\ J-s}{0.2\ kg\times \sqrt{2\times 9.8\ m/s^2\times 50\ m}}[/tex]

[tex]\lambda=1.05\times 10^{-34}\ m[/tex]

Hence, this is the required solution.

Final answer:

The maximum coefficient of performance (COP) of the heat pump absorbing heat from the outside air at -10°C and transferring it into a home at 30°C is 0.75.

Explanation:

The coefficient of performance (COP) of a heat pump is a measure of its efficiency and is defined as the ratio of the heat delivered to the heat absorbed. In this case, we have a heat pump that absorbs heat from the outside air at -10°C and transfers it into a home at 30°C. To determine the maximum COP of the heat pump, we can use the formula:

COP = T_h / (T_h - T_c)

where T_h is the temperature of the hot reservoir (in this case, 30°C) and T_c is the temperature of the cold reservoir (in this case, -10°C).

Plugging in the values, we get:

COP = 30 / (30 - (-10)) = 30 / 40 = 0.75

Therefore, the maximum COP of the heat pump is 0.75.

Answer:

option (b)

Explanation:

Mass of moon = m

Mass of earth = 81.25 x mass of moon = 81.25 m

Radius of moon = r

radius of earth = 3.668 x radius of moon  = 3.668 r

Frequency on earth = 2 Hz

Let the frequency on moon is f.

The formula for the frequency is given by

[tex]f = \frac{1}{2\pi }\times \sqrt{\frac{g}{l}}[/tex]

The value of acceleration due to gravity on earth is g.

ge = G Me / Re^2

ge = G x 81.25 m / (3.668 r)^2

ge = 6.039 x G m / r^2 = 6.039 x gm

ge / gm = 6.039

Now use the formula for frequency

[tex]\frac{fe}{fm} = \sqrt{\frac{ge}{gm}}[/tex]

[tex]\frac{2}{fm} = \sqrt{\frac{6.039 gm}{gm}}[/tex]

[tex]\frac{2}{fm} = 2.46[/tex]

fm = 0.814 Hz

Final answer:

The speed of a satellite in circular orbit is calculated using the period and the radius of the orbit. Without the average altitude of the satellite's orbit, we cannot provide a numerical speed but can describe the method to find it.

Explanation:

To calculate the speed at which a satellite travels in a circular orbit around the Earth, we can use the satellite's period, which is the time it takes to complete one orbit. The formula relates the orbital speed (v), the radius of the orbit (r), and the period (T). Since we are given the mass of Earth (ME) and the period (T), we can calculate the radius of the orbit using the equation for gravitational force, F = G*ME*m/r^2, and centripetal force, F = m*v^2/r. Once we have the radius, we can determine the speed by using the formula v = 2πr/T.

Unfortunately, we're missing the average altitude (therefore the radius) of the satellite's orbit necessary to calculate the speed. Without that information, we can only outline the method to find the speed as described above but cannot provide a numerical answer.