A piccolo and a flute can be approximated as cylindrical tubes with both ends open. The lowest fundamental frequency produced by one kind of piccolo is 516.1 Hz, and that produced by one kind of flute is 257.0 Hz. What is the ratio of the piccolo's length to the flute's length?

Answer:

The power of top half of the lens is 0.55 Diopters.

Explanation:

Since, the person can see an object at a distance between 34 cm and 180 cm away from his eyes. Therefore, 180 cm must be the focal length of the upper part of lens, as the top half of the lens is used to see the distant objects.

The general formula for power of a lens is:

Power = 1/Focal Length in meters

Therefore, for the top half of the lens:

Power = 1/1.8 m

Power = 0.55 Diopters

Answer:

a. Δx = 2.59 cm

Explanation:

mb = 0.454 kg , mp = 5.9 x 10 ⁻² kg , vp = 8.97 m / s , k = 21.0 N / m

Using momentum conserved

mb * (0) + mp * vp = ( mb + mp ) * vf

vf = ( mp / mp + mb) * vp

¹/₂ * ( mp + mb) * (mp / mp +mb) ² * vp ² = ¹/₂ * k * Δx²

Solve to Δx '

Δx = √ ( mp² * vp² ) / ( k * ( mp + mb )

Δx = √ ( ( 5.9 x 10⁻² kg ) ² * (8.97  m /s) ²  / [ 21.0 N / m * ( 5.9 x10 ⁻² kg + 0.454 kg ) ]

Δx = 0.02599 m  ⇒ 2.59 cm

Answer:

In an elastic collision, the momentum and the kinetic energies are conserved.

Momentum:

[tex]\vec{P_i} = \vec{P_f}\\\vec{P}_1 + \vec{P}_2 = \vec{P}_1' + \vec{P}_2'\\m\vec{v_0} + 0 = m\vec{v_1}' + 3m\vec{v_2}}' \\v_0 = v_1 + 3v_2[/tex]

Kinetic energy:

[tex]K_i = K_f\\K_1 + K_2 = K_1' + K_2'\\\frac{1}{2}mv_0^2 + 0 = \frac{1}{2}m{v_1'}^2 + \frac{1}{2}3m{v_2'}^2\\v_0^2 = {v_1'}^2 + 3{v_2'}^2[/tex]

We have two equations and two unknowns:

[tex]v_0 = v_1' + 3v_2'\\v_0^2 = {v_1'}^2 + 3{v_2'}^2\\\\3v_2' = v_0 - v_1'\\3{v_2'}^2 = {v_0}^2 - {v_1'}^2\\\\3{v_2'}^2 = (v_0 - v_1')(v_0 + v_1') = 3{v_2}'(v_1' + v_0)\\\\v_2' = v_1' + v_0\\3v_2' = v_0 - v_1'\\\\4v_2' = 2v_0\\\\v_2' = v_0/2\\v_1' = -v_0/2[/tex]

Explanation:

The first cart hits the second cart at rest and turns back with half its speed.

The second cart starts moving to the right with half the initial speed of the first cart.

Answer:

v1 = -v0/3 ,v2 = 2v0/3

Explanation:

Let us start from considering monochromatic light as an incidence on the film of a thickness t whose material has an index of refraction n determined by their respective properties.

From this point of view part of the light will be reflated and the other will be transmitted to the thin film. That additional distance traveled by the ray that was reflected from the bottom will be twice the thickness of the thin film at the point where the light strikes. Therefore, this relation of phase differences and additional distance can be expressed mathematically as

[tex]2t + \frac{1}{2} \lambda_{film} = (m+\frac{1}{2})\lambda_{film}[/tex]

We are given the second smallest nonzero thickness at which destructive interference occurs.

This corresponds to, m = 2, therefore

[tex]2t = 2\lambda_{film}[/tex]

[tex]t = \lambda_{film}[/tex]

The index of refraction of soap is given, then

[tex]\lambda_{film} = \frac{\lambda_{vacuum}}{n}[/tex]

Combining the results of all steps we get

[tex]t = \frac{\lambda_{vacuum}}{n}[/tex]

Rearranging, we find

[tex]\lambda_{vacuum} = tn[/tex]

[tex]\lambda_{vacuum} = (278)(1.33)[/tex]

[tex]\lambda_{vacuum} = 369.74nm[/tex]

Answer:

Frequency = 658 Hz

Explanation:

The third harmonics of A is,

[tex]f_{A}=(3)(440Hz)=1320Hz[/tex]

The second harmonics of E is,

[tex]f_{E}=(2)(659Hz)=1318Hz[/tex]

The difference in the two frequencies is,

delta_f = 1320 Hz - 1318 Hz = 2 Hz

The beat frequency between the third harmonic of A and the second harmonic of E is,

delta_f = [tex]3f_{A}-2f_{E}[/tex]

[tex]f_{E}=\frac{3f_{A}-delta_f}{2}[/tex]

We have calculate the frequency of the E string when she hears four beats per second, then

delat_f = 4 Hz

[tex]f_{E}=\frac{3(440Hz)-4Hz}{2}[/tex]

[tex]f_{E}=658Hz[/tex]

Hope this helps!

Answer:

(B) The total internal energy of the helium is 4888.6 Joules

(C) The total work done by the helium is 2959.25 Joules

(D) The final volume of the helium is 0.066 cubic meter

Explanation:

(B) ∆U = P(V2 - V1)

From ideal gas equation, PV = nRT

T1 = 21°C = 294K, V1 = 0.033m^3, n = 2moles, V2 = 2× 0.033=0.066m^3

P = nRT ÷ V = (2×8.314×294) ÷ 0.033 = 148140.4 Pascal

∆U = 148140.4(0.066 - 0.033) = 4888.6 Joules

(C) P2 = P1(V1÷V2)^1.4 =148140.4(0.033÷0.066)^1.4= 148140.4×0.379=56134.7 Pascal

Assuming a closed system

(C) Wc = (P1V1 - P2V2) ÷ 0.4 = (148140.4×0.033 - 56134.7×0.066) ÷ 0.4 = (4888.6 - 3704.9) ÷ 0.4 = 1183.7 ÷ 0.4 = 2959.25 Joules

(C) Final volume = 2×initial volume = 2×0.033= 0.066 cubic meter

Answer:

(a) maximum shear stress t=22.5mm

(b)maximum distortion energy t=19.48mm

Explanation:

Ф₁(sigma)=pd/2t

Ф₁=(5×10⁶×1.5)/2t

Ф₁=3.75×10⁶/t

Ф₂=pd/4t

Ф₂=1.875×10⁶/t

(a) According to maximum shear stress theory

|Ф₁|=ФY/1.5

3.75×10⁶/t=250×10⁶/1.5

t=22.5 mm

(b)According to distortion energy theory

Ф₁²+Ф₂²-(Ф₁Ф₂)=(ФY/1.5)²

(3.75×10⁶/t)²+(1.875×10⁶/t)-{(3.75×10⁶/t)(1.875×10⁶/t)}=(250×10⁶/1.5)²

t=19.48mm

Answer:

Explanation:

Given

mass of object [tex]m=2 kg[/tex]

inclination [tex]\theta =50^{\circ}[/tex]

[tex]\mu _k=0.3[/tex]

[tex]\mu _s=0.4[/tex]

initial velocity [tex]u=3 m/s[/tex]

acceleration of block during upward motion

[tex]a=g\sin \theta -\mu _kg\cos \theta [/tex]

[tex]a=g(\sin 50-0.3\cos 50)[/tex]

[tex]a=5.617 m/s^2[/tex]

using relation

[tex]v^2-u^2=2a\cdot s[/tex]

where [tex]s=distance\ moved [/tex]

[tex]v=final\ velocity[/tex]

v=0 because block stopped after moving distance s

[tex]0-(3)^2=2\cdot (-5.617)\cdot s[/tex]

[tex]s=\frac{4.5}{5.617}[/tex]

[tex]s=0.801[/tex]

If block stopped after s m then force acting on block is

[tex]F=mg\sin \theta =[/tex]friction force [tex]f_r=\mu mg\cos \theta [/tex]

[tex]F>f_r[/tex] therefore block will slide back down to the bottom            

Answer:

D) resistance, resistivity

Explanation:

Resistance is a physical quantity that indicates the opposition of an object to conduct electricity, this quantity depends on different factors such as temperature, material, object length, among other things. The resistance of two objects of the same material may be different, because it depends on the specifications of the object.

On the other hand, resistivity is a more general quantity, since it is assigned to materials and depends only on the nature of the material and its temperature.

So the resistivity is related to the meterial rather than the object.

The answer is: Resistance is a property of an object while resistivity is a property of a material.

Answer:

dear can you provide the circuit of the robot

To find the mass of the cylindrical bar, calculate the volumes of the two halves using the formula V = πr²h, where r is the radius and h is the height, and multiply them by their respective densities. Then divide the total mass by the total length of the bar.

To find the mass of the cylindrical bar, we need to consider the densities of its left and right halves. The left half has a density of 5 g/cm, while the right half has a density of 6 g/cm. The total length of the bar is 6 m, so we can calculate the volumes of the two halves using the formula V = πr²h, where r is the radius and h is the height.

Let's assume the left half has a radius of r1 and a height of 6 m, and the right half has a radius of r2 and a height of 6 m. The total mass can then be calculated by multiplying the volume of each half by its respective density and summing the results. Finally, we divide the mass by the total length of the bar to get the mass per meter.

Answer:

Part 1)

- 224.6 J

Part 2)

- 339.4 J

Explanation:

[tex]P[/tex] = Constant pressure acting on gas = 0.643 atm = (0.643) (1.013 x 10⁵) Pa = 0.651 x 10⁵ Pa

[tex]V_{i}[/tex] = initial volume = 5.46 L = 0.00546 m³

[tex]V_{f}[/tex] = final volume = 2.01 L = 0.00201 m³

Work done on the gas is given as

[tex]W = P (V_{f} - V_{i})\\W = (0.651\times10^{5}) ((0.00201) - (0.00546))\\W = - 224.6 J[/tex]

Part 2)

[tex]\Delta U[/tex] = Change in the internal energy

[tex]Q[/tex] = Heat energy escaped = - 564 J

Using First law of thermodynamics

[tex]Q = W + \Delta U\\- 564 = - 224.6 +  \Delta U\\ \Delta U = - 339.4 J[/tex]

Answer:

Explanation:

1 . When the Celsius temperature doubles, the Fahrenheit temperature doubles  - FALSE

A change of temperature from 300 F to 600 F changes celsius degree from 148 to 315 °C

2. When heat is added to a system, the temperature must rise.

- FALSE

When we add heat to a system of mixture of ice and water , temperature does not rise until whole of ice melts.

3. In a bimetallic strip of aluminum and brass which curls when heated, the aluminum is on the inside of the curve

- FALSE

Coefficient of linear thermal expansion of aluminium is more so it will be on the outer side.

4. An iron plate has a hole cut in its center. When the plate is heated, the hole gets smaller.

- FALSE

hole will be bigger. There will be photogenic expansion .

5.When the pendulum of a grandfather clock is heated, the clock runs more slowly.

TRUE

Time period is directly proportional to square root of length of pendulum.

when time period increases , clock becomes slow.

6.Cold objects do not radiate heat energy

- FALSE

Object radiates energy  at all temperature .

6 .

The statements are (1)False, (2)False, (3)True, (4)False, (5)True, (6)False

Here are the answers to your statements:

Answer:

a. 1.0 eV

Explanation:

Given that

Voltage difference ,ΔV = 1 V

From work power energy

Work =Change in the kinetic energy

We know that work on the charge W= q ΔV

For electron ,e= 1.6 x 10⁻¹⁹ C

q=e= 1 x 1.6 x 10⁻¹⁹ C

Change in the kinetic energy

ΔKE= q ΔV

Now by putting the values

ΔKE=  1 x 1.6 x 10⁻¹⁹   x 1   C.V

We can also say that

ΔKE=  1 e.V

Therefore the answer will be a.

a). 1.0 eV

Answer:

Δ T = 2.28°C

Explanation:

given,

mass of marble = 100 Kg

height of fall = 200 m

acceleration due to gravity = 9.8 m/s²

C_marble = 860 J/(kg °C)

using conservation of energy

Potential energy = heat energy

  [tex]m g h = m C_{marble}\Delta T[/tex]

  [tex]g h =C_{marble}\Delta T[/tex]

  [tex]\Delta T= \dfrac{g h}{C_{marble}}[/tex]

  [tex]\Delta T= \dfrac{9.8 \times 200}{860}[/tex]

        Δ T = 2.28°C

The temperature change which occurs as a result of the fall, if we ignore energy gained or lost is 2.28°C

This is defined as the degree of hotness or coldness of a substance.

mass of marble = 100 Kg

height of fall = 200 m

acceleration due to gravity = 9.8 m/s²

C of marble = 860 J/(kg °C)

Using conservation of energy

mgh = mcΔT

ΔT = gh/c

= 9.8 × 200 / 860

 = 2.28°C

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The order of difficulty from the hardest to the easiest would be subject to the concept we have of Torque.

The Torque principle defines us that

[tex]\tau = Fd[/tex]

Where,

F = Force

d = Distance

As the distance increases, the force applied must be less to make the movement of the object so we have to

[tex]F \propto \frac{1}{d}[/tex]

Hence we have to be the distance inversely proportional to the force to turn the door the order would be:

As close to the hinges as possible (Hardest)> The center of the door> the edge farthest from the hinges (Easies)

1>2>3

The correct ranking of the difficulty of opening the door from hardest to easiest is as follows: 1. As close to the as possible,  2. The center of the door, 3. The edge farthest.

To understand the ranking, consider the physics of opening a door. The difficulty of opening a door is related to the torque required to rotate it around. Torque [tex](\(\tau\))[/tex] is calculated by the equation [tex]\(\tau = r \times F\)[/tex], where [tex]\(r\)[/tex] is the distance from the axis of rotation to the point where the force [tex](\(F\))[/tex] is applied.

1. As close possible: When you apply force close, the value of [tex]\(r\)[/tex] is smallest. This results in the smallest torque, meaning you have to exert more force to achieve the necessary torque to open the door, making it the hardest location to open the door.

2. The center of the door: Applying force at the center of the door increases the distance [tex]\(r\)[/tex]. This results in a larger torque for the same amount of force compared, but it is still not the most efficient point to open the door.

3. The edge farthest: The farthest edge provides the longest lever arm, meaning [tex]\(r\)[/tex] is at its maximum. This allows for the greatest torque for a given force, making it the easiest location to open the door. This is also why door handles are typically placed farthest.

For there to be a reaction there must also be action. In the horizontal movement there is a balance in which the magnitude of the Forces in opposite directions must be in total 0. The only horizontal forces are friction and the force exerted by the spring scale. For this reason the correct answer is B:

The frictional force and force exerted by the spring scale on the block, because they are a Newton's third-law pair.

Answer

given,

[tex]y(x,t)=B cos[2\pi (\dfrac{x}{L} - \dfrac{t}{\tau})][/tex]

B = 6.40 mm ,  L = 26 cm ,    τ = 3.90 × 10⁻² s

general wave equation

  y = A cos (k x - ωt)

where A is the amplitude of the

a) Amplitude of the given wave

      B = 6.40 mm

b) Wavelength of the given wave

       λ = L

       λ = 26 cm

c)  wave frequency

     [tex]f = \dfrac{1}{\tau}[/tex]

     [tex]f = \dfrac{1}{3.9 \times 10^{-2}}[/tex]

            f = 25.64 Hz

d) speed of wave will be equal to

     v = f λ

     v = 25.64 x 0.26

     v = 6.67 m/s

e) direction of propagation will be along +ve x direction because sign of k x and ωt is same as general equation.

To solve this problem it is necessary to apply the concepts related to the elastic potential energy from the simple harmonic movement.

Said mechanical energy can be expressed as

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

Where,

k = Spring Constant

A = Cross-sectional Area

From the angular movement we can relate the angular velocity as a function of the spring constant and the mass in order to find this variable:

[tex]\omega^2 = \frac{k}{m}[/tex]

[tex]k = m\omega^2\rightarrow \omega = 2\pi f [/tex]  for f equal to the frequency.

[tex]k = 1.53(2\pi 1.95)^2[/tex]

[tex]k = 229.44[/tex]

Finally the energy released would be

[tex]E = \frac{1}{2} (229.44)(0.075)^2[/tex]

[tex]E = 0.6453J \approx 0.646J[/tex]

Therefore the correct answer is B.

The correct answer is option A. The total mechanical energy of the system is [tex]\( 0.844 \, \text{J} \)[/tex]

To find the total mechanical energy of the system, we need to calculate both the elastic potential energy (due to the spring) and the gravitational potential energy (due to the height above the equilibrium position) at the maximum amplitude point.

 First, let's calculate the spring constant [tex]\( k \)[/tex] using the formula for the frequency[tex]\( k \)[/tex] of a mass-spring system:

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

where \( m \) is the mass of the iron piece. Solving for [tex]\( k \)[/tex], we get:

[tex]\[ k = (2\pi f)^2 m \][/tex]

[tex]\[ k = (2\pi \times 1.95 \, \text{Hz})^2 \times 1.53 \, \text{kg} \][/tex]

[tex]\[ k \approx 244.73 \, \text{N/m} \][/tex]

Next, we calculate the elastic potential energy [tex]\( U_{\text{elastic}} \)[/tex] at the maximum amplitude [tex]\( A \)[/tex]:

[tex]\[ U_{\text{elastic}} = \frac{1}{2} k A^2 \][/tex]

[tex]\[ U_{\text{elastic}} = \frac{1}{2} \times 244.73 \[/tex], [tex]\text{N/m} \times (0.0750 \[/tex], [tex]\text{m})^2 \] \[ U_{\text{elastic}} \approx 0.683 \[/tex], [tex]\text{J} \][/tex]

Now, let's calculate the gravitational potential energy [tex]\( U_{\text{gravitational}} \)[/tex]at the maximum amplitude:

[tex]\[ U_{\text{gravitational}} = m g h \][/tex]

where [tex]\( g \)[/tex]is the acceleration due to gravity (approximately [tex]\( 9.81 \, \text{m/s}^2 \[/tex])) and [tex]\( h \)[/tex] is the height at maximum amplitude. Since the amplitude is given in centimeters, we convert it to meters:

[tex]\[ h = 7.50 \, \text{cm} = 0.0750 \, \text{m} \][/tex]

[tex]\[ U_{\text{gravitational}} = 1.53 \, \text{kg} \times 9.81 \, \text{m/s}^2 \times 0.0750 \, \text{m} \][/tex]

[tex]\[ U_{\text{gravitational}} \approx 1.130 \, \text{J} \][/tex]

The total potential energy [tex]\( U_{\text{total}} \)[/tex] at the maximum amplitude is the sum of the elastic and gravitational potential energies:

[tex]\[ U_{\text{total}} = U_{\text{elastic}} + U_{\text{gravitational}} \] \[ U_{\text{total}} \approx 0.683 \, \text{J} + 1.130 \, \text{J} \] \[ U_{\text{total}} \approx 1.813 \, \text{J} \][/tex]

However, we must consider that the total potential energy is zero at the equilibrium position. Therefore, the total mechanical energy [tex]\( E \)[/tex] of the system is equal to the total potential energy at the maximum amplitude:

[tex]\[ E = U_{\text{total}} \] \[ E \approx 1.813 \, \text{J} \][/tex]

Since the potential energy at the equilibrium position is zero, the total mechanical energy is simply the sum of the elastic and gravitational potential energies at the maximum amplitude, which is approximately [tex]\( 1.813 \, \text{J} \)[/tex]. However, the options given are in the range of [tex]\( 0.633 \, \text{J} \) to \( 0.955 \, \text{J} \)[/tex], which suggests that there might be a mistake in the calculation or interpretation of the problem.

Upon re-evaluating the calculation, it seems that the gravitational potential energy was incorrectly calculated. The correct calculation should consider that the gravitational potential energy is zero at the equilibrium position, not at the maximum amplitude. Therefore, we should only consider the change in gravitational potential energy from the equilibrium to the maximum amplitude, which is half the amplitude squared divided by the spring constant, as the mass will oscillate symmetrically around the equilibrium position.

The correct gravitational potential energy [tex]\( U_{\text{gravitational}} \)[/tex] at the maximum amplitude is:

[tex]\[ U_{\text{gravitational}} = \frac{1}{2} k \left(\frac{h}{2}\right)^2 \][/tex]

[tex]\[ U_{\text{gravitational}} = \frac{1}{2} \times 244.73 \, \text{N/m} \times \left(\frac{0.0750 \, \text{m}}{2}\right)^2 \][/tex]

[tex]\[ U_{\text{gravitational}} \approx 0.160 \, \text{J} \][/tex]

Now, the total mechanical energy [tex]\( E \)[/tex] of the system is:

[tex]\[ E = U_{\text{elastic}} + U_{\text{gravitational}} \] \[ E \approx 0.683 \, \text{J} + 0.160 \, \text{J} \] \[ E \approx 0.844 \, \text{J} \][/tex]

The spring will stretch by 13.79 cm when 51.7 grams is hung on it.

To find the stretch of the spring when a weight of 51.7 grams is hung on it, we will use Hooke's Law. First, we need to convert the weight to Newtons. Since 1 g is equal to 0.0098 N, the weight in Newtons is 51.7 grams * 0.0098 N/g = 0.50546 N. Now we can rearrange Hooke's Law equation, F = -k * s, to solve for s, the stretch of the spring. Plugging in the values, we get 0.50546 N = -k * s. Rearranging further, we have s = 0.50546 N / -3.662 = -0.1379 m. Since the question asks for the answer in centimeters, we can convert -0.1379 m to centimeters by multiplying by 100. Therefore, the spring will stretch by 13.79 cm when 51.7 grams is hung on it.

The length of the neck that blood can still reach the brain depends on blood pressure, flow speed, and the cross-sectional area of capillaries. Using the given values, the approximate length of the neck is 9.8 meters.

The length of your neck that blood can still reach your brain depends on the blood pressure, flow speed, and the cross-sectional area of the capillaries. The blood enters the capillaries in the brain with a much smaller velocity of about 0.7 mm/s due to the large total cross-sectional area. To determine the length of the neck, we need to consider the time it takes for blood to travel from the heart to the brain. Using the given velocity, we can calculate that the time it takes for blood to reach the brain is approximately 14 seconds. Assuming a constant velocity, the length of the neck can be calculated using the formula: length = velocity x time, which gives us a result of 9.8 meters.

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Answer:

0.91125 km/s

Explanation:

[tex]v_1[/tex] = Velocity of planet initially = 54 km/s

[tex]r_1[/tex] = Distance from star = 0.54 AU

[tex]v_2[/tex] = Final velocity of planet

[tex]r_2[/tex] = Final distance from star = 32 AU

As the angular momentum of the system is conserved

[tex]mv_1r_1=mv_2r_2\\\Rightarrow v_1r_1=v_2r_2\\\Rightarrow v_2=\dfrac{v_1r_1}{r_2}\\\Rightarrow v_2=\dfrac{54\times 0.54}{32}\\\Rightarrow v_2=0.91125\ km/s[/tex]

When the exoplanet is at its farthest distance from the star the speed is 0.91125 km/s

Answer:

L = 0.44 [m]

Explanation:

Here we can use the Lorentz transformation related to length to solve it:

[tex]L=L_{0}\sqrt{1-\beta^{2}} [/tex]

Where:

L₀ is the length of the moving reference frame (penguin #1)

L is the length of the fixed reference frame (penguin #2)

β is the ratio between v and c

We know that v = 0.9c so we can find β.

[tex]\beta = \frac{0.9c}{c}=0.9[/tex]

[tex]L=1 [m]\sqrt {1-0.9^{2}} = 0.44 [m] [/tex]

Therefore, the length of the meter stick of #1 observed by #2 is 0.44 m.

I hope it helps you!

The amount of spilled turpentine due to temperature rise can be calculated by comparing the changes in volume of the steel container and the contained turpentine, using the principles and mathematical formulas of thermal expansion.

The question asks us to determine how much turpentine, which exhibits a greater rate of thermal expansion compared to the steel container, will spill over when the temperature rises. We need to apply the principles of thermal expansion to calculate this. Both the steel container and the turpentine expand with the increase in temperature, but since turpentine has a higher coefficient of volume expansion than steel, more turpentine will expand than the container can accommodate, resulting in some turpentine spilling over.

To calculate the amount of spilled turpentine, we need to find the change in volume for both the container and turpentine, and subtract the former from the latter. The change in volume due to thermal expansion can be calculated by using the equation ΔV = βV0*(T2 - T1), where β is the coefficient of volume expansion, V0 is the initial volume, and T2 and T1 are the final and initial temperatures respectively.

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To find how much turpentine will overflow, calculate the change in volume due to thermal expansion for both the steel container and the turpentine, and subtract the change in volume of the steel from that of the turpentine.

To solve this problem, we need to consider the thermal expansion of both the steel container and the turpentine. Thermal expansion is the increase in size of a body due to a change in temperature. This is described mathematically by the formula ΔV = βV₀ΔT, where ΔV is the change in volume, β is the coefficient of volume expansion, V₀ is the original volume, and ΔT is the change in temperature.

First, calculate the change in volume for the steel container and the turpentine separately. For the steel, β is 11 x 10^-6 (°C)^-1 and for turpentine, β is 9.0 x 10^-4 (°C)^-1. The original volume, V₀, is 55 gallons for both, and the change in temperature, ΔT, is 25.5°C - 10.0°C = 15.5°C.

Performing these calculations will give you the change in volume for the steel and the turpentine. The difference in these two volumes will tell you how much turpentine will overflow as the temperature increases.

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To solve this problem it is necessary to apply the concepts related to the adiabatic process that relate the temperature and pressure variables

Mathematically this can be determined as

[tex]\frac{T_2}{T_1} = (\frac{P_2}{P_1})^{(\frac{\gamma-1}{\gamma})}[/tex]

Where

[tex]T_1 =[/tex]Temperature at inlet of turbine

[tex]T_2 =[/tex] Temperature at exit of turbine

[tex]P_1 =[/tex] Pressure at exit of turbine

[tex]P_2 =[/tex]Pressure at exit of turbine

The steady flow Energy equation for an open system is given as follows:

[tex]m_i = m_0 = m[/tex]

[tex]m(h_i+\frac{V_i^2}{2}+gZ_i)+Q = m(h_0+\frac{V_0^2}{2}+gZ_0)+W[/tex]

Where,

m = mass

[tex]m_i[/tex] = mass at inlet

[tex]m_0[/tex]= Mass at outlet

[tex]h_i[/tex] = Enthalpy at inlet

[tex]h_0[/tex] = Enthalpy at outlet

W = Work done

Q = Heat transferred

[tex]V_i[/tex] = Velocity at inlet

[tex]V_0[/tex]= Velocity at outlet

[tex]Z_i[/tex]= Height at inlet

[tex]Z_0[/tex]= Height at outlet

For the insulated system with neglecting kinetic and potential energy effects

[tex]h_i = h_0 + W[/tex]

[tex]W = h_i -h_0[/tex]

Using the relation T-P we can find the final temperature:

[tex]\frac{T_2}{T_1} = (\frac{P_2}{P_1})^{(\frac{\gamma-1}{\gamma})}[/tex]

[tex]\frac{T_2}{1400K} = (\frac{0.8bar}{8nar})^{(\frac{1.4-1}{1.4})}[/tex]

[tex]T_2 = 725.126K[/tex]

From this point we can find the work done using the value of the specific heat of the air that is 1,005kJ / kgK

So:

[tex]W = h_i -h_0[/tex]

[tex]W = C_p (T_1-T_2)[/tex]

[tex]W = 1.005(1400-725.126)[/tex]

[tex]W = 678.248kJ/Kg[/tex]

Therefore the maximum theoretical work that could be developed by the turbine is 678.248kJ/kg

Final answer:

The maximum theoretical work that could be developed by the turbine, assuming ideal gas behavior, is approximately 0.3195 kJ per kg of air flow.

Explanation:

The maximum theoretical work that could be developed by the turbine can be calculated using the ideal gas law equation:

W = Cv(Tin - Tout)

where W is the work done per unit mass, Cv is the specific heat capacity at constant volume, Tin is the inlet temperature, and Tout is the outlet temperature.

First, we need to find the value of Cv for air. For ideal gases, the specific heat capacity at constant volume can be calculated using the equation:

Cv = (R/M)

where R is the gas constant and M is the molar mass of the gas.

In this case, we will use the molar mass of air, which is approximately 28.97 g/mol. The gas constant R is 8.314 J/(mol·K).

Substituting the values into the equation, we get:

Cv = (8.314 J/(mol·K)) / (28.97 g/mol)

Cv = 0.287 J/(g·K)

Now we can calculate the work:

W = (0.287 J/(g·K))(1400 K - 288 K)

W = 0.287 J/(g·K) x 1112 K

W = 319.544 J/g

Finally, we convert the work from Joules to kilojoules:

W = 319.544 J/g * (1 kJ/1000 J)

W ≈ 0.3195 kJ/g

Answer:

option (c)

Explanation:

mass of iron = 0.10 kg

mass of copper = 0.16 kg

rise in temperature, ΔT = 35°C

specific heat of iron = 450 J/kg°C

specific heat of copper = 390 J/kg°C

Heat by iron (H1) = mass of iron x specific heat of iron x ΔT

H1 = 0.10 x 450 x 35 = 1575 J

Heat by copper (H2) = mass of copper x specific heat of copper x ΔT

H1 = 0.16 x 390 x 35 = 2184 J

Total heat H = H1 + H2

H = 1575 + 2184 = 3759 J

by rounding off

H = 4000 J

Answer:b

Explanation:

Given

mass of iron Gear [tex]m_{iron}=0.1 kg[/tex]

mass of copper [tex]m_{cu}=0.16 kg[/tex]

specific heat of iron [tex]c_{iron}=450 J/kg-^{\circ}C[/tex]

specific heat of copper [tex]c_{cu}=390 J/kg-^{\circ}C[/tex]

heat gain by iron gear [tex]=m_{iron}c_{iron}\Delta T[/tex]

[tex]Q_1=0.1\times 450\times 35=1575 J[/tex]

heat gain by iron gear [tex]=m_{cu}c_{cu}\Delta T[/tex]

[tex]Q_2=0.16\times 390\times 35=2184 J[/tex]

Total heat [tex]Q_{net}=Q_1+Q_2[/tex]

[tex]Q_{net}=1575+2184=3759 J\approx 3800 J[/tex]

Answer

given,

mass of the car = 2510 Kg

angle of inclination = 10°

initial speed = v₁ = 20 m./s

skid length = 20 m

coefficient of friction = 0.5

Using conservation of energy

[tex]\Delta E = \Delta KE + \Delta U[/tex]

[tex]\Delta E = \dfrac{1}{2}mv^2 + m g h[/tex]

h = d sin θ

[tex]\Delta E = \dfrac{1}{2}mv^2- m g (dsin\theta)[/tex]

[tex]\Delta E = \dfrac{1}{2}\times 2510 \times 20^2- 2510\times 9.8 \times (20 sin10^0)[/tex]

[tex]\Delta E =416572.04\ J[/tex]

now, calculating the  magnitude of frictional force is equal to

E = F_f d

[tex]F_f = \dfrac{E}{d}[/tex]

[tex]F_f = \dfrac{416572.04}{20}[/tex]

[tex]F_f = 20828\ N[/tex]

Answer:

Explanation:

The body can be split into two parts

1 ) cylinder part of mass 7/8 x 64 = 56 kg of radius 20 cm

2 ) In the form of rod attached with cylinder having length 40 cm and mass

of 1/8 x 64 = 8kg

moment of inertia of cylinder

= 1/2 mr²

= .5 x 56 x ( 20 x 10⁻²)²

= 1.12 kg m²

moment of inertia of rods

= 1/3 ml²

= 1/3 x 8 x ( 40 x 10⁻²)²

= .4267 kg m²

Total MI = 1.5467 Kg m²

Answer:

b. 16.5°C

Explanation:

[tex]m_{c}[/tex] = mass of piece of copper = 80 g

[tex]c_{c}[/tex] = specific heat of piece of copper = 0.0920 cal/g°C

[tex]T_{ci}[/tex] = Initial temperature of piece of copper = 295 °C

[tex]m_{w}[/tex] = mass of water = 250 g

[tex]c_{w}[/tex] = specific heat of water = 1 cal/g°C

[tex]T_{wi}[/tex] = Initial temperature of piece of copper = 10 °C

[tex]m_{al}[/tex] = mass of calorimeter  = 300

[tex]c_{al}[/tex] = specific heat of calorimeter = 0.215 cal/g°C

[tex]T_{ali}[/tex] = Initial temperature of calorimeter = 10 °C

[tex]T[/tex] = Final equilibrium temperature

Using conservation of heat

Heat lost by piece of copper = heat gained by water + heat gained by calorimeter

[tex]m_{c} c_{c} (T_{ci} - T) = m_{w} c_{w} (T - T_{wi})+ m_{al} c_{al} (T - T_{ali})\\(80) (0.092) (295 - T) = (250) (1) (T - 10) + (300) (0.215) (T - 10)\\T = 16.5 C[/tex]

The final temperature of the system is 16.4 ⁰C.

The final temperature of the system is determined by applying the principle of conservation of energy as shown below;

Heat lost by piece of copper = heat gained by water + heat gained by calorimeter

mCc(Tc - T) = mCw(T - Tw) + mCl(T - Tl)

80 x 0.09 x (295 - T) = 250 x 1 x (T - 10) + 300 x 0.215 x (T - 10)

2124 - 7.2T = 250T - 2500 + 64.5T - 645

5269 = 321.7T

T = 5269/321.7

T = 16.4 ⁰C

Thus, the final temperature of the system is 16.4 ⁰C.

Learn more about conservation of energy here: https://brainly.com/question/166559

Answer:

You have just driven across the Cold front.

Explanation:

Weather Front:

In Meteorology, weather fronts are simply boundaries between two air masses of different densities. There are four weather fronts and one of them is cold front and other fronts are warm front, stationary front and occluded front.

Cold Front:

In Meteorology, cold front is a boundary of cold air mass that is advancing under the warm air mass.

In our scenario, as the driver was moving in the west and he listened on radio, the next country on north is under tornado warning. So, when he passed the cold front, he experienced the conditions described.