What effect does the diameter of the string have on the lever arm? explain why we can ignore this effect

Answers

Answer 1

The effective lever arm will be enhanced if we utilize a big diameter string.

What is Lever Arm?

The perpendicular distance from the axis of rotation to the force's line of action is specified as the lever arm.

When a big diameter string is utilized, the effect of the diameter on the string of the lever arm will be enhanced.

This is due to the reason that if the radius of the pulley is R and the radius of the string is r, then the effective lever arm becomes R+r.

If the radius,r of the string is very minute such that its addition to the radius of the pulley, R will hardly make a change to the effective lever arm, then it is avoided. However, if the radius of the string is a big number then it can not be avoided as it can make significant errors in the calculation of the effective lever arm.

Hence, The effective lever arm will be enhanced if we utilize a big diameter string.

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Related Questions

Certain car can accelerate from rest to the speed v in t seconds. if the power output of the car remains constant, (a) how long does it take for the car to accelerate from v to 2v? (b) how fast is the car moving at 2t seconds after starting

Answers

(a) time taken for the car to accelerate from v to 2v = t = [tex]\frac{2V-V}{a}[/tex]

(b) velocity of the car moving at 2t seconds = ΔV = 2at

(a) we know that,

a=[tex]\frac{V_{F}-V_{0} }{t}[/tex]

where, [tex]V_{F}[/tex] is the final velocity

[tex]V_{0}[/tex] is the initial velocity

a = acceleration

t = time

Time taken to accelerate from V to 2V:

t = [tex]\frac{2V-V}{a}[/tex]

(b) We know that,

a=[tex]\frac{V_{F}-V_{0} }{t}[/tex]

where, [tex]V_{F}[/tex] is the final velocity

[tex]V_{0}[/tex] is the initial velocity

a = acceleration

t = time

how fast is the car moving at 2t seconds after starting,

we can represent [tex]V_{F}[/tex] - [tex]V_{0}[/tex] = ΔV

at time = t= 2t, it becomes

a=[tex]\frac{V_{F}-V_{0} }{t}[/tex] = a = ΔV/2t

t= ΔV/2a

ΔV = 2at

What is acceleration?

Rate of change of velocity with time, both in terms of speed and direction is known as acceleration.

What is speed?the rate at which an object's location changes in any direction. The distance traveled in relation to the time it took to travel that distance is how speed is defined. Since speed simply has a direction and no magnitude, it is a scalar quantity.

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What is the distance traveled by an object that moves with an average velocity of 8.0 m/s for a total of 4.0 seconds? please show your work in order to earn credit for this question.

Answers

The distance traveled by the object is 32 m.

What is Kinematic equation?The motion of an object with constant acceleration is described by a set of equations known as the kinematic equations. Integrals, derivatives, and rates of change must all be understood in order to solve kinematics problems.Calculation for determining distance traveled

If an object is traveling with a consistent velocity, this is referred to as uniform motion.

The equation below gives the average speed of an item moving uniformly:

v = d/t

where

v= average speed

d = traveled distance

t= The amount of time used

The object in this problem is as follows:

v = 8.0 m/s is the average speed

The time was t = 4.0 s.

We determine the distance traveled by solving for d:

d = vt = (8.0)(4.0) = 32 m

Hence, the distance traveled by the object is 32 m.

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19. when the wave speed increases, will the wavelength need to increase, decrease or stay the same to get the same standing wave pattern (such as the one with 3 antinodes)?

Answers

When the wave speed increases the wave stay the same to get the same standing wave pattern

Standing wave are the combination of two waves moving in opposite directions . Amplitude of both the waves is same and frequency is also same . The phenomenon is the result of interference

Wavelength and frequency are inversely related to each other .

frequency = c / wavelength

so if one get  change then the other changes. As one get decrease other will increase and vise versa. . The speed of the wave depends on the medium. Change in the frequency of the wave changes its form to go into the next harmonic so the wavelength changes .Also in order to maintain the wave pattern the wavelength remain same

Hence , speed of wave will not affect the wavelength of wave.

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Consider the two vectors a 3i-2j & b = -i-4j calculate the direction of a+b and a-b?

Answers

Direction of |a+b| is south east and that of |a-b| is north east.

Calculation:

Given

a = 3i - 2j

b = -i - 4j

To find,

a+b =?

a-b =?

|a+b| = |(3i - 2j - i - 4j)|

        = |2i - 6j|

        = [tex]\sqrt{2^{2} + (-6^{2}) }[/tex]

        = [tex]\sqrt{4+36}[/tex]

        = [tex]\sqrt{40}[/tex]

        = [tex]2\sqrt{10}[/tex]

|a-b| = |(3i - 2j) - (-i - 4j)|

       = |3i -2j + i + 4j|

       = |4i + 2j|

       = [tex]\sqrt{4^{2} + 2^{2} } \\[/tex]

       = [tex]\sqrt{16+ 4}[/tex]

       = [tex]\sqrt{20}[/tex]

       = [tex]2\sqrt{5}[/tex]

Direction of |a+b| is south east (|2i - 6j|, this shows 2 units to the right and 6 units down)

Direction of |a-b| is north east (|4i + 2j|, this shows 4 units right & 2 units up)

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How far apart would you have to place the poles of a 1. 5 v battery to achieve the same electric field?

Answers

To place the poles of a 1. 5 v battery to achieve the same electric field is 1.5×10−2 m

The potential difference is related to the electric field by:

∆V=Ed

where,

∆V is the potential difference

E is the electric field

d is the distance

what is potential difference?

The difference in potential between two points that represents the work involved or the energy released in the transfer of a unit quantity of electricity from one point to the other.

We want to know the distance the detectors have to be placed in order to achieve an electric field of

E=1v/cm=100v/cm

when connected to a battery with potential difference

∆v=1.5v

Solving the equation,we find

[tex]d = \frac{ \:Δv}{e} [/tex]

[tex] = \frac{1.5v}{100v/m} [/tex]

[tex] = 1.5 \times 10 {}^{ - 2} m[/tex]

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What type of number is 3π + 1?
Choose all answers that apply:
A. whole number
B. integer
C. rational
D. Irrational

Answers

Answer: It's D

Explanation:

2. What would be the correct military time if the clock reads 3:00 p.m. in Greenwich time: A. 1200 B. 1500 C. 1600 D. 0300

Answers

The military time corresponding to 3:00p.m is 1500, and it is pronounced as fifteen hundred hours.

To find the answer, we have to know more about the Military time.

What is Military time?Military time is sometimes referred to as "24 Hour Time," and this system does away with "am" and "pm." The use of straightforward time ideas makes it easier to understand and is the preferred time reference in the scientific, medical, and military communities. Given that so many regions of the world use this system of telling the time, it has increasingly come to be regarded as the global time. Military time is used and understood in numerous countries, including the Philippines, Germany, Australia, and India.The military time corresponding to 3:00p.m is 1500, and it is pronounced as fifteen hundred hours.

Thus, we can conclude that the option B is right.

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though its economics question can anybody help me​

Answers

A is opportunity cost
a is opportunity cost

Open the resistance in a wire simulation, adjust only the length of the resistor, what happens to resistor?

Answers

If we increase the length of the resistor, resistance will also increase and vice-versa.

It is given that in a wire simulation, we have to adjust only the length of the resistor.

It required to find the effect on resistor when adjust only the length of the resistor.

What happens to resistor when adjust only the length of the resistor?

As we know that the length is directly proportional to the resistance of the wire that means is we increase the size or length of the wire then it also increase the resistance present in the wire. On the other hand if we decrease the length of the wire, it will decrease the resistance. This can be represented as:

Resistance = resistivity × length/area

This is also because there is more collision of the flowing electrons in the wire to the metal ions present there.

Thus if we increase the length of the resistor, resistance will also increase and vice-versa.

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Two point charges, feel a force of 1. 0 n when they are 2. 0 cm apart. if they are moved further apart to 8. 0 cm. What is the electric force between them?

Answers

Two point charges, feel a force of 1. 0 n when they are 2. 0 cm apart. if they are moved further apart to 8. 0 cm. The electric force between them will be F2 = 1/16 J

A charged particle, also called an ion, is an atom with a positive or negative charge. This happens whenever something called an ionic bond forms. Two particles that have different numbers of electrons (the smallest particle in an atom which is negative) start reacting to each other.

According to Coulomb's law, the force of attraction or repulsion between two charged bodies is directly proportional to the product of their charges and inversely proportional to the square of the distance between them. It acts along the line joining the two charges considered to be point charges.

F1 = K q1*q2 / [tex]r1^{2}[/tex]

1 =  K q1*q2 / [tex]2^{2}[/tex]

F2 =  K q1*q2 / [tex]r2^{2}[/tex]

F2 =  K q1*q2  / [tex]8^{2}[/tex]

F1 / F2 = 64 / 4

1 / F2 = 16 / 1

F2 = 1/16 J

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A stretched string is observed to have four equal segments in a standing wave driven at a frequency of 480 hz. what driving frequency will set up a standing wave with five equal segments?

Answers

600Hz is the driving frequency needed to create a standing wave with five equal segments.

To find the answer, we have to know about the fundamental frequency.

How to find the driving frequency?The following expression can be used to relate the fundamental frequency to the driving frequency;

                                        f(n) = n * f (1)

where, f(1) denotes the fundamental frequency and the driving frequency f(n).

The standing wave has four equal segments, hence with n=4 and f(n)=4, we may calculate the fundamental frequency.

                                          f(4) = 4× f (1)

                                          480 = 4× f(1)

                                         f(1) = 480/4 =120Hz.

So, 120Hz is the fundamental frequency.

To determine the driving frequency necessary to create a standing wave with five equally spaced peaks? For, n = 5,

                      f(n) = n 120Hz,

                      f(5) = 5×120Hz=600Hz.

Consequently, 600Hz is the driving frequency needed to create a standing wave with five equal segments.

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The peak magnetic field strength in a residential microwave oven is 9. 2 x 10-5 t. what is the intensity of the microwave?

Answers

The intensity of the microwave is 10.09 × 10⁵ W/m².

The unit of magnetic induction is the tesla (T). The magnetizing force, which induces the lines of force through a material, is called the field intensity, H (or H-field), and by convention has the units ampere per meter (A m−1) .

The portion of a material's magnetic field that results from an external current and is not intrinsic to the material itself is known as the magnetic field strength, also known as magnetic intensity or magnetic field intensity. It is measured in amperes per meter and represented as the vector H.

Magnetic Field, B = 9.2 × 10⁻⁵ T

[tex]I_{avg} = \frac{CB_0^2}{2\mu _0}[/tex]

       [tex]= \frac{(2.998*10^8 m/s) (9.2 * 10^-^5 T)^2}{2 ( 4\pi * 10^-^7)}[/tex]

      [tex]= 10.09[/tex] × [tex]10^5 \frac{W}{m^2}[/tex]

Therefore, the intensity of the microwave is 10.09 × 10⁵ W/m².

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Please help me!! 1 a) Compare the speed that light waves travel in air to the speed that sound waves travel in the air. (Show results in meters/second) 1 b) How many times faster do light waves travel in the air in comparison to sound waves in air? (show working out) 2) Compare the speed of light in water to the speed of sound in water. (Show results in meters/second)

Answers

The speed of light waves travel in air is 3.0 * 10⁸ m/s, while the speed of sound waves in air at 25° C is 346.3 m/s.

Light waves travels 8.66 * 10⁵ times faster in air in comparison to sound waves in air.

The speed of light in water is 3.0 * 10⁸ m/s while the speed of sound in water is 1.481 m/s

What is wave speed?

The distance covered by a wave per second is known as the wave speed.

The speed of a wave varies according to the density of the medium it is travelling as well as the due to the frequency of the wave.

The speed that light waves travel in air = 3.0 * 10⁸ m/s

The speed that sound waves travel in the air at 25° C = 346.3 m/s

The ratio of the speed of speed that light waves travel in air to that of the speed that sound waves travel in the air at 20° C = 3.0 * 10⁸/346.3 = 8.66 * 10⁵

Therefore, light waves travels 8.66 * 10⁵ in the air in comparison to sound waves in air

The speed of light in water = 3.0 * 10⁸ m/s

The speed of sound in water = 1,481 m/s

Therefore, light waves travels much faster water than sound waves in water.

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What charge in microcoulombs needs to be plaaced at the orgin to create an electric force?

Answers

It follows coulombs law.          

According to Coulomb’s law, the force of attraction or repulsion between two charged bodies is directly proportional to the product of their charges and inversely proportional to the square of the distance between them. It acts along the line joining the two charges considered to be point charges.

In Short: F ∝ q1q2/d2

where,

ε is absolute permittivity,

K or εr is the relative permittivity or specific inductive capacity

ε0 is the permittivity of free space.

K or εr is also called a dielectric constant of the medium in which the two charges are placed.

One coulomb of charge is that charge which when placed at rest in vacuum at a distance of one metre from an equal and similar stationary charge repels it and is repelled by it with a force of 9 x 109 newton.

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Find the equivalent resistance of this
circuit.
R₁
www
960 92
I
R₂
www
640 Ω
Reg?
Ra
W
180

Answers

Explanation:

1/R = 1/R1 + 1/ R2

1/R = 1/960 + 1/640

1/R = 5 / 1920

R = 384 ohm

So , Req = 384 + R3

Req = 384 + 180

Req = 564 ohm

[tex]\huge\red{A}\pink{N}\orange{S}{W}\blue{E}\green{R} [/tex]

Req = 564 ohm

If a violin string vibrates at 430 hz as its fundamental frequency, what are the frequencies of the first four harmonics?

Answers

If a violin string vibrates at 430 hz as its fundamental frequency,then the frequencies of the harmonics are 880, 1320, 1760

The frequency in physics is the number of waves passing a fixed location in a unit of time. It also indicates how many cycles or vibrations a body in periodic motion experiences in a given unit of time.

How frequently something occurs is what is meant by the word frequency. A person blinking their eyelids 47 times in a minute is an example of frequency. the quality or state of happening frequently.

Integer (whole-number) multiples of the fundamental frequency are used to define harmonics, which are voltages or currents that function at certain frequencies. This means that for a waveform with a fundamental frequency of 50 Hz, the second harmonic frequency would be 100 Hz (2 x 50 Hz), the third harmonic would be 150 Hz (3 x 50 Hz), etc.

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Which best explains the forces acting on the objects?

Objects W and X have balanced forces, and objects Y and Z have unbalanced forces.
Objects W and Y have balanced forces, and objects X and Z have unbalanced forces.
Objects X and Y have balanced forces, and objects W and Z have unbalanced forces.
Objects X and Z have balanced forces, and objects W and Y have unbalanced forces.

Answers

The option that best explains the forces acting on the objects is that option b. Objects W and Y have balanced forces, and objects X and Z have unbalanced forces.

How do you know if forces are balanced or unbalanced?

When the motion of an object is said to be altered, the forces are known to be in a sate that is seen as unbalanced.

Note that  Balanced forces are said to be one that are equal in size and also opposite in direction.

Hence, if forces are balanced, there is no alteration in motion and it is seen in cases if a person is pushed or pulled on an object that is seen from opposite directions but also has the same force.

Therefore, The option that best talks about the forces acting on the objects is that option b. Objects W and Y have balanced forces, and objects X and Z have unbalanced forces as it does better justice to it.

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What does an alpha particle consist of? one proton and two neutrons two protons and two neutrons two protons and one electron one proton and two electrons

Answers

They are helium nuclei, which consist of two protons and two neutrons. The net spin on an alpha particle is zero. They result from large, perilous atoms via a process called alpha decay.

What is helium nuclei?The nucleus of the helium atom also understood as the α-particle, includes two protons and two neutrons, encompassed by two electrons.Alpha particles are helium nuclei with two protons and two neutrons attached. The development of their high mass and an electrical charge is their inability to infiltrate as deep as other particles such as protons and electrons.Particle beams contain α (alpha)-particles, β (beta)-particles, neutron beams, etc. α-particles are helium middles consisting of two protons and two neutrons that have lived removed at high speed, while β-particles are electrons removed from a nucleus. Particle shafts also include neutron beams and proton beams.

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Answer:

A process in which a large nucleus splits into two or more parts is called ?

(A) nuclear fission

An alpha particle is made up of _____.

(C) two protons and two neutrons

Which statement best describes the type of radioactive decay shown in the model?

(D) The model shows alpha decay, which is a type of nuclear fission.

Is beta decay a form of nuclear fission?

Responses

(A) No, it is not because the mass number does not change.

Which statement correctly classifies gamma emission?

(D) Gamma emission is a type of radioactive decay, but it is not a fission reaction.

Explanation:

i just did the quick check, hope this helps.

Stellar nurseries, such as the orion nebula, contain hundreds or more fragmenting and contracting regions, as well as many protostars and stars. What condition would allow a protostar to become a stable star?.

Answers

The hydrogen fusion process will begin after the protostar reaches a temperature of 10 million degrees kelvin, and it will then turn into a stable star.

How does a protostar become a stable star?

The interstellar medium can sometimes be gathered into a large nebula, which is a cloud of gas and dust. A nebula can span a number of light years. These nebulae are where gas and dust can combine to produce stars. Until a star can combine hydrogen into helium, it cannot be considered a star. They are referred to as protostars before then. As gravity starts to gather the gases into a ball, a protostar is created. Accrution is the term for this procedure.

Gravitational energy starts to heat the gasses as gravity draws them into the ball's core, which causes the gasses to radiate radiation. Radiation initially just dissipates into space. However, much of the radiation is retained inside the protostar as it draws in stuff and becomes denser, which causes the protostar to heat up even more quickly.

The hydrogen fusion process will begin after the protostar reaches a temperature of 10 million degrees kelvin, and it will then turn into a star.

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When you have two of the same charges along a horizontal line, where is the electric field the greatest? is there ever a point where the field will be zero?

Answers

When you have two of the same charges along a horizontal line, The electrical field is the greatest the closest it is to the charges. And there will be a zero charge in between the two like charges.

Electric field can be considered as an electric property associated with each point in the space where a charge is present in any form. An electric field is also described as the electric force per unit charge.

The formula of electric field is given as;

E = F /Q

Where,

E is the electric field.

F is a force.

Q is the charge.

The electrical field is the greatest the closest it is to the charges because there will be high electric strength and electric field strength is greatest where the lines are closest together and weakest where lines are furthest apart.  Also , there will be a zero charge in between the two like charges.

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What is the half-life of an isotope if 125 g of a 500 g sample of the isotope remains after 3.0 years?

Answers

Answer:

125 / 500 = 1/4    of the sample left after 3.0 yrs

1/2 * 1/2 = 1/4        sample has decayed thru 2 half-lives

2 * HL = 3

1 Half-Life = 1.5 yrs

When charging a system with vapor refrigerant from a refrigerant cylinder the cylinder will become:_________

Answers

When charging a system with vapor refrigerant from a refrigerant cylinder the cylinder will become cold .

When refrigerant is added in the vapor state, the refrigerant cylinder will lose pressure as the vapor is pushed out of the cylinder.The volume of the refrigerant changes with the ambient air so the graduated cylinder must be calibrated before each use.

What is a refrigerant charging cylinder used for?

A cylinder used to transfer refrigerant from the transportation cylinder into the system during the charging process. It has several scales on the exterior that indicate various refrigerant charges.

What type of refrigerant can be added as a liquid or a vapor?

Blends like R410a or 404a must be added to a system as a liquid. Pure refrigerants like R22 can be added in liquid or vapor states.

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A transmission line strung 7.0 m above the ground carries a current of 500 A. What is the magnetic field on the ground directly below the wire

Answers

Answer:

Approximately [tex]143\; {\rm T}[/tex] assuming that this transmission line is straight and infinitely long.

Explanation:

Lookup the permeability of free space: [tex]\mu_{0} = 4\, \pi\; {\rm T \cdot m \cdot A^{-1}[/tex].

Consider an infinitely-long straight wire in empty space carrying a current of [tex]I[/tex]. At a distance of [tex]r[/tex] from this wire, the magnitude of the magnetic field from the wire would be:

[tex]\begin{aligned} B &= \frac{\mu_{0}\, I}{2\, \pi\, R}\end{aligned}[/tex].

In this question, it is given that [tex]I = 500\; {\rm A}[/tex]. At a distance of [tex]R = 7.0\; {\rm m}[/tex] from this wire, the magnitude of the magnetic field from this cable would be:

[tex]\begin{aligned} B &= \frac{\mu_{0}\, I}{2\, \pi\, R} \\ &= \frac{(4\, \pi \; {\rm T \cdot m \cdot A^{-1}}) \, (500\; {\rm A})}{(2\, \pi)\, (7.0\; {\rm m})} \\ &\approx 143\; {\rm T}\end{aligned}[/tex].

An fm radio station broadcasts at 98. 6 mhz. What is the wavelength of the radiowaves?.

Answers

The wavelength of the radio waves is 3.04 cm.

Calculation:

λf = c

λ = c/f

where,

λ = wavelength

c = speed of light

f = frequency

Given,

f = 98.6 MHz = 98.6 × 10⁶

c = 3 × 10⁸

To find,

λ =?

Put the values in the formula,

λ = c/f

λ = 3 × 10⁸/98.6 × 10⁶

  = 0.0304 × 10²  m

  = 3.04 cm

Therefore, the wavelength of the radio waves is 3.04 cm.

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The cells in the middle latitude atmospheric circulations on earth are called the__________?

Answers

The cells in the middle latitude atmospheric circulations on earth are called the ferrel, westerlies.

What is latitude atmosphere?

The high latitude is roughly defined as being above 60° magnetic latitude; the middle latitudes are between 50° and 60° magnetic latitude; and everything below 50° magnetic latitude is regarded to be in the low latitude category. However, the precise location of this barrier is unknown.

Wait, what? magnetic horizons? And what is that? In any case, we usually refer to magnetic latitudes rather than geographic latitudes when discussing aurora and the various latitudes. You can claim that you have a better chance of seeing aurora when you are at a high geographic latitude (near the north or south pole). The earth's magnetic poles do not exactly align with the geographic poles, which makes what is generally true about it somewhat misleading.

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Define resistance and describe what would happen to a light bulb if the voltage increased but the resistance stayed the same. (hint: look back in the lesson under the section title ""resistance"")

Answers

The light bulb would glow brighter.

What is Resistance?

a force that works against a body's direction of motion and seeks to stop or slow down motion, such as friction. a measure of how much a material prevents an electric current from flowing as a result of a voltage.

What is the law of resistance?

Resistance and Ohm's Law. According to Ohm's law, the resistance of the circuit and the current or energy travelling through the resistance are both exactly proportional to the voltage or potential difference between two places.

The current would grow since it is exactly proportionate to the voltage, increasing the light bulb's brilliance, or simply making it brighter.

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An electron is ejected from the cathode by a photon with an energy slightly greater than the work function of the cathode. How will the final kinetic energy of the electron upon reaching the anode compare to its initial potential energy immediately after it has been ejected?.

Answers

It will be approximately equal.

How will the final kinetic energy change?

We can infer that all of the energy in the electron is Potential energy (PE) because the energy provided by the photon is hardly enough to outweigh the work function.

It will gain kinetic energy (KE) as it advances in the direction of the anode because it is moving through an electric field. All of the PE will have been transformed to KE by the time it reaches the anode.

According to the question

K = hf - W

W = Work function

The energy of photons is comparable. After conversion, there was only a little amount of KE remaining.

Therefore, PE (W) essentially equals KE (K).

It will about be equal.

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What is the volume of a solution, in milliliters, that contains 1. 5 g lino3 and has a concentration of 0. 40 m?

Answers

The volume of a solution, in milliliters, that contains 1. 5 g lino3 and has a concentration of 0. 40 m will be 54.35 m L.

Molarity is defined as the moles of a solute per liters of a solution. Molarity is also known as the molar concentration of a solution.

Molarity = n / V

where

n = number of moles

V = volume of solution in l

Molar mass of [tex]LiNO_{3}[/tex] = M of Li + M of N + 3 * M of O

                                    = 7 + 14 + (3*16)

                                    = 69 g/ mole

since , M = n / V

           n = m / molar mass of  [tex]LiNO_{3}[/tex]

substituting the value of n

Molarity  = (m / molar mass of  [tex]LiNO_{3}[/tex]  ) / V

V = m / molar mass of  [tex]LiNO_{3}[/tex]  * Molarity

   = 1.5 / 69 * 0.40

   = 54.35 mL

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What is the maximum velocity (in m/s) of electrons ejected from a material by 85 nm photons, if they are bound to the material by 4. 66 ev?

Answers

The maximum velocity of electrons is  v = 3.20 × 10¹⁵ m/s

The wavelength of photons λ = 85 nm

W = 4.66 ev

What is photoelectric effect and how velocity of photoelectrons is calculated?

     The emission of electrons happened and absorbed through the electromagnetic radiation is said to be photoelectric effect.

Photoelectric cells, photodiodes works on the principle of photoelectric effect.

According to of photoelectric effect,

                          E = hν

        Here,  hc / λ = W + KE max

                    hc / λ =  W + 1/2 mv² max

               

                   v² =  sqrt of (( hc / λ - W) (2/m))

                   I cap denotes λ ,

substituting all the values,

 v = sqrt of ( (6.623 × 10⁻³⁴ Js ) ( 3 × 10⁸ m/s) / (85 nm) - 4.66ev) (2/  9.1× 10⁻³¹

   v = sqrt of ((1.987800 ×  10⁻²⁵ / 85 × 10 ⁹ ) - 4.66 ev ) ( 2.197 × 10³⁰)          

   v = sqrt of ((2.338588 × 10⁻³⁶) - 4.66 ev ) ( 2.197 × 10³⁰)3.2

   v = 3.20 × 10¹⁵ m/s

Thus, the maximum velocity is calculated as  v = 3.20 × 10¹⁵ m/s.

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A grating has 470 lines/mm. how many orders of the visible wavelength 538 nm can it produce in addition to the m = 0 order?

Answers

Three complete orders on each side of the m=0 order can be produced in addition to the m=0 order.

The ruling separation is d=1/(470mm-1)

[tex] = 2.1 \times 10 {}^{ - 3}mm [/tex]

Diffraction lines occurs at an angle θ such that dsin=mλ,when λ is the wavelength and m is an integer.

Notice that for a given order,the line associated with a long wavelength is produced at a greater angle than the line associated with shorter wavelength.

we take λ to be the longest wavelength in the visible spectrum (538nm) and find the greatest integer value of m such that θ is less than 90°.

That is,find the greater integer value of m for which mλ<d.

since,d/λ

[tex] = 538 \times 10 {}^{ - 9} m/2.1 \times 10 {}^{ - 6} [/tex]

There are three complete orders on each side of the m=0 order.

The second and third orders overlap.

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