prove that acceleration due to gravity is independent to the mass of falling object.
​

The pressure will 14. 0 g of co exert in a 3. 5 l container at 75°c is 4.1atm.

Therefore, option A is correct option.

Given,

Mass m = 14g

Volume= 3.5L

Temperature T= 75+273 = 348 K

Molar mass of CO = 28g/mol

Universal gas constant R= 0.082057L

Number of moles in 14 g of CO is

n= mass/ molar mass

= 14/28

= 0.5 mol

As we know that

PV= nRT

P × 3.5 = 0.5 × 0.082057 × 348

P × 3.5 = 14.277

P = 14.277/3.5

P = 4.0794 atm

P = 4.1 atm.

Thus we concluded that the pressure will 14. 0 g of co exert in a 3. 5 l container at 75°c is 4.1atm.

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Electric potential energy of that charge at origin  = 40 V

Electric potential, the amount of work needed to move a unit charge from a reference point to a specific point against an electric field.

The electric potential energy of any given charge or system of changes is termed as the total work done by an external agent in bringing the charge or the system of charges from infinity to the present configuration without undergoing any acceleration.

Electric potential energy is defined as the total potential energy a unit charge will possess if located at any point in the outer space.

Potential energy at a point = change in electric potential to bring it from infinity to that point

Potential energy = Potential at that point - Potential at infinity

conventionally , potential at infinity is taken as zero

Potential energy = Potential at that point

hence , Potential energy of that charge at origin = Electric Potential at the origin

Potential energy of that charge at origin  = 40 V

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The components that are a possible representation of vector w if the magnitude of vector -3w is ||-3w||=15 are:

From the question, we were given:

|-3w| = 15

3|-w| = 3|w| = 15

Hence:

|w|  = 15/3

|w| = 5

If vector w is represented by <-3,4>, then:

 [tex]\sqrt{(-3)^2 + (4)^2} \\\\\\\sqrt{25} = 5[/tex]

If vector w is represented by <0,-5>

 [tex]\sqrt{(0)^2 + (-5)^2} \\\\\\\sqrt{25} = 5[/tex]

Therefore, The components that are a possible representation of vector w if the magnitude of vector -3w is ||-3w||=15 are:

See full question below

Which components are a possible representation of vector w if the magnitude of vector -3w is ||-3w||=15?

<1,-9>

<-3,4>

<4,5>

<-5,-3>

<0,-5>

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The terminal speed of the marble is 0.588 m/s.

Given:

We know that,

F = mg                          ......(1)

where,

F = force

m = mass

g = acceleration due to gravity

Also,

v = F/k                            ......(2)

where,

v = terminal speed

k = proportionality constant

Substituting the value of F from equation (1) in equation (2)

v = mg/k                             .......(3)

Given,

m = 30 g = 0.030 kg

k = 0.500 kg/s

g = 9.8 m/s²

To find,

v =?

Put the values in equation (3)

v = mg/k        

v = 0.03(9.8)/ 0.500

= 0.294/0.500

= 0.588 m/s

​

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The runner's achilles tendon stretch is 5mm.

What is Young's modulus?

Young's modulus (Y) is described by the following expression.

[tex]Y = \frac{F \times L}{ΔL \times A } [/tex]

where,

F=force exerted on the tendon

A=area

∆L=change in length (streching)

The force in this case is 8 times the weight of the runner

F=8×m×g

F=8×70×9.8

F=5488N

therefore,the change in length of the tendon is given by

[tex]Δ = \frac{F \times L}{ Y \times A } [/tex]

[tex]ΔL = \frac{5488 \times 0.15}{0.15 \times 10 {}^{10} \times 1.1 \times 10 {}^{ - 9} } [/tex]

ΔL=0.00498m

The runner's achilles tendon will stretch by 0.004989m which is approx.5mm

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If the partial pressure of nitrogen in the human body is approximately 593 mm hg at sea level, the partial pressure of nitrogen cannot be 760mm Hg in a scuba diver that is at a depth of 30 feet.

Nitrogen narcosis :

The partial pressure of nitrogen increases with pressure, which produces a narcotic effect. Nitrogen narcosis affects both scuba divers and free divers. It causes depression of the central nervous system, which leads to feelings of euphoria, disorientation and irrational behavior. Divers need to consider absorption rates of different gases in order to avoid conditions such as nitrogen narcosis, and decompression sickness.

What is the partial pressure of the nitrogen?

Therefore, at sea level, where atmospheric pressure is known to be 760 mm Hg, the partial pressures of the various gases can be estimated to have partial pressures of approximately 593 mm Hg for nitrogen, 160 mm Hg for oxygen, and 7.6 mm Hg for argon.

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Answer:

They're are useful in providing larger frictional force

Explanation:

The football shoes have spikes or studs because the studs or spikes provides larger frictional force than normal shoes while running on the grass.

The studs helps to prevent a player from slipping on the grass and help to run faster and change direction quickly without slipping.

The visible radiation produced by new stars within a molecular cloud get absorbed by dust grains and heats up the cloud

A molecular cloud is an interstellar cloud of gas and dust in which molecules can form, the most common of which is hydrogen .

The formation of stars occurs exclusively within molecular clouds because of their low temperatures and high densities, because the gravitational force acting to collapse the cloud must exceed the internal pressures that are acting "outward" to prevent a collapse.

Visible radiation are absorbed by dust grains and heats up the cloud as it cannot penetrate through the cloud instead get absorbed by the cloud . Newly formed stars are visible nearby, their images reddened by blue light which got scattered by the pervasive dust.

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The empirical formula of the antimony chloride is [tex]SbCl_{3}[/tex].

Chemical formulas for compounds that simply specify the proportions of the elements they contain rather than the exact number or arrangement of atoms are known as empirical formulas. The element in the compound with the lowest whole number ratio would be this one.

Data obtained from the question

Antimony (Sb) = 0.338 g

Chlorine (Cl) = 0.295 g

Divide by their molar mass.

Sb = 0.338 / 122 = 0.0028

Cl = 0.295 / 35.5 = 0.0083

Divide by the smallest.

Sb = 0.0028 / 0.0028 = 1

Cl = 0.0083 / 0.0028 = 3

Thus, the empirical formula of the compound is SbCl₃.

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At depth of  h = 10.31 m  the surface of a lake would the pressure be double that at the surface

Liquid pressure is the increase in pressure at increasing depths in a liquid. This pressure increases because the liquid at lower depths has to support all of the water above it.

We calculate liquid pressure using the equation liquid pressure = density x acceleration due to g  x depth in fluid.

At the surface of the lake , pressure Po is = 1.01 * [tex]10^{5}[/tex]  Pa

to find = depth under the surface of a lake would the pressure be double that at the surface

Pressure under the surface will be = 2 *  1.01 * [tex]10^{5}[/tex]  Pa = 2.02 *  [tex]10^{5}[/tex]  Pa

Pressure under the surface = Po + ( rho * g * h )

                    2.02 *  [tex]10^{5}[/tex]        = 1.01 * [tex]10^{5}[/tex]   + (1000 * 9.8 * h)

                     1.01 * [tex]10^{5}[/tex]   = 1000 * 9.8 * h

                     h = 10.31 m

At depth of  h = 10.31 m  the surface of a lake would the pressure be double that at the surface

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It will now emit at a rate of 160 W.

the proportion of an emitter's energy to that of a blackbody, a perfect emitter with the same temperature, wavelength, and viewing circumstances. It ranges from 0 (for the optimum reflector) to 1 and has no dimensions (for a perfect emitter).

The ability to reliably measure temperature using an infrared temperature sensor or a thermal imaging camera depends critically on emissivity, which measures a material's capacity to radiate infrared energy from its surface.

The type of surface affects a surface's emissivity in addition to the material. A smooth and polished metal surface will have a low emissivity in contrast to a roughened and oxidized metal surface, which will have a high emissivity.

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The property of a body to remain at rest or to remain in motion with constant velocity is called inertia.

Newton's first law is often called the law of inertia.As we know from experience some objects have more inertia than others.It is obviously more difficult to change the motion of a larger boulder than that of basketball.For example the inertia of an object is measured by its mass.Mass can be determined by measuring how difficult an object is to accelerate.The more mass an object has,the harder it is to accelerate.

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The acceleration of the car at impact is 15m/s².

Newton's second law provides a precise explanation of the modifications that a force can make to a body's motion. According to this, a body's momentum changes at a rate that is equal to the force acting on it over time in both magnitude and direction. A body's momentum is equal to the sum of its mass and velocity. Similar to velocity, momentum has both a magnitude and a direction, making it a vector quantity.

acceleration - rate of change of velocity with time, both in terms of speed and direction. A point or object going straight forward is accelerated when it accelerates or decelerates.

There are three types of accelerated motions :

express all the units in their most basic form.

kg, newton = kg*m/s², acceleration =m/s²

[tex]\frac{ 30000 kg*m/s^{2} }{ 2000 kg} = 15m/s^{2}[/tex]

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Magnitude of Net force Required to accelerate a 1200kg car uniformly from 0m/s to 27m/s in 10s is 3240N.

Force can be found out using the relation of Force, mass and acceleration.

The relation of Force, mass and acceleration is as follows:

∴ Force = Mass × Acceleration

⇒ Force = 1200kg × Acceleration

Given:

Mass = 1200kg

Final Velocity = 27m/s

Initial Velocity = 0m/s

time = 10s

Now, to find out the acceleration we can use the first equation of motion:

∴ Final Velocity = Initial Velocity + Acceleration × time                

⇒ 27   = 0 + 10a                  

⇒ a = 2.7m/s²        

Putting acceleration in the above mentioned equation,  

∴ Force = 1200kg × Acceleration

⇒ Force = 1200kg × 2.7

⇒ Force = 3240N

Hence, the net force required to accelerate the car uniformly is 3240N.

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The answer is 3240 N.

Intial velocity [tex]$\mathrm{u}=0 \mathrm{~m} / \mathrm{s}$[/tex]

final velocity [tex]$\mathrm{v}=27 \mathrm{~m} / \mathrm{s}$[/tex]

time [tex]$t=10$[/tex] sec.

Newton's first equation of motion

[tex]$v=u+a t$[/tex], here a = acceleration

[tex]$\mathrm{so}_{0}=(v-u) / t$[/tex]

[tex]$a=(27.0-0) / 10$[/tex]

[tex]$a=2.7 \mathrm{~m} / \mathrm{sec}^{2}$[/tex]

Force [tex]$F=m a$[/tex]

Mass [tex]$\mathrm{m}=1200 \mathrm{~kg}$[/tex]

[tex]$F=1200 \times 2.7$[/tex]

[tex]$F=3240 N$[/tex]

What is acceleration?

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An energy of 25kJ is given out hence the reaction is exothermic.

Chemical reaction is said to occur when reactants combine leading to the formation of products. In a plot of the energy against the reaction profile, the topmost point of the graph is called the activation energy.

We know that a reaction is exothermic when reactants posses more energy than the products. Hence the enthalpy change for this reaction is;

ΔH = 5kJ - 30kJ = -25kJ thus the reaction is an exothermic reaction.

Now, the activation energy for the lighting of the match stick is high that is why a spark is required before the reaction gets underway. Heat is evolved in the process hence the reaction is exothermic. The energy of the reactants is greater than the energy of the products.

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The angular momentum of earth is

7×10^33 kgm^2/sec

Given:

mass of earth = 5.98×1024 kg

radius of earth = 6.38×10^6 m

To Find:

angular momentum

Solution:

For earth we have moment of inertia as

I = 2/5mR^2

and angular velocity as ω = 2π/T

Thus angular momentum is given as

L= 2/5mR^2*2π/T

L = 2/5*5.98×10^24*(6.38×10^6)^2*2*3.14/86400s

L = 7 × 10^33 kg/m^2/sec

So, angular momentum of earth is

So, angular momentum of earth is 7×10^33 kgm^2/sec

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The force on the electron is (F)= 9.2 nN.

To calculate the value of the force on the electron here we use the formula,

[tex]F=k\frac{q_{1} q_{2} }{r^{2} }[/tex]

Here we are given,

[tex]q_{1}[/tex]= The charge of an atomic nucleus= 40e = [tex]40 \times 1.6 \times 10^{-19}[/tex] C.

[tex]q_{2}[/tex]= The charge of an electron = [tex]1.6 \times 10^{-19}[/tex] C.

r= The distance between the nucleus and the electron = [tex]10^{-9}[/tex] m.

k= The Coulomb's constant = [tex]8.99 \times10^9 N m ^2 /C^ 2[/tex]

We have to find the value of the of the force on the electron = F

Now , we substitute the known values in the above equation, we can get

[tex]F=k\frac{q_{1} q_{2} }{r^{2} }[/tex]

Or, [tex]F=8.99\times 10^{9} \frac{40\times 1.6\times 10^{-19} \times 1.6\times 10^{-19} }{(10^{-9})^{2} }[/tex]

Or,[tex]F=8.99\times 10^{9}\times {40\times (1.6\times 10^{-19} )^2\times (10^{9})^{2} }[/tex]

Or, [tex]F= 9.2 \times 10^{-9} N[/tex]

Or, F= 9.2nN

So, from the above calculation we can conclude that the amount of force applied on the electron is 9.2nN.

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The transistor is a great improvement over the vacuum tube because it is much more energy efficient is a True statement .

A transistor is a miniature semiconductor that  controls current or voltage flow and also amplifies and generates  electrical signals and  can also act as a switch/gate for them.

A vacuum tube, also called a valve in British English, is an electronic device used in many older model radios, television sets, and amplifiers to control electric current flow. The cathode is heated, as in a light bulb, so it will emit electrons. This is called thermionic emission.

Transistors consume lower power consumption , less waste heat, and are highly efficient than equivalent tubes, especially in small-signal circuits.

Vacuum tubes runs with D.C voltage which ranges from 400 V to 500 V. Vacuum tubes require much higher power than transistor device. Hence , are less efficient . This is the main advantages of the transistor.

Another advantage of transistors are that they are portable and lightweight equipment. Can operate on lower-voltage supplies for greater safety, also have lower costs and tighter clearances.

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No, it's not necessary for the object with constant velocity to move in a straight line.

It can can also move in a uniform circular path.

Only when no forces are present or when all of the forces acting on an item are equal and opposite to one another, or when the total force acting on the object is zero, will its velocity remain constant. It's commonly known as equilibrium. The sum of the forces exerted on an object must be zero since, in accordance with Newton's first law of motion, an object moving at a constant speed experiences no net external force.

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The frequency of the third harmonic if the pipe is closed at one end is = 102.93  Hz.

To find the frequency of the third harmonic if the pipe is closed at one end, we use the formula,

[tex]f_{n} =nf_{1}[/tex]=[tex]n\frac{v}{4L}[/tex]  , in this case n= 1,3,5,7,9.....

Here we are given,

L= The length of the pipe = 4.137 m.

v= speed of the sound at 16.164°C .

[tex]v_{0}[/tex]= speed of the sound at 0°C.=331 m/s

Before finding the frequency we have to find the speed of the sound at 16.164°C. To find v, we are using the formula,

[tex]v=v_{0 } \sqrt{\frac{T_{2} }{T_{1} } }[/tex]=[tex]331\times \sqrt{\frac{(273+16.164) }{273 }[/tex]=340.65 m/s.

We have to find the frequency of the third harmonic, so according to the question, n=5

Now we put the known values in the first equation, we can find that

[tex]f_{n}=n\frac{v}{4L}[/tex]

Or,[tex]f_{n} = 5\times\frac{340.65}{4\times 4.137}[/tex]=102.93 Hz.

Therefore, from the above calculation we can conclude that if the pipe is closed at one end the frequency of the third harmonic is 102.93 Hz.

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The average current is 0.10 A.

Charge moving through a location on a circuit at a constant rate is called current. When numerous coulombs of charge pass over a wire's cross section in a circuit, it produces a large current. It is not necessary for a wire to be moving at a fast speed in order to have a high current if the charge carriers are tightly packed into the wire. To put it another way, many charge carriers traveling through the cross section is sufficient; they do not need to travel a great distance in a single instant. The amount of charges that flow through a cross section of wire on a circuit, as opposed to how far they travel in a second, is what determines current.

A charge of 12 c passes through an electroplating apparatus in 2. 0 min. what is the average current?

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The wavelength of the emitted photon is([tex]\lambda[/tex])= 690nm

To calculate the wavelength of the photon we are using the formula,

[tex]\triangle E= \frac{h\times c}{\lambda}[/tex]

Or,[tex]\lambda= \frac{h\times c}{\triangle E}[/tex]

We are given here,

[tex]\triangle E[/tex]= The energy difference between the two levels = 1. 8 ev= [tex]1.8\times 1.6 \times 10^{-19}[/tex] C.

h= Planck constant = [tex]6.626\times 10^{-34}[/tex] Js.

c= speed of light = [tex]3\times10^8[/tex] m/s.

We have to find the wavelength of the emitted photon =[tex]\lambda[/tex] m.

Therefore, we substitute the known parameters in the above equation, we can find that,

[tex]\lambda= \frac{h\times c}{\triangle E}[/tex]

Or,[tex]\lambda= \frac{6.626\times 10^{-34}\times 3\times 10^8}{1.8\times 1.6 \times 10^{-19}}[/tex]

Or,[tex]\lambda= 690\times 10^{-9}[/tex] m

Or,[tex]\lambda[/tex]=690 nm.

From the above calculation we can conclude that the wavelength of the emitted photon is 690nm.

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All electromagnetic waves have the same manner of propagation; alternating electric and magnetic fields that's why electromagnetic waves of all wavelengths have the same speed in a vacuum

An altering magnetic field will cause an altering electric field and vice versa. Electromagnetic waves are created from these shifting fields. In contrast to mechanical waves, electromagnetic waves can travel without a medium. The oscillations between an electric field and a magnetic field produce waves known as electromagnetic waves or EM waves.

In other words, magnetic and electric fields oscillate to form electromagnetic (EM) waves. Almost the majority of the energy that sustains life on our planet comes from electromagnetic waves that flow from the sun to Earth through space. Technology is a necessity for many additional electromagnetic wave sources. Examples include X-rays, radio waves, and microwaves.


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Separately derived system generators shall have the neutral conductor sized not smaller than required to carry the maximum unbalanced current as determined by NEC Article 220.61.

Charged material experiences a force when it is exposed to an electromagnetic field due to the physical property of electric charge. You can have a positive or negative electric charge.

Electric current is defined as the charge per unit of time.

The mathematical relation between current and the electric charge

I =Q/T

Generators are basically motors that operate in reverse—they produce electricity when rotated, instead of rotating when supplied with electricity

The conductors that come from generators must be sized, and overload protection is required. But compared to similar considerations for motors, these considerations are much simpler.

Thus, The neutral conductor on separately derived system generators must be no smaller than necessary to carry the maximum unbalanced current as specified by NEC Article 220.61.

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8.16m is the required height, a 5kg stone need to be raised.

One sort of potential energy is gravitational potential energy, which is equal to the product of the object's mass (m), the gravitational acceleration (g), and the object's height (h) as measured in relation to the ground's surface (the body).

We obtain the formula by considering the work done in raising a mass m through a height h.

Work in elevating mass m through height h is equal to force times distance.

The force must be greater than the mass m's weight, hence F = mg.

Work done = mgh = gravitational potential energy

Energy =  Mass of the object × gravitational acceleration × height.

Mass of the stone = 5kg

Equating ;

∴ 400 J = 5 kg × 9.8 m/s² × height

  Height = 8.16 m

Therefore, 8.16m is the required height.

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The distance between slit and the screen is 1.214m.

To find the answer, we have to know about the width of the central maximum.

                           [tex]w=\frac{2*wavelength*d}{a}[/tex]

where, d is the distance between slit and the screen, and a is the slit width.

                           [tex]d=\frac{w*a}{2*wavelength} =\frac{8*10^{-3}*0.17*10^{-3}}{560*10^{-9}*2} \\\\d=1.214m[/tex]

Thus, we can conclude that, the distance between slit and the screen is 1.214m.

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(d) is increasing its velocity by 2.0 m/s every second.

An acceleration of 2 m/s² means that the object is is increasing its velocity by 2.0 m/s every second.

The rate at which an object's velocity changes over a predetermined period of time is referred to as its acceleration. Acceleration is mathematically defined as an object's change in velocity divided by the amount of time it took for that change to occur.

                                [tex]Acceleration = \frac{change in velocity}{time}[/tex]

The positive sign of the acceleration denotes a change in velocity that is positive and growing, whereas the negative sign denotes a change in velocity that is decreasing.

Consequently, an acceleration of 2 m/s² indicates that the object's velocity is increasing by 2 m/s every second.

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option(d) is increasing its velocity by 2.0 m/s every second is the right answer.

An object moving in the x direction experiences an acceleration of           2.0 m/[tex]s^{2}[/tex] this means the object  is increasing its velocity by 2.0 m/s every second.

An object's acceleration is the rate at which its velocity alters over a given amount of time. Calculating acceleration involves dividing the change in velocity of an object by the time it takes for that change to take place.

Acceleration =[tex]\frac{change in velocity}{time}[/tex]

The acceleration's positive sign indicates a change in velocity that is growing and positive, whereas the acceleration's negative sign indicates a change in velocity that is declining.

Consequently, an acceleration of 2 m/s² indicates that the object's velocity is increasing by 2 m/s every second.

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The dripping faucet onto the wave causes the frequency to stay the same throughout, it just moves up and down.

When a wave is passed through the single slit, diffraction occurs. The light spreads out and after it passes through the slit, it interferes with itself.

The distance between the two adjacent nodes = λ/2.

A periodic wave's wavelength is its spatial period, or the length over which its form repeats. It is a property of both travelling waves and standing waves as well as other spatial wave patterns. It is the distance between two successive corresponding locations of the same phase on the wave, such as two nearby crests, troughs, or zero crossings. The spatial frequency is the reciprocal of wavelength. The Greek letter lambda (λ) is frequently used to represent wavelength. The term wavelength is also occasionally used to refer to modulated waves, their sinusoidal envelopes, or waves created by the interference of several sinusoids.

The distance between the two adjacent nodes = λ/2.

for the standing wave ,the distance between any two adjacent nodes or antinodes is 1/2 λ.

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The speed of the wave is 0.68 m/s.

Wave speed is the distance the wave travels in a given amount of time, such as the number of meters it travels per second.

V = Fλ

where;

This is the distance between two sequential troughs = 1.1 m

The frequency is number of complete oscillation per second.

f = n/t

where;

f = (9)/(14.5)

f = 0.62 Hz

V = 0.62 x 1.1

V = 0.68 m/s

Thus, the speed of the wave is 0.68 m/s.

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