Sometimes, when the wind blows across a long wire, a low-frequency "moaning" sound is produced. The sound arises because a standing wave is set up on the wire, like a standing wave on a guitar string. Assume that a wire (linear density = 0.0180 kg / m ) sustains a tension of 350 N because the wire is stretched between two poles that are 17.43 m apart. The lowest frequency that an average, healthy human ear can detect is 20.0 Hz. What is the lowest harmonic number n that could be responsible for the "moaning" sound?

Answer:

(C) both tech A and tech B

Explanation:

both technicians are correct because an accident could cause faults due to hidden damages which might not have been detected at the time of the accident and some faults could be related to previous repair probable due to human error from the repair man or even improper repair due to lack of adequate knowledge on the vehicle.

Answer:

Wavelength, [tex]\lambda=0.011\ m[/tex]

Explanation:

Given that,

Number of cycles in a spiral spring is 2.91 in every 3.67 s

The velocity of the pulse in the spring is 0.925 cm/s, v = 0.00925 m/s

To find,

Wavelength

Solution,

Number of cycles per unit time is called frequency of a wave. The frequency of the longitudinal pulse is,

[tex]f=\dfrac{2.91}{3.67}=0.79\ Hz[/tex]

The wavelength of a wave is given by :

[tex]\lambda=\dfrac{v}{f}[/tex]

[tex]\lambda=\dfrac{0.00925\ m/s}{0.79\ Hz}[/tex]

[tex]\lambda=0.011\ m[/tex]

So, the wavelength of the longitudinal pulse is 0.011 meters. Hence, this is the required solution.

To find the wavelength, the frequency is calculated by dividing the number of cycles by the total time. The velocity is then converted from cm/s to m/s. The wavelength is calculated using these values in the equation for wave speed to get approximately 0.012 meters.

In the scenario described in your question, your hand completes 2.91 back-and-forth cycles every 3.67 seconds, resulting in longitudinal pulses in a spiral spring. Here, we have frequency and wave velocity, and we need to find the wavelength. We can determine the frequency by dividing the number of cycles by the total time and the wavelength using the formula for wave speed: v = fλ, where v is the velocity, f is the frequency, and λ is the wavelength.

Frequency (f) = number of cycles / total time = 2.91 cycles / 3.67 s = 0.793 Hz

Velocity (v) = 0.925 cm/s = 0.00925 m/s (since we need the answer in meters)

To find the wavelength, we can use the formula v = fλ, to rearrange this to solve for λ, we get λ = v/f. So, λ = 0.00925 m/s / 0.793 Hz = 0.01166 meters or approximately 0.012 meters.

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Answer:

0.06683

Explanation:

m = Mass of block = 3.85 kg

g = Acceleration due to gravity = 9.81 m/s²

[tex]\mu[/tex] = Coefficient of kinetic friction

x = Compression of spring = 0.103 m

k = Spring constant = 138 N/m

Work done against friction is given by

[tex]W=m\mu gs\\\Rightarrow W=\mu 3.85\times 9.81\times 0.29\\\Rightarrow W=10.952865\mu[/tex]

The potential energy of the spring is given by

[tex]P=\frac{1}{2}kx^2\\\Rightarrow P=\frac{1}{2}\times 138\times 0.103^2\\\Rightarrow P=0.732021\ J[/tex]

The potential energy and the work done against friction will balance the system

[tex]0.732021=10.952865\mu\\\Rightarrow \mu=\frac{0.732021}{10.952865}\\\Rightarrow \mu=0.06683[/tex]

The coefficient of kinetic friction between the horizontal surface and the block is 0.06683

Answer:

option C

Explanation:

The correct answer is option C

A light that transmits through n₂ travels t distance before reflection off the n₁ medium and again travels distance t before reaching the point from where it entered n₂  medium. Hence it travels 2 t distance more than the light that is reflected off n₂.

It( light entering n₂) also travels an additional distance equal to, half of the wavelength, when reflected off n₁ ( as n₁ is greater than n₂).  

Wavelength in n₂ is = [tex]\dfrac{\lambda}{n_2}[/tex]  

Hence, path length difference = [tex]2t +\dfrac{\lambda}{2 n_2}[/tex]

The effective path length difference between the light that reflected off of the n2 medium and the light that reflected off the n1 medium is

Path length difference = 2t+λ/(2n2)

Generally, Wavelength is simply defined as the distance between points in the adjacent cycles of a waveform signal channeled through a space.

In conclusion, A light that travels through n2, travels in a time t, a distance before reflection from the n1 channel,  travels a distance d before reaching the point from where it entered n2  channel.

Path length difference = 2t+λ/(2n2)

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Answer: 3.5units

Explanation:

Gravitational force existing between the two masses is directly proportional to the product of their masses and inversely proportional to the square of the distances between the masses.

Mathematically, F = GMm/r^2

G is the gravitational constant

M and m are the masses

r is the distance between the masses.

If the force of attraction between the masses is 16units, it becomes,

16 = GMm/r^2... (1)

If the mass of object 1 is doubled and distance tripled, we will have

F= G(2M)m/(3r)^2

F=2GMm/9r^2... (2)

Solving eqn 1 and 2 to get the new Force

Dividing eqn 1 by 2, we have

16/F = GMm/r^2 ÷ 2GMm/9r^2

16/F = GMm×9r^2/r^2×2GMm

16/F = 9/2(upon cancelation)

Cross multiplying we have

9F=32

F= 32/9

F= 3.5units

Answer:

Answer: F = 4 units

Explanation:

If the distance is increased by a factor of 2, then force will be decreased by a factor of 4 (22). The new force is then 1/4 of the original 16 units.

F = (16 units ) / 4 = 4 units

Wind-driven currents are found NEAR THE SURFACE of the oceans

Explanation:

Surface currents are at the interphase between the hydrosphere and atmosphere. Therefore the feel the greatest effect of drag by wind currents, especially prevailing winds (that blow predominantly in one direction like westerlies and easterlies) within the lower atmosphere.  The deep currents, on the other hand, are more influenced by Coriolis effect of the earth’s rotation. It is these differences in influences of surface and deeper currents that cause Ekman transport in oceans.

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Answer:

Explanation:

Convergent lens is the lens which converges the rays of light falling on it. It is thicker at the middle and thinner at the edges. It is also known as convex lens.

Divergent lens is the lens which diverge the rays of light falling on it. It is thinner at the middle and thicker at the edges. It is also called as concave lens.

Convergent lenses, or convex lenses, thicken in the middle and focus light rays to a point, forming real or virtual images; divergent lenses, or concave lenses, are thinner in the middle, causing the light rays to spread out and only form virtual images. Snell’s law describes the refraction process in both lens types as being influenced by differences in the index of refraction.

Difference Between Convergent and Divergent Lenses

Lenses are often categorized as either convergent (convex) or divergent (concave) depending on how they refract light. A converging lens is thicker at the middle and causes parallel light rays entering the lens to converge, or come together, at a single point known as the focal point. This lens can create both real and virtual images, the nature of which depends on the position of the object relative to the lens. In contrast, a divergent lens is thinner at the middle and causes parallel light rays to spread apart or diverge after passing through the lens. Divergent lenses only form virtual images.

Snell's law helps explain the refraction in both types of lenses, considering the difference in the index of refraction between the lens material and the surrounding air. The lens power is determined by its ability to bend light, described by the lens's focal length, with more powerful lenses having shorter focal lengths.

Answer:

 W = 24.28 kN

Explanation:

given,

Mass of satellite = 5850 Kg

height , h = 4.1 x 10⁵ m

Radius of planet = 4.15 x 10⁶ m

Time period = 2 h

                    = 2 x 3600 = 7200 s

Time period of satellite

[tex]T = \dfrac{2\pi}{R}\sqrt{\dfrac{(R+h)^3}{g}}[/tex]

R is the radius of planet

h is the height of satellite

[tex]T^2 = \dfrac{4\pi^2}{R^2}\ {\dfrac{(R+h)^3}{g}}[/tex]

now calculation of acceleration due to gravity

[tex]g = \dfrac{4\pi^2}{R^2}\ {\dfrac{(R+h)^3}{T^2}}[/tex]

[tex]g = \dfrac{4\pi^2}{(4.15\times 10^6)^2}\ {\dfrac{(4.15\times 10^6+4.1\times 10^5)^3}{(7200)^2}}[/tex]

g = 4.15 m/s²

True weight of satellite

W = m g

W = 5850 x 4.15

W = 24277.5 N

 W = 24.28 kN

True weight of the satellite is   W = 24.28 kN

The true weight of the satellite, when the satellite is at rest on the surface of the planet, is 24.28 kN.

Time period of satellites is the total time taken by a satellite to complete a full orbit around a body. It can be given as,

[tex]T=\dfrac{2\pi}{R}\sqrt{\dfrac{(R+h)^3}{g}}[/tex]

Here, (R) is the radius of the body, and (g) is the gravitational acceleration force.

In a circular orbit 4.1 x10 to the 5th power m above the surface of a planet. The period of the orbit is 2 hours and the radius of the planet is 4.15 x 10 to the 6th power m.

To find the weight of the satellite, first find the value of gravitation acceleration using the time period formula as,

[tex]2=\dfrac{4\pi^2}{4.15\times10^6}\sqrt{\dfrac{(4.15\times10^6+4.1\times10^5)^3}{g}}\\g=4.15\rm m/s^2[/tex]

The weight of the body is mass time gravity. As the satellite has a mass of 5850 kg and value of g is 4.15 m/s². Thus, the weight of it is,

[tex]W=5850\times4.15\\W=24277.5\rm N\\W=24.28\rm \; kN[/tex]

Thus, the true weight of the satellite, when the satellite is at rest on the surface of the planet, is 24.28 kN.

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Answer:

2388078.86544 N/C

Explanation:

[tex]\rho[/tex] = Charge density = 9.22 mC/m³

r = Distance = 7.35 cm

[tex]r_o[/tex] = Outer radius = 3.5 cm

[tex]r_i[/tex] = Inner radius = 2.98 cm

l = Length of cylinder

[tex]\epsilon_0[/tex] = Permittivity of free space = [tex]8.85\times 10^{-12}\ F/m[/tex]

V = Volume

E = Electric field

Charge is given by

[tex]Q=\rho V\\\Rightarrow Q=\rho\pi l(r_o^2-r_i^2)[/tex]

Area

[tex]A=2\pi rl[/tex]

From Gauss law the flux through a cylindrical surface is given by

[tex]EA=\frac{Q}{\epsilon_0}\\\Rightarrow E=\frac{Q}{\epsilon_0A}\\\Rightarrow E=\frac{\rho\pi l(r_o^2-r_i^2)}{\epsilon_02\pi rl}\\\Rightarrow E=\frac{\rho(r_o^2-r_i^2)}{\epsilon_02r}\\\Rightarrow E=\frac{9.22\times 10^{-3}(0.035^2-0.0298^2)}{8.85\times 10^{-12}\times 2\times 0.0735}\\\Rightarrow E=2388078.86544\ N/C[/tex]

The electric at the given distance is 2388078.86544 N/C

Answer:

e. Reduced conflict.

Explanation:

Outsourcing is a tool that allows you to hire a provider outside the company for the execution of secondary activities, such as cleaning or mail, or covering other areas of the company, such as financial or accounting systems or the human resources area

- Advantages of Outsourcing

- Cost reduction

- Focus on the main activity

- Transformation of fixed costs into variables

- Reduce risk

- Improve quality

- Productivity increase

- Improve innovation processes

- Greater flexibility

- Access to the latest technologies

- Increase in competitiveness

Advantages of outsourcing project work include increased flexibility, higher level of expertise, and reduced costs.

The advantages of outsourcing project work may likely include increased flexibility because organizations can access a global talent pool and adapt to changing markets. Outsourcing can also provide a higher level of expertise as specialized firms or individuals with specific skills can be hired. Additionally, outsourcing can lead to reduced costs by eliminating the need for in-house resources and infrastructure.

However, one advantage that is unlikely to be associated with outsourcing project work is reduced conflict. When different parties are involved in a project, conflicts may arise due to differences in goals, perspectives, or communication barriers. Outsourcing does not automatically guarantee a reduction in conflict.

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Answer:

A. Bohr's model focused on the nucleus

Answer:

False

Explanation:

We know that if path difference is even multiple of wavelength then bright fringes are formed and if path difference is odd multiple of wavelength then dark fringes are formed .

For bright fringes

Path difference Δx = m λ

m = 0 , 2 , 4 , 6.......

If m = 2 then the path difference will be

Δx = 2 λ

therefore the above statement if false.

False

Explanation:

When a electron is collided with a photon with exactly the same energy it would require to get to any of the farther orbits,electron transition takes place to an orbit depending on the energy of the photon.

When electrons emit exactly the same amount energy that is difference between the current energy level and the new level,then the electron makes a transition to the new level.

An electron in an atom is likely to move from one energy level to another when it gains or loses energy.

Explanation:

The change in an electron’s position with respect to energy levels is termed as Atomic electron transition. In spite of having similar charge and mass, the energy level of any electron in an atom, surrounding the nucleus, differs depending on its orbital position from the nucleus.

Electrons positioned nearest to the atomic nucleus carry least energy. To move an electron from its original ground state energy level to a higher level; energize the atom and it will excite the electrons thus making it move from its lower energy stable state to an unstable state with higher energy level. Releasing energy of an atom decreases the energy level of its excited electrons, de-energizing it and thus stabilizing the atom.

To calculate the value of 'do' in the given pulley system, we need to know the efficiency.

In order to calculate the value of 'do' in the given pulley system, we need to understand the concepts of actual mechanical advantage (AMA) and ideal mechanical advantage (IMA).

AMA is the ratio of the output force (load) to the input force (effort). In this case, the load is the engine with a weight of 2,000 newtons and the effort force is 250 newtons. So, AMA = Load/Effort = 2000 N/250 N = 8.

IMA is the theoretical mechanical advantage calculated by counting the number of ropes supporting the load. In this case, since there is only one rope supporting the load, IMA = 1.

The relationship between AMA and IMA is given by the equation: AMA = IMA x efficiency.

Since the efficiency is not provided in the question, we cannot directly calculate the value of 'do' without this information.

Answer:

A perfect example of wave reflection is an echo.

Explanation:

A wave reflection takes place when waves cannot pass through a surface and in turn they bounce back. It is not necessary that wave reflections can only happen with sound waves, they can also take place in light waves. Also, the waves which are reflected have the same frequency as the original wave, but their direction is different. When a wave strikes an object in the same angle, they bounce back straight but when they hit an object with different angle, their direction changes.

Answer:

Option B

Explanation:

Maintenance-free battery uses Recom­bination Electrolyte in order to limit   the oxygen and hydrogen formation during charging.

Each plate of the battery uses a glass micro-fiber separator that absorbs the whole liquid electrolyte in its pore thus resulting in no free acid.

As the battery charges to its fullest, the oxygen produced at the positive plate moves via the pores of the separator to the negative plate.

Initially it reacts and forms [tex]PbSO_{4}[/tex], i.e., Lead Sulphate, then on further charging it gets converted to Pb, i.e., lead.

Due to this, the negative plate is not able to reach the correct potential in order to liberate hydrogen, and hence no water formation takes place.

Thus technician B is correct.

Answer:

Current, I = 3 A

Explanation:

It is given that,

Length of the wire, l = 1 m

Magnetic field acting on the wire, B = 0.2 T

The magnetic force acting on the wire, F = 0.6 N

Let the current flowing through the wire is given by I. The magnetic force acting on an object in the uniform magnetic field is given by :

[tex]F=ILB\ sin\theta[/tex]

Here, [tex]\theta=90^{\circ}[/tex]

[tex]F=ILB[/tex]

[tex]I=\dfrac{F}{LB}[/tex]

[tex]I=\dfrac{0.6\ N}{1\ m\times 0.2\ T}[/tex]

I = 3  A

So, the current flowing through the rod 3 A.

Answer:

1.556 N , 0.989 N, 0.567 N

Explanation:

Radius of sphere, r = 1.21 cm = 0.0121 m

density of platinum , d = 2.14 x 10^4 kg/m^3

density of mercury, d' = 13.6 x 10^3 kg/m^3

Volume of sphere, [tex]\frac{4}{3}\pi \times r^{3}= \frac{4}{3}\times 1.34\times \left (0.0121  \right )^{3}[/tex]

V = 7.42 x 10^-6 m^3

Weight of sphere = volume of sphere x density of platinum x gravity

W = V x d x g = 7.42 x 10^-6 x 2.14 x 10^4 x 9.8 = 1.556 N

Buoyant force, B = Volume x density of mercury x gravity

B = 7.42 x 10^-6 x 13.6 x 10^3 x 9.8 = 0.989 N

Apparent weight = True weight - Buoyant force

Apparent weight = 1.556 - 0.989 = 0.567 N

To find the weight of the platinum sphere, calculate the mass of the sphere using its density and volume. Then, use the formula weight = mass × gravitational acceleration. The buoyant force acting on the sphere is equal to the weight of the fluid displaced, which in this case is the weight of an equivalent volume of mercury. The sphere's apparent weight can be calculated by subtracting the buoyant force from its actual weight.

To find the weight of the platinum sphere, we can use the formula:

Weight = Mass × Gravitational acceleration

Given the density of platinum and the radius of the sphere, we can calculate the mass of the sphere using the formula:

Mass = Density × Volume

Using the volume of a sphere formula, we can determine the volume of the sphere. Once we have the mass, we can calculate the weight of the sphere.

The buoyant force acting on the sphere can be calculated using Archimedes' principle, which states that the buoyant force equals the weight of the fluid displaced. In this case, the fluid is mercury. Since the sphere is totally immersed in mercury, the buoyant force would be the weight of an equivalent volume of mercury.

The sphere's apparent weight can be calculated by subtracting the buoyant force from the weight of the sphere. This gives us the net force acting on the sphere when it is immersed in mercury.

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Answer:

option D.

Explanation:

The correct answer is option D.

The irony is the figure of speech which represents the contradiction between what is stated and what actually the scenario is.

the statement by the poet does not have any contradictory statements.

The extended metaphor is a part of speech which is used when there is a comparison between two unlike things in the paragraph.

in the given statement of the poem, there is no comparison.

Personification is the part of speech where human quality are given to non-living things.

in the give statement wind in the wire took up the story can be taken as the human quality.

so, the statement part of speech is personification.

Answer:

The alternative energy sources are defined as those resources that are used in place of the natural and non-renewable resources. This resources plays an important role in the conservation of natural resources.

The fossil fuels are the resources on which the people are directly dependent. Burning up of these fossils leads to the emission of carbon, which has a direct impact on earth. A small increase in the amount of carbon dioxide can lead to the increase in the surface temperature of earth.

In addition to this, these fossil fuels such as coal, petroleum, oil and natural gases are found to be present in a limited proportion, and it is a very expensive process to obtain these resources, so sustainable development method must be adopted in order to save this natural resources for the future generation.

Some of the examples of alternative resources that are widely used in place of fossil fuels are wind energy, solar energy, tidal energy, biomass energy and bio-fuels.

Thus, it is very important to develop and use alternative resources.

Final answer:

Developing alternative energy sources is vital for mitigating climate change, reducing reliance on finite fossil fuels, and enhancing economic opportunity and security. Renewable energy such as solar, wind, and hydropower are crucial for the sustainable transition.

Explanation:

Developing alternative energy sources is crucial for a number of reasons. First, as renewable energy sources like solar and wind become more technically superior and cost-effective compared to fossil fuels, market forces will naturally encourage a transition away from non-renewable resources. This helps prevent dependency on finite resources that will eventually deplete.

Second, climate change concerns necessitate the development of alternative energy sources. Political measures may impose financial penalties on fossil fuel use to mitigate harmful ecological impacts, prompting a migration towards more sustainable energy choices.

Lastly, alternative energy sources like solar, wind, and hydropower can provide increased economic opportunity, job creation, and energy security. Especially in light of climate-related disasters that reveal the vulnerabilities of fossil-fuel-dependent energy systems, diversification is key. It is also critical to plan now for a transition to sustainable energy to avoid the potential "energy trap" where too much energy is consumed in building new infrastructure, leaving insufficient resources for society's needs.

Final answer:

The speed of an object of mass m when it hits the planet's surface after being dropped from height h is found by using the conservation of energy, yielding the formula v = √[2GM(1/R - 1/(R+h))] where G is the gravitational constant, M the planet's mass, and R its radius.

Explanation:

To find the speed v of an object of mass m when it hits the surface of a planet, we will use the principles of energy conservation in the context of gravitational fields. The total mechanical energy (potential plus kinetic) at the beginning and at the end must be equal since we are ignoring air resistance and any other non-conservative forces.

The initial potential energy when the object is at height h above the planet is given by the gravitational potential energy formula U = -G(Mm)/(R+h) and the initial kinetic energy is zero as the object is initially at rest. When the object reaches the surface of the planet, its potential energy is U = -G(Mm)/R and its kinetic energy is K = (1/2)m*v^2. Conservation of energy dictates that the initial total energy equals the final total energy:

-G(Mm)/(R+h) = -G(Mm)/R + (1/2)m*v^2

Solving for v, the speed of the object at the planetary surface, we get:

v = √[2GM(1/R - 1/(R+h))]

This expression shows that the object's speed increases with a greater initial height h, a more massive planet M, and decreases with a larger planetary radius R.

Answer:

Amplitude of the resultant wave = 15.72 cm

Explanation:

If two identical waves are traveling in the same direction, with the same frequency, wavelength and amplitude; BUT differ in phase the waves add together.    

A = 9cm (amplitude)

φ = 45 (phase angle)

The two waves are y1 and y2

y =  y1 + y2

where y1 = 9 sin (kx - ωt)    

and   y2 = 9 sin (kx - ωt + 45)

y       = 9 sin(kx - ωt) + 9 sin(kx - ωt + 45)  =  9  sin (a)   +   9  sin (b)

where a =  (kx - ωt)

abd b = (kx - ωt + 45)

Apply trig identity: sin a + sin b = 2 cos((a-b)/2) sin((a+b)/2)

A  sin (   a    )   +   A  sin (     b    ) = 2A cos((a-b)/2) sin((a+b)/2)

We have that

9  sin (   a    )   +   9  sin (     b    ) = 2(9) cos((a-b)/2) sin((a+b)/2)

= 2(9) cos[(kx - wt -(kx - wt + 45))/2] sin[(kx - wt +(kx -wt +45)/2]

y       = 2(9) cos (φ /2) sin (kx - ωt + 45/2)

The resultant sinusoidal wave has the same frequency and wavelength as the original waves, but the amplitude has changed:  

Amplitude equals 2(9) cos (45/2) = 18 cos (22.5°) = 18 * -0.87330464009

= -15.7194835217 cm ≅ 15.72 cm

since amplitudes cannot be negative our answer is 15.72 cm

Answer:

e. is definitely zero

Explanation:

Given that

At initial condition the speed of the pop cans is zero.

We know that linear momentum

P = Mass x velocity

P =  m v

At initial condition v = 0

P= 0

If there is no any external force then the linear momentum of the system will be conserve.And given that ,consider the system isolated.

Therefore the answer is e.

Considering the gasses law and all the parameters, 1) the pressure inside the cylinder is 3249.4 Pa, 2) the height of the piston at 18ºC is 0.4452 m.

The law of gasses is a group of chemical and physical laws that allows understanding the behavior of gasses in a close system.

The law of gasses considers different parameters, such as

When talking about standard conditions in gas, we refer to 1 atm pressure, 273 K of temperature (0ºC), and 22.4 L/mol of volume.

The different laws are,

The relationship between these three laws and the variables is as follows,

                                 (P₁V₁) / T₁ = (P₂V₂) / T₂

According to this framework, we can answer the questions in this porblem.

Available data:

A) What is the gas pressure inside the cylinder?

We know that P is defined by the relationship between force and area.

P = F/A

So, let us define Force and Area.

F is the force applied by the piston. So we need to get the F of the piston.

To do it, we will use the following formula,

 W = mg             ⇒  Where m is mass (15 kg) and g is gravity (9.8m/s²)

Since W is a type of force, we can replace this value in the previous general formula,

P = F/A = W/A = mg/A

Area A is defined by the following formula

A = π r²

Where

- π = 3.1416

- r = D/2

Now, we can replace A in the general formula as follows,

P = mg/A = mg / π (D/2)²

The pressure inside the cylinder is,

P = mg / π (D/2)²

P = (15 x 9.8) / 3.1416 (12)²

P = 147 / 452.39

P = 0.32494

P = 3249.4 Pa

The gas pressure inside the cylinder 3249.4 Pa.

B) What will the height of the piston be if the temperature is lowered to 18 ∘C?

T₁ = 588 K

T₂ = 18 ºC ⇒ 18 + 273 = 291 K

Now, volume can be calculated as follows,

V = π r² h = A h

Where

- π = 3.1416

- r = D/2 = 12

- h₁ = 0.9 m

- A = 452.39 cm² = 0.4524 m²

Replacing,

V₁ = A h₁

V₁ = 0.4524 m² x  0.9 m

V₁ = 0.4071 m³

Now, we have the initial volume V₁, and the inicial and final temperatures, T₁ and T₂. We will use this values and the Charles law to get the final volume, V₂.

V₁/T₁ = V₂/T₂

V₂ = T₂ (V₁/T₁)

V₂ = 291 (0.4071/588)

V₂ = 291 (0.4071/588)

V₂ =0.2014

Now that we have the final volume, we can use this value to get the final height.

V₂ = A h₂

h = V₂/A

h₂ = 0.2014 m³ / 0.4524 m²

h₂ = 0.4452 m

The height of the piston when the temperature is lowered to 18ºC is 0.4452 m.

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Final answer:

Starting with Part A, the gas pressure inside the cylinder is calculated using the piston's weight and area of the cylinder's cross-section, plus atmospheric pressure. For Part B, the height of the piston at 18 °C is found using the combined gas law, with the final volume corresponding to the new height under constant pressure.

Explanation:

To answer the student's questions regarding the cylinder and piston system, we must use the principles of gas laws and mechanics.

Part A: Gas Pressure Inside the Cylinder

The pressure exerted by the piston onto the gas can be calculated using the formula P = F/A, where F is the force and A is the area. The force due to the piston's weight (F) is the mass of the piston times the gravitational acceleration (F = m * g). The area (A) is the cross-sectional area of the cylinder, which is πr² for a circle. Adding the atmospheric pressure above the piston gives us the total pressure exerted on the gas inside the cylinder.

Part B: Height of the Piston at 18 °C

Assuming the process is isobaric (constant pressure), the change in height can be found using the combined gas law which relates pressure, volume, and temperature of a gas. In this case, P1V1/T1 = P2V2/T2, where V1 and V2 are the initial and final volumes, respectively, determined by the product of the cross-sectional area and the height of the piston, P is pressure, and T is temperature in Kelvin. We are looking for the final volume, and thus the final height of the piston when the temperature is lowered.

Answer:

0.027m

Explanation:

the bolt loses contact with the piston only when acceleration due to gravity equals acceleration of piston

ω² * A = g where ω is angular velocity, A amplitude, g acceleration due to gravity

ω is given by 2πf, ω² is 4π²f²

A= g/4π²f² depending on the value of g used either 10m/s² or 9.8m/s²,

i used 10m/s² in this answer

Answer:

(A) l = 0.39 m      

(B)  l =0.38 m  

(C) l = 0.14 m

Explanation:

Answer:

Explanation:

Answer:

Explanation:

from the question we are given the following values:

mass (m) = 1.6 kg

height (h) = 1.05 m

compression of spring (l) = ?

spring constant (k) = 330 N/m

acceleration due to gravity (g) = 9.8 m/s^{2}

(A) initial potential energy of the object = final potential energy of the spring

         potential energy of the object = mg(1.05 + l)  

         potential energy of the spring = 0.5 x k x l^{2}  (k= spring constant)

 therefore we now have

              mg(1.05 + l)  = 0.5 x k x l^{2}

              1.6 x 9.8 x (1.05 + l)  = 0.5 x 300 x l^{2}

               15.68 (1.05 + l) = 150 x l^{2}

                   16.5 + 15.68l = 150l^{2}

l = 0.39 m        

(B)   with constant air resistance the equation applied in part A above becomes

initial P.E of the object - air resistance = final P.E of the spring

mg(1.05 + l) - 0.750(1.05 + l) = 0.5 x k x l^{2}        

     1.6 x 9.8 x (1.05 + l) - 0.750(1.05 + l)  = 0.5 x 300 x l^{2}

         (16.5 + 15.68l) - (0.788 + 0.75l) = 150l^{2}        

          16.5 + 15.68l - 0.788 - 0.75l = 150l^{2}

            15.71 + 14.93l = 150^{2}

            l =0.38 m  

(C)   where g = 1.63 m/s^{2} and neglecting air resistance

      the equation mg(1.05 + l)  = 0.5 x k x l^{2} now becomes

        1.6 x 1.63 x (1.05 + l)  = 0.5 x 300 x l^{2}

        2.608 (1.05 +l) = 0.5 x 300 x l^{2}

        2.74 + 2.608l = 150 x l^{2}

l = 0.14 m

The compression of the spring when it is dropped from 1.05 m is 0.37 m.

The compression of the spring when air resistance is considered 0.36 m.

The compression of the spring when air resistance is neglected and gravity is 1.63 is 0.14 m.

The given parameters;

The compression of the spring is determined by applying the principle of conservation of energy;

[tex]\frac{1}{2} kx^2 = mgh\\\\\frac{1}{2} kx^2 = mg(1.05 + x)\\\\kx^2 = 2mg(1.05 + x)\\\\330x^2 = 2\times 1.6 \times 9.8(1.05 + x)\\\\330x^2 = 32.93 + 31.36x\\\\330x^2 - 31.36x - 32.93 = 0\\\\a = 330, \ b = -31.36, \ c = -32.93\\\\x = \frac{-b \ \ +/- \ \sqrt{b^2 -4ac} }{2a} \\\\x = \frac{-(-31.36) \ \ +/- \ \sqrt{(-31.36)^2 -4(330\times -32.93)} }{2(330)}\\\\x = 0.37 \ m[/tex]

Considering air resistance, the compression of the spring is calculated as follows;

[tex]\frac{1}{2} kx^2 = mg(1.05+ x) - F(1.05+ x)\\\\\frac{1}{2} \times 330 x^2 = 1.6\times 9.8(1.05 + x) - 0.75(1.05 + x)\\\\165x^2 = 16.46 + 15.68x - 0.79 - 0.75x \\\\165x^2 -14.93x - 15.67 = 0\\\\a = 165, \ \ b = -14.93 \ \ c = -15.67 = 0\\\\x = \frac{-b \ \ +/- \ \sqrt{b^2 - 4ac} }{2a} \\\\x = \frac{-(-14.93) \ \ +/- \ \sqrt{(-14.93)^2 - 4(15.67)} }{2(165)}\\\\x = 0.36 \ m[/tex]

The compression of the spring when air resistance is neglected and gravity is 1.63;

[tex]\frac{1}{2} kx^2 = mg(1.05 + x)\\\\\frac{1}{2} \times 330 x^2 = 1.6 \times 1.63(1.05 + x)\\\\165 x^2 = 2.74 + 2.61x \\\\165 x^2 - 2.61x- 2.74 = 0\\\\a = 165, \ \ b = -2.61, \ c = \ -2.74\\\\x = \frac{-b \ \ +/- \ \ \sqrt{b^2 - 4ac} }{2a} \\\\x = \frac{-(-2.61) \ \ +/- \ \ \sqrt{(-2.61) ^2 - 4(165\times -2.74)} }{2(165)}\\\\x = 0.14 \ m[/tex]

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We can calculate the kinetic energy of the ejected electrons in the photoelectric effect by applying the equation KE = hf - BE, where 'KE' is kinetic energy, 'h' is Planck's constant, 'f' is the frequency of the light, and 'BE' is the binding energy or work function of a metal (in this case, titanium).

The photoelectric effect is the process where light of sufficient energy (in this case, frequency) shone on a metal surface can release electrons (photoelectrons). Kinetic energy of these ejected electrons can be calculated according to the equation: KE = hf - BE. Here, 'KE' is the kinetic energy we're striving to find, 'h' is Planck's constant, 'f' is the frequency of the incident light, and 'BE' is the binding energy or work function of the electron.

For titanium metal, you've provided that the work function (BE) is 6.93 × 10⁻¹⁹ J. The frequency ('f') of the light used is 1.216 × 10¹⁵ s⁻¹. And, Planck's constant ('h') approximately equals 6.63 × 10⁻³⁴ Js.

To execute the calculation: KE = (6.63 × 10⁻³⁴ Js x 1.216 × 10¹⁵ s⁻¹) - 6.93 × 10⁻¹⁹ J. The solution will provide your kinetic energy in Joules

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The rollercoaster initially had 78,000 J of energy. It converted two-thirds of the energy into kinetic energy and later doubled it on a curve. Therefore, the coaster's new total mechanical energy is 182,000 J.

In this energy problem, the roller coaster car starts out with 78,000 J of potential energy. It then converts two-thirds of its energy into kinetic energy, which is 2/3 * 78,000 J = 52,000 J. However, this isn't the end of the energy conversion. As the roller coaster car takes a curve, it doubles its kinetic energy to become 2 * 52,000 J = 104,000 J. Therefore, the new total mechanical energy of the car, considering both its remaining potential and newly gained kinetic energy, is its original potential energy (78,000 J) minus the potential energy converted to kinetic and then doubled (2/3 * 78,000 J * 2), which gives us 78,000 J - (2/3 * 78,000 J * 2) = 78,000 J - 104,000 J = -26,000 J. However, energy can't be negative, so it means the question might be flawed or we need to ignore the energy conservation law in this case and simply sum up potential and kinetic energies getting 78,000 J + 104,000 J = 182,000 J.

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To find the mechanical energy of the roller coaster car, we calculate the converted kinetic energy and then account for it being doubled during the ride. The car's total mechanical energy remains at 78,000 J due to conservation of energy.

The problem involves calculating the mechanical energy of a roller coaster car after it has converted some of its initial potential energy into kinetic energy and then doubled that kinetic energy. Initially, the car starts with 78,000 J of potential energy. As the problem states, the car converts two-thirds of this energy into kinetic energy. This conversion can be calculated as (2/3) × 78,000 J = 52,000 J of kinetic energy. Then, as the car takes a curve, it doubles this kinetic energy, resulting in 2 × 52,000 J = 104,000 J of kinetic energy. Due to the conservation of mechanical energy, and considering that no energy is lost to friction or other forces, the total mechanical energy of the car will be the same as the initial potential energy it had at the top of the first rise. Therefore, the car now has a total mechanical energy of 78,000 J.

Answer:

9.49596 m

Explanation:

[tex]\omega_f[/tex] = Final angular velocity = 0

[tex]\omega_i[/tex] = Initial angular velocity = 19 rad/s

[tex]\alpha[/tex] = Angular acceleration = -1.26 rad/s²

[tex]\theta[/tex] = Angle of rotation

Equation of rotational motion

[tex]\omega_f^2-\omega_i^2=2\alpha \theta\\\Rightarrow \theta=\frac{\omega_f^2-\omega_i^2^2}{2\alpha}\\\Rightarrow \theta=\frac{0^2-19^2}{2\times -1.26}\\\Rightarrow \theta=143.25396\ rad[/tex]

Converting to m

[tex]143.25396\times \pi d=143.25396\times \pi\times 0.0211=9.49596\ m[/tex]

The distance the coin rolls before it stops is 9.49596 m

Answer:

405.3m

Explanation:

Since the CD spin rate is 500 rpm, or revolution per minutes, its angular speed in rad per second is

[tex]\omega = 500 rev/min * 2\pi rad/rev * 1/60 min/sec = 52.36 rad/s[/tex]

The dusk is 4.3 cm from center, so its velocity must be

[tex]v = R\omega = 4.3 * 52.36 = 225.14 cm/s[/tex]

Then the distance traveled by the dusk after 3 minutes, or 180 seconds is

[tex]d = v*t = 225.14 * 180 = 40526.54 cm[/tex] or 405.3m