Two planets, john and mary, are identical in density and temperature, but mary is larger in size (radius) than john. Mary will have more substantial atmosphere because mary is larger in size .
A substantial atmosphere is one dense enough to significantly affect the surface
Gravity is the force by which a planet or other body draws objects toward its center. The force of gravity keeps all of the planets in orbit around the sun.
The thickness of a planet's atmosphere depends on the planet's gravity and the temperature of the atmosphere. A planet with weaker gravity does not have as strong a hold on the molecules that make up its atmosphere as a planet with stronger gravity.
As the planet grows in size, its mass and therefore gravity increases, allowing it to capture not only the accumulated dust and rocks, but also the gas, which forms an atmosphere.
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Light of a given wavelength is used to illuminate the surface of a metal, however, no photoelectrons are emitted. in order to cause electrons to be ejected from the surface of this metal you should:_________
We will decrease the wavelength of light in order to cause electrons to be ejected from the surface of this metal.
We have a Light of a given wavelength that is used to illuminate the surface of a metal, however, no photoelectrons are emitted.
We have to find out what can we do in order to cause electrons to be ejected from the surface of this metal.
What is Photoelectric Effect ?The emission of electrons from the surface of the metal when the light of specific frequency (greater than the threshold frequency) falls over it is called photoelectric effect.
Light consists of photons. The energy associated with the photons is used to emit out the electrons from the surface of metal. We know that - Energy can neither be created nor be destroyed and it can only be transferred from one body to another. Hence, the energy of these moving photons is used to emit electrons from the metal surface. The energy associated with the photon is given by -
E = hμ
Where - μ is the frequency of light an h is Planck's constant.
Now, we can see that the energy of the photon is directly proportional to the frequency of light. The minimum frequency required to eject the electron from the metal surface is called Threshold frequency. Thus, we can emit the electron from the metal surface by using the light of frequency greater than threshold frequency.
Hence, we will increase the frequency of light in order to cause electrons to be ejected from the surface of this metal
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An electron moving at in a 1. 25-t magnetic field experiences a magnetic force of. what angle does the velocity of the electron make with the magnetic field? there are two answers
The angle the velocity of the electron make with the magnetic field is sin(∅) = 90° answer.
The equation F = qv X B may be damaged down into two elements, the significance and the path. The importance is given by F = qv B sin(∅),
Magnetic field = 1. 25-tesla
F = qv B sin(∅)
= sin(∅) = F/qv B
sin(∅) = qv X B/qv B
sin(∅) = 90° answer.
The most importance of the magnetic pressure appearing at the electron whilst its velocity v is perpendicular to B i.e magnetic discipline. The route of the force acting on the electron is the course the palm of the left hand faces. The path of the magnetic area, the direction of the transferring rate, and the route of the pressure on the particle are all perpendicular to each other.
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Metallic gold crystallizes in a face-centered cubic lattice, with one au atom per lattice point. if the edge length of the unit cell is found to be 408 pm, what is the metallic radius of au in pm?
The metallic radius (r) of au is 144.2pm
A face-centered cubic unit cell structure is made up of atoms arranged in a cube with six additional whole atoms placed in the centre of each cube face and a fraction of an atom at each of the cube's four corners. Eight additional unit cells share the atoms at the cube's corner.
Atoms in an FCC crystal are in contact along the unit cell's diagonal. 4r = √2 a, where r is the radius of an atom and a is the edge length of a unit cell.
Putting the values in the above expression,we get
r = √2×408 / 4
r = [tex]\frac{1.414*408}{4}[/tex]
r = [tex]\frac{576.9}{4}[/tex]
r = 144.2 pm
Therefore, The metallic radius (r) of au is 144.2pm
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A spring has a spring constant k = 8. 75 n/m. if the spring is displaced 0. 150 m from its equalibirum position. what is the force that the spring exerts?
The force that the spring exerts is 1.31 N.
What is Spring force?The displacement (compression or expansion) and force constant of the specific spring determine the spring's force. It always takes action to get mass back to where it should be for equilibrium.The force applied to the spring and the energy it has stored are shown in the formulas below:[tex]E_{stored} =\frac{1}{2} kx^{2}[/tex]
F = kx
Where,
x = displacement in the spring
k = spring force constant
Calculation of spring force:Given,
k = 8.75 n/m
x = 0.150 m
Force exerted by the spring, F = kx
putting the values,
F = 8.75 x 0.150
= 1.3125 N
Hence, the force that the spring exerts is 1.31 N.
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If he were able to maintain this constant rate of acceleration, what would have been his speed as he finished the race?
a) 4.8 m/s² his average acceleration during the first 2.5 s
b) 15 m distance he cover during the first 2.5 seconds.
c) 31 m/s his speed as he finished the race.
(a) How to calculate the Average Acceleration ?Average acceleration is calculated by using Newtons first law of motion
v = u + at
where
u is initial velocity
v is final velocity
a is constant acceleration
t is time
Given u = 0m/s , v = 12 m/s and t = 2.5 sec
Therefore average acceleration is given by
[tex]a=\frac{v}{t}[/tex]
[tex]a=\frac{12}{2.5}[/tex]
a = 4.8 m/sec²
b) Here we will use newtons second law of motion
[tex]s=ut+\frac{1}{2}at^{2}[/tex]
On substituting value we get
s = 15m
c) Here we will use newtons third law of motion
v² = u² + 2as
Here u = 0 , a = 4.8 m/s² and s = 100 m
Therefore
v² = 960
v = 31 m/s
Disclaimer: the question was given incomplete in the portal. Here is the complete question.
Question: Usain Bolt's 100m sprint Runner set the world record for the100 meter sprint during the 2009World Championships in Berlin with a time of 9.58 s, reaching a top speed of 12 m/s in about 2.5 s.
a. What was his average acceleration during the first 2.5 s?
b. What distance did he cover during the first 2.5 seconds, assuming his acceleration was constant?
c. If he were able to maintain this constant rate of acceleration, what would have been his speed as he finished the race?
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To determine whether a celestial body is approaching or receding from earth, astronomers employ?
To determine whether a celestial body is approaching or receding from Earth, astronomers employ The Doppler principle.
There is a Doppler effect for both light and sound.
For instance, astronomers regularly measure the amount to which a star or galaxy's light is "stretched" towards the lower frequency, red region of the spectrum to calculate how quickly the object is travelling away from us.
A wave's frequency changes in response to an observer moving in respect to the wave source, which is known as the Doppler effect or Doppler shift.
The Doppler effect results from the fact that as the wave source moves in the direction of the observer, the crest of each succeeding wave emerges from a location that is closer to the observer than the crest of the previous wave.
As a result, each wave travels to the observer slightly faster than the one before it. As a result, the interval between successive wave crests arriving at the observer is shorter, increasing the frequency.
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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
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.To learn more about helium nuclei, refer to:
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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.
Wolfgang pauli hypothesized an exclusion principle. This principle says two electrons in an atom cannot have the same what?.
No two electrons in an atom or molecule may have the same four electronic quantum numbers, according to the Pauli Exclusion Principle. Only two electrons can fit into an orbital at a time, hence they must have opposing spins.
What is Pauli's exclusion principle ?According to Pauli's Exclusion Principle, no two electrons in the same atom can have values for all four of their quantum numbers that are exactly the same. In other words, two electrons in the same orbital must have opposing spins and no more than two electrons can occupy the same orbital.
The reason it is known as the exclusion principle is because it states that all other electrons in an atom are excluded if one electron in the atom has the same specific values for all four quantum numbers.Learn more about Pauli's exclusion principle here:
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At what rate would the current in a 100-mh inductor have to change to induce an emf of 1000 v?
The current must change at a rate of [tex]10^{4}[/tex] A/sec to induce an emf of 1000 volts.
We have a inductor of inductance 100 millihenry.
We have to calculate at what rate the current in the inductor have to change to induce an emf of 1000 Volts.
What is the faraday's law of induced voltage?According to the faraday's law of induced voltage, the voltage induced in the conductor present in the time changing magnetic field is directly proportional to the negative of the rate of change of magnetic flux passing through it per unit time. Mathematically -
ε = [tex]- N\frac{d\phi}{dt}[/tex]
Where -
ε is the induced voltage
N is the number of turns
[tex]\frac{d\phi}{dt}[/tex] represents the rate of change of magnetic flux
Now, in the question it is given that -
L = 100 mH = 0.1 H
ε = 1000 Volts
Now - the voltage across the inductor is given by :
[tex]V = L \frac{di}{dt}[/tex]
[tex]\frac{di}{dt} = \frac{V}{L} = \frac{1000}{0.1} = 10^{4}[/tex] A/sec
Hence, the current must change at a rate of [tex]10^{4}[/tex] A/sec to induce an emf of 1000 volts.
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The flow of electricity can be compared of water in
The flow of electricity can be compared of water in the pipes because both water and electricity moves in the channel.
How we compare the flow of electricity to water?Water flowing in pipes is like flowing of electricity in a circuit. A battery is like a pump from where electricity comes and moves in the circuit. Electrons flowing through wires are like water molecules flowing through pipes. So in comparison between water and electricity, both water and electricity are similar to each other in flowing and movement.
So we can conclude that the flow of electricity can be compared of water in the pipes because both water and electricity moves in the channel.
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Fleas have remarkable jumping ability. a 0.50 mg flea, jumping straight up, would reach a height of 40 cm if there were no air resistance. in reality, air resistance limits the height to 20 cm.
a. what is the flea's kinetic energy as it leaves the ground?
b. at its highest point, what fraction of the initial kinetic energy has been converted to potential energy?
The theorem of conservation of mechanical energy is used
a) The initial kinetic energy is, K = 1.33 10⁻⁶ J
b) The fraction of kinetic energy converted to potential energy, U/K = 1.96
Calculation:The total mechanical energy which is defined as the sum of kinetic energy plus potential energies, is given as
E = K + U
To find the speed of the flea jump when there is no friction,
Initial point
E₁ = K = ½ m v²
Final point.
At the highest height h = 30 cm = 0.30 m because there is no friction
E₂ = U = mgh
Energy is conserved
E₁ = E₂
½ mv² = mgh
v = [tex]\sqrt{2gh}[/tex]
v = [tex]\sqrt{2(10)(0.4)}[/tex]
v = [tex]\sqrt{4}[/tex] m/s
v = 2 m/s
A) Now we have to find the initial kinetic energy
K = ½ m v²
K = ½ (0.5 × 10⁻⁶) (2)²
K = 1 × 10⁻⁶ J
B) Now we have to find the fraction of energy lost if we take into account the friction of the air
The initial kinetic energy
K = ½ m v²
Now we have to look for the potential energy until h’= 20 cm = 0.20 m
U = mgh'
The fraction of energy lost,
U/K = mgh'/½ mv²
= 2gh'/v²
= 2 × 9.8 × 0.2/ 2
= 1.96
Therefore,
a) The initial kinetic energy is, K = 1 × 10⁻⁶ J
b) The fraction of kinetic energy converted to potential energy, U/K = 1.96
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If the resistance in a circuit connected to a constant current is halved, how is the voltage in the circuit affected?.
The voltage is reduced by a factor of 2.
What is resistance?
Resistance is a proportion of the opposition to flow stream in an electrical circuit. Opposition is estimated in ohms, represented by the Greek letter omega (Ω). Ohms are named after Georg Simon Ohm (1784-1854), a German physicist who concentrated on the connection between voltage, current and resistance.The equation to compute the obstruction utilizing Ohm's Law is given as keeps:R = V I.
where,
R is the resistance of the resistor R in ohms (Ω)
V is the voltage drop in the resistor in volts.
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A car moving 18.2 m/s starts to coast up a frictionless 10.0 degree hill. how far does it roll before coming to a stop
The distance covered by the car before it stops is 98.58 m.
Calculation:Force acting on the car will be
ma = -mg sinθ
where,
m = mass of the car
a = acceleration of the car
g = acceleration due to gravity
θ = angle of inclination
Given,
θ = 10°
Put the values in the above equation,
ma = -mg sinθ
a = -g sin 10°
a = -10 (0.173)
a = -1.73 m/s²
We know the initial velocity is 18.2m/s and when the car comes to a stop the final velocity becomes zero.
u = 18.2 m/s
v= 0 m/s
Using one of the kinematics equations,
v² - u² = 2as
0 - (18.2)² = 2 (-1.73) (s)
331.24 = 3.36 (s)
s = 98.58 m
Hence, the distance covered by the car before it stops is 98.58 m.
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The lift on a spinning circular cylinder in a freestream with a velocity of 50m/s and at standard sea level conditions is 10n/m of span. calculate the circulation around the cylinder
The circulation around the cylinder is 0.163Js/kg.
To find the answer, we have to know more about the stream flow.
How to find the circulation around the cylinder?We have,[tex]v=50m/s\\L=10N/m\\d=1.23kg/m^3[/tex] , where d is the density at the sea level.
We have the expression for lift per unit circulation as,[tex]L=dvc\\[/tex]
Thus, the circulation around the cylinder is,[tex]c=\frac{L}{dv} =\frac{10}{1.23*50}=0.163Js/kg[/tex]
Thus, we can conclude that, the circulation around the cylinder is 0.163Js/kg.
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What's true about the elliptical path that the planets follow around the sun?
Answer:
well, it is not a solid path and thats a teeny tiny fact
Give one example of a thermodynamic cycle that does not account for the carnot efficiency.
Thermo-Electrochemical converter (UTEC) is a thermodynamic cycle that does not account for the Carnot Efficiency.
What is Thermo-Electrochemical converter ?Thermo-Electrochemical converter converts potential energy difference during oxidation and reduction of hydrogen in two cell structure to heat energy.
It uses Ericsson cycle which has less efficiency compared to Carnot cycle efficiency. It converts heat into electrical energy in a closed system. There is no external input and output.This means there is no mechanical work to be done and also there will not be any exhaust. So, Carnot efficiency is not accounted in this cycle. The other options like turbine and engine accounts for Carnot efficiency.Learn more about Thermo-Electrochemical converter here:
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Light has been measured as traveling at 3×108 m/s in a vacuum. Which of the following also travels at the speed of light, and why?
A
Ultrasound waves in a vacuum travel at the speed of light because there is no matter to reduce their speed.
B
Radio waves in a vacuum travel at the speed of light because they are a type of electromagnetic radiation like light.
C
Electrons in a current carrying wire travel at the speed of light because they have very little mass.
D
Gas particles at the center of an atomic explosion travel at the speed of light because the explosion creates an extreme outward force.
Radio waves in a vacuum travel at the speed of light because they are a type of electromagnetic radiation like a light has been measured as traveling at 3×10^8 m/s in a vacuum.
Charged particles that are accelerating, like time-varying electric currents, are what produce radio waves. Radio and television signals are transmitted using radio waves, and microwaves used in radar and microwave ovens are also radio waves. Radio waves are emitted by a lot of celestial bodies, including pulsars. High RF exposure levels have the potential to heat biological tissue and raise body temperature. The body's inability to handle or remove the extra heat that could be generated by high RF exposure in humans could result in tissue damage.
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how to solve this? help
The resistance value of the sliding rheostat is 15 ohms.
What is resistance?
Resistance is a measure of the opposition to current flow in an electrical circuit. Resistance is measured in ohms.
Total resistance of the circuitThe total resistance of the circuit can be calculated from the total current in the circuit and the total voltage in the circuit.
R = V/I
R = 50 /2
R = 25 ohms
Resistance value of the sliding rheostatThe resistance value of the sliding rheostat is calculated as follows;
R(rheostat) = 25 ohms - 10 ohms = 15 ohms
Thus, the resistance value of the sliding rheostat is 15 ohms.
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Electrolysis can be used to purify silver. What mass of silver would plate onto the pure electrode if a current of 6. 8 a flowed through the cell for 72 minutes?
32.88grams of (Ag) silver would plate onto the pure electrode if a current of 6. 8A flowed through the cell for 72 minutes.
Silver can be electroplated at the cathode of an electrolysis cell by the half-reaction:
Ag+(aq)+e→Ag(s).
By Using the equation
Q= I×t, where Q = charge
I = current = 6.8 A
t= time in seconds= 72×60=4320s
So,
Q=6.8×4320
Q = 29,376C
We see that 1 mole of electrons produces 1 mole of Ag from the half reaction.
1mole of electrons= 96,500C
xmoles of electrons= 29,376C
Cross multiplying;
29,376= 96,500 × x
Now , dividing both sides of the by 96,500
29,376/96,500=x
0.3044 moles of electrons will produce
0.3044×108 = 32.88grams of Ag
Therefore, 32.88grams of (Ag) silver would plate onto the pure electrode if a current of 6. 8A flowed through the cell for 72 minutes.
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An object having a fixed emissivity of 0. 725 radiates heat at a rate of 10 w when it is at an absolute temperature t. If its temperature is doubled to 2t, at what rate will it now radiate?.
If the temperature is doubled to 2t, the rate at which it will now radiate is 160 W.
What is meant by emissivity?The ability of a substance to reflect heat radiation from its surface is measured by its emissivity. Thermal radiation is a type of electromagnetic radiation that includes infrared radiation, which the human eye cannot perceive, as well as visible radiation (light). According to the Stefan-Boltzmann law, emissivity is the quantitative comparison between the thermal radiation of a surface and that of an ideal black surface at a given temperature. Between 0 and 1 is the ratio's range.What is energy radiation?The emissivity of a substance is a measurement of how well it reflects heat radiation from its surface. Two elements that affect power dissipation in the form of radiation are the material's surface emissivity and the temperature difference between the chip surface and the surrounding air.To learn more about emissivity visit:
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The central pitch around which a scale and its associated harmonies is built is called _______.
The central pitch around which a scale and its associated harmonies is built is called Tonic.
What is tonic?As the first and last notes of the scale used to compose a piece of music, the tonic pitch serves as both the focal point of the composing process and the pitch designation for the key.What is a wave? the regular, systematic spread of disturbances from one location to another. The waves that travel on water's surface are the most well-known, but waves also exist in sound, light, and the movement of subatomic particles. The disturbance periodically oscillates with a set frequency and wavelength in the simplest waves.Types of waves:Transverse and longitudinal waves are the two types of waves. While longitudinal waves are similar to those of sound, consisting of alternating compressions and rarefactions in a medium. Transverse waves are like those on water, with their surface moving up and down.To learn more about tonic visit:
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An electron is traveling at 0. 85c. what is its mass? (the rest mass is 9. 11 × 10-31 kg. )
The mass of the electron is [tex]1.72\times 10^{-30}[/tex] Kg.
How can we calculate the mass of the electron?To calculate the mass of the electron we are using the formula,
[tex]m=\frac{m_{0} }{\sqrt{1-\frac{v^{2} }{c^{2} } } }[/tex]
Here we are given,
[tex]m_0[/tex]=The rest mass of an electron = [tex]9. 11 \times 10^{-31}[/tex] kg.
v= The velocity of electron = 0. 85c.
c= The velocity of light = c. (c=[tex]3\times 10^8[/tex] m/s)
We have to found the mass of an electron = m Kg.
Now we substitute the known values, we found that,
[tex]m=\frac{9. 11 \times 10^{-31} }{\sqrt{1-\frac{(0.85c)^{2} }{c^{2} } } }[/tex]
Or,[tex]m=\frac{9. 11 \times 10^{-31} }{\sqrt{1-(\frac{0.85c}{c})^2 } }[/tex]
Or,[tex]m=\frac{9. 11 \times 10^{-31} }{\sqrt{1-({0.85})^2 } }[/tex]
Or, [tex]m=1.72\times 10^{-30}[/tex] Kg.
From the above calculation we can conclude that, The mass of the electron is [tex]1.72\times 10^{-30}[/tex] Kg.
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A process with a negative change in enthalpy and a negative change in entropy will generally be:________
A process with a negative change in enthalpy and a negative change in entropy will generally be: spontaneous.
Gibbs free energy:Since the Gibbs free energy is a parameter that tells us whether a chemical reaction is spontaneous (Gibbs free energy less than 0) or nonspontaneous (Gibbs free energy greater than 0) in this situation, we can describe it mathematically as:
ΔG = ΔH - TΔS
Therefore, any process with a negative change in enthalpy and a positive change in entropy will be spontaneous. If the enthalpy and the entropy are both negative, the subtraction becomes always negative, for which the Gibbs free energy is also negative.
One of the most crucial thermodynamic functions for the characterization of a system is the Gibbs free energy. It influences results like the voltage of an electrochemical cell and the equilibrium constant for a reversible reaction, among others.
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When ever nitrogen is used to pressurize or blow debris out of the system the nitrogen?
What is the energy (in ev) of an x-ray photon that has a wavelength of 2. 4 nm ?
_______________
λ=2,4 nm = 2,4·10⁻⁹ m
c=3·10⁸ m/s
h=6,63·10⁻³⁴ J·s = 4,14·10⁻¹⁵ eV·s
_______________
E - ?
_______________
[tex]\displaystyle \boldsymbol{E}=h\nu =h \frac{c}{\lambda} =4,14\cdot 10^{-15} \; eV\cdot s\cdot \; \frac{3\cdot 10^8\; m/s}{2,4\cdot 10^{-9}\; m} =517,5\; eV\approx \boldsymbol{518\; eV}[/tex]
What is the name given to the portion of the electrocardiogram between two waves?.
Segment
The space between two waves is known as a segment in an ECG. Beginning at the end of the P wave and ending at the beginning of the QRS complex is the PR segment. Beginning at the end of the QRS wave and ending at the beginning of the T wave is the ST segment.
What is ECG ?An electrocardiogram (ECG) is a quick test that can be used to examine the electrical activity and rhythm of your heart. The electrical signals that your heart beats out each time it beats are picked up by sensors that are affixed to your skin.
A test that captures the electrical activity of the heart is called an electrocardiogram (ECG). The ECG shows what is occurring in various heart regions and aids in identifying any issues with heart rate or rhythm.Learn more about ECG here:
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If you wanted to see a star behind an interstellar dust cloud, what "colour" of light should you look for?
RED colour of light you should look for if you wanted to see a star behind the interstellar cloud.
In our galaxy and other galaxies, an interstellar cloud is often a buildup of gas, plasma, and dust. In other words, an interstellar cloud is a portion of the interstellar medium (ISM), the matter and radiation that is present in the space between star systems in a galaxy, that is denser than typical.
Interstellar dust has an extremely saturated orange to brownish-red tint that turns saturated red when there is a modest quantity of hydrogen emission.
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Abu Dhabi classical FM Radio station Broadcasts on a frequency of 91.6 MHz calculate the wavelength of the electromagnetic radiation emitted by the transmitter. Which part of the electromagnetic spectrum does it belongs?
Answer:
C=F×W
so, W=C/F
Explanation:
frequency=F
wavelength=W
speed of light =C in that medium
Block 2 has four times the mass of Block 1. Assume a frictionless pulley and that both the rope and pulley are massless. Use g=9.8 m/s2.
Calculate the magnitude of acceleration of the blocks.
The magnitude of acceleration of the block is 5.88 m/s²
Block and tackle system of pulleysPulley are often used in construction sites to raise or lower heavy load. Pulley system is one of the most widely used type of machine. and Block and tackle system of pulleys is the practical system of pulleys in which one or more pulleys are mounted on the same axle, with one continuous rope passing all round the pulleys.
Given that Block 2 has four times the mass of Block 1. Assume a frictionless pulley and that both the rope and pulley are massless and g = 9.8 m/s2.
That means M2 = 4M1
The acceleration will be toward the M1
To calculate the magnitude of acceleration of the blocks, we will consider the following
T - [tex]m_{1}[/tex]g = [tex]m_{1}[/tex]a ...... (1)
T - [tex]m_{2}[/tex]g = -[tex]m_{2}[/tex]a ..... (2)
Where
T = tension in the rope which is the same g = acceleration due to gravity[tex]m_{1}[/tex] = mass of the block 1[tex]m_{2}[/tex] = mass of the bloc 2a = accelerationMinus equation 2 from equation 1
( [tex]m_{1}[/tex] + [tex]m_{2}[/tex] )a = ( [tex]m_{2}[/tex] - [tex]m_{1}[/tex])g
But [tex]m_{2}[/tex] = 4[tex]m_{1}[/tex]
Substitute in the equation above.
([tex]m_{1}[/tex] + 4[tex]m_{1}[/tex])a = (4[tex]m_{1}[/tex] - [tex]m_{1}[/tex])g
5[tex]m_{1}[/tex]a = 3[tex]m_{1}[/tex]g
[tex]m_{1}[/tex] will cancel out
5a = 3 x 9.8
a = 29.4/5
a = 5.88 m/s²
Therefore, the magnitude of acceleration of the block is 5.88 m/s²
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Find the first three harmonics of a string of linear mass density 2. 00 g/m and length 0. 600 m when the tension in it is 50. 0 n.
The first three harmonics of the string are 131.8 Hz, 263.6 Hz and 395.4 Hz.
Velocity of the wave
The velocity of the wave is calculated as follows;
v = √T/μ
where;
T is tensionμ is mass per unit length = 2 g/m = 0.002 kg/mv = √(50/0.002)
v = 158.1 m/s
First harmonic or fundamental frequency of the wavef₀ = v/λ
where;
λ is the wavelength = 2Lf₀ = v/2L
f₀ = 158.1/(2 x 0.6)
f₀ = 131.8 Hz
Second harmonic of the wavef₁ = 2f₀
f₁ = 2(131.8 Hz)
f₁ = 263.6 Hz
Third harmonic of the wavef₂ = 3f₀
f₂ = 3(131.8 Hz)
f₂ = 395.4 Hz
Thus, the first three harmonics of the string are 131.8 Hz, 263.6 Hz and 395.4 Hz.
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