1.47$ eV is the maximum kinetic energy of the photoelectrons when the light of wavelength 300.0 nm falls on the metal surface.
The maximum kinetic energy of the photoelectrons is directly proportional to the frequency of the incident light. The frequency of light with a wavelength of 400 nm is given by the formula
$f=c/\lambda$, where $c$ is the speed of light and $\lambda$ is the wavelength of the light.Plugging in the values, we get $f=3.00 \times 10^8 \text{ m/s}/400\text{ nm}=7.50 \times 10^{14}$ Hz.
The maximum kinetic energy of the photoelectrons when the light of this frequency falls on the metal surface is 1.10 eV.
The maximum kinetic energy when light with a frequency of
$f'=3.00 \times 10^8 \text{ m/s}/300.0\text{ nm}=10^{15}$ Hzfalls on the metal surface is therefore given by the formula
$E'=E\frac{f'}{f}=1.10\text{ eV}\frac{10^{15}\text{ Hz}}{7.50 \times 10^{14}\text{ Hz}}=1.47$ eV.Note: This assumes that the other conditions (such as the intensity of the light and the material of the metal surface) are the same in both cases. If these conditions change, the maximum kinetic energy of the photoelectrons will also change.
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an athlete at the gym holds a 3.0 kg steel ball in his hand. his bio arm is 70 cm long and has a mass of 4.0 kg. what is the magni- tude of the torque about his shoulder if he holds his arm a. straight out to his side, parallel to the floor?
The magnitude of the torque about an athlete shoulder is 48.02N-m if he is holding steel ball in his hand.
We know that torque is defined as the cross product of distance of point from applied point to the force applied by the external source at that point, in other words
Torque=distance × Force
=>τ = r × F
Total mass hold by the athlete is = 3+4=7kg.
Now, we need to focus on the force acting on an athlete. So we are assuming an athlete is standing on the surface, so acceleration due to gravity have some role to exert some amount of force on athlete.
Therefore, Force=mg
=>F=7×9.8
=>F=68.6Kg-m/sec²
Now, distance of force from applied point is 70cm=0.7m
Therefore, Torque=0.7×68.6
=>Torque= 48.02N-m
Hence, value of Torque is 48.02N-m.
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Use the information from the graph to answer the
question.
What is the acceleration of the object?
The magnitude of the velocity change increases with lengthier acceleration. When acceleration is constant, the change in velocity is directly proportional to time.
What change in acceleration due to linear velocity?The rate at which the velocity of any moving object changes is measured by acceleration. The velocity change divided by the time represents the acceleration. Both the magnitude and the direction of acceleration are present.
Therefore, An object's motion can be depicted by a velocity-time (or speed-time) graph if it moves in a straight line. The line's gradient is equal to the object's acceleration.
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a tall tree is growing across a river from you. you would like to know the distance between yourself and the tree,as well as its height, but are unable to make the measurements directly. however, by using a mirror to form an image of the tree and then measuring the image distance and the image height, you can calculate the distance to the tree as well as its height. suppose that this mirror produces an image of the sun, and the image is 0.8501 m from the mirror. the same mirror is then used to produce an image of the tree. the image of the tree is 0.9605 m from the mirror. (a) how far away is the tree? (b) the image height of the tree has a magnitude of o. 14 m. how tall is the tree?
a)how far the tree was found to be 0.9605 m
b) the height of the tree was found to be 0.14m
What exactly is object distance?
Object Distance, denoted by s, is the distance between an object and an optical element.
What are the qualities of a mirror image?
• The image obtained is fictitious.
•The picture is flipped laterally.
• The picture is upright.
• The picture has the same dimensions as the thing.
• The distance between the image acquired from the mirror and the item gained from the mirror is the same.
As a result, the distance between the tree and the mirror is the same as the distance between the picture and the mirror, i.e. 0.9605 m, and the height of the tree is the same as the height of the image, which is 0.14 m.
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a)how far the tree was found to be 0.9605 m
b) the height of the tree was found to be 0.14m
What exactly is object distance?
Object Distance, denoted by s, is the distance between an object and an optical element.
What are the qualities of a mirror image?
• The image obtained is fictitious.
•The picture is flipped laterally.
• The picture is upright.
• The picture has the same dimensions as the thing.• The distance between the image acquired from the mirror and the item gained from the mirror is the same?
As a result, the distance between the tree and the mirror is the same as the distance between the picture and the mirror, i.e. 0.9605 m, and the height of the tree is the same as the height of the image, which is 0.14 m.
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What is the change in internal energy AU for a reaction that gives off 65 J of heat and does 38 J of work?
The change in internal energy will be 27J when heat is released.
Every time a process occurs, it is usually accompanied by an energy shift. Energy comes in many forms, such as heat, light, and work.
The generation or absorption of energy in various processes dictates that each substance must be associated with a certain amount of energy. Its actual value depends on the nature of the material and the conditions of temperature, pressure, volume and composition.
The sum of various types of energy associated with atoms and molecules, such as electronic energy (Ee), nuclear energy (En), chemical bond energy (Ec), potential energy (Ep), and kinetic energy (Ek). Sum of translational energy (Et), vibrational state energy (Ev), and rotational energy (Er).
Represented by the symbol U or E.
U or E = Ee + En + Ec + Ep + Ek
The energy stored in matter in this way is called internal energy.
U=65-38=27J
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order the structures that a pressure wave passes through in the cochlea, beginning from the oval window and ending at the round window.
The cochlea is the organ responsible for hearing, and it is composed of several interconnected structures through which a pressure wave passes. Beginning at the oval window, the pressure wave then moves through:
Scala vestibuliReissner's membrane Scala tympaniBasilar membraneAnd finally exits through the round window.
The Structures of the Cochlea: A Journey from the Oval Window to the Round WindowOrder the structures that a pressure wave passes through in the cochlea:
Oval windowScala vestibuliReissner's membraneScala tympaniBasilar membraneRound windowThis chain of structures creates a pathway that allows the pressure wave to pass through the cochlea, converting sound waves into signals that are then sent to the brain and interpreted as sound.
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A piece of clay was thrown so that it has a momentum of 34 kg·m/s. It hits a 0.25 kg motionless cart and sticks to it. What is the momentum of the clay and cart combined? (ignore friction)
The momentum of the clay and the cart is 34 kgm/s.
What is momentum?Momentum can be defined as the product of mass and velocity.
To calculate the momentum of the clay and the cart, we use the formula below.
Formula:
M' = M+mu..............................Equation 1Where:
M' = Momentum of the clay and the cartM = Momentum of the claym = Mass of the cartu = Initial velocity of the cartFrom the question,
Given:
M = 34 kgm/sm = 0.25 kgu = 0 m/s (motionless)Substitute these values into equation 1
M' = 34+(0.25×0)M' = 34 kgm/sHence, their momentum is 34 kgm/s.
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. unpolarized light is incident upon a smooth surface. when light reflected from this surface is totally polarized, the incident light angle is named the
Brewster's angle
When unpolarized light is incident at Brewster's angle on a smooth glass surface, the reflected light is totally polarized while the refracted light is partially polarized
Polarization:
Polarization is a assets making use of to transverse waves that specifies the geometrical orientation of the oscillations. In a transverse wave, the route of the oscillation is perpendicular to the direction of motion of the wave.In contrast, for longitudinal waves, such as sound waves in liquids or gases, the particles are always displaced in the direction of propagation during oscillation, so these waves have no polarization. Transverse waves that indicate polarization include electromagnetic waves such as light and radio waves, gravitational waves, and sound waves in solids (transverse waves).
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The total momentum of a system of two moving identical bodies is zero. What should be true about the velocities of the bodies?.
The momentum of system is zero because velocities of the bodies may be equal to zero or may be be equal in magnitude but opposite in direction.
We know very well that momentum of body is given by the product of mass of that body with the velocity of that body, or in other words
Momentum=mass × velocity
=>p=m × v
Since, we are given that total momentum of the system is zero. In this universe every object has some mass ,so mass never be zero and never be negative. Now, talking about the velocity of the body. If velocity of all bodies is zero, in that total momentum of the system remains zero. So, this will be possible.
Now, there is one more possibility in the system two bodies have same velocity in magnitude but their direction of propagation is opposite to each other. In that case also their velocity cancel each other, due to that momentum remain as it is zero. So, this is one of possibility.
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Nancy is knitting a scarf. It takes her 0. 2 of an hour to knit each inch of the scarf. She wants the length of the scarf to be 60 inches. How many hours will it take her to make the scarf?.
Nancy is hard at work on a scarf. She spends twenty seconds on every inch of the scarf she knits. Her desired scarf length is sixty inches. Given, It takes 0.2 of an hour to knit a single inch of the scarf. Here, 0.2 of an hour refers to 12 minutes. Therefore, It takes 12 minutes to knit an inch of a scarf.
Since Nancy takes 12 mins to knit an inch of a scarf, then for 60 inches, it would be,
1 inch -> 12 minutes
60 inches -> 12 * 60 minutes = 720 mins to knit 60 inches of a scarf.
Now, convert the minutes into hours,
720 mins -> 720 / 60 = 12 hours.
Therefore, it takes 12 hours to knit 60 inches of a scarf.
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The specific gravity of an material is defined as the ratio of the density of the material to the density of water. The specific gravity of ice is 0.917, whereas that of seawater is 1.025.
What fraction of an iceberg is above the surface of the water?
\frac{V_{above}}{V_{total}} = ____________
The fraction of the iceberg that is above the surface of the water is 8.3 %.
The specific gravity of any material is defined as the ratio of the density of the material to the density of water.
Mathematically, the formula for specific gravity of materials =
= S.G = density of the material / density of water
Specific gravity of the iceberg = 0.917
Specific gravity of the seawater = 1.025
The fraction of the iceberg submerged in the seawater =
= 0.917 = 0.917 x 100 %
= 91.7 %
The fraction of the iceberg that is above the surface of the water =
= 1 - 0.917
= 0.083
= 0.083 x 100 %
= 8.3 %
Thus, the fraction of the iceberg submerged in the water is a function of the specific gravity of the iceberg.
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while on mars, you drop your martian detector while climbing out of the rover. if you're standing on a platform 8 meters from the ground and the acceleration due to gravity on mars is -3.8 m/s^2, how long does it take for the martian detector to hit the ground? report an error 1.3 s 9.9 s 2.1 s 13 s 21 s
It take 1.45s to the Martian detector to hit the ground.
We are know that,
Acceleration = a = - 3.8 m/s²
Distance = r = 8m
Final velocity = v = 0 (The rock's velocity is zero at its maximum height.)
Time = ?
Thus to calculate the hitting time of the Mars ground we can use the formula,
acceleration = change in velocity / time
First of all we have to calculate the initial velocity (u) of the Martian i.e.
a = u²/r
u² = a.r
u² = (-3.8m/s²)× 8m
u² = -30.4m²/s²
u = - 5.51 m/s
Putting the value of initial velocity in the above equation we can get the hitting time,
-3.8 m/s² = 0 - (5.51m/s)/t
t = (-5.51m/s)/(-3.8m/s²)
t = 1.45s
The Martian detector hits the ground in 1.45 seconds.
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Which phenomenon is shown in this diagram?
Earth's _________
Answer:
outer layer
Explanation:
a personal foul occurs when a player has unsportsmanlike conduct, illegal entry or excessive timeouts.
a. true
b. false
Answer:
true
Explanation:
basic sports knowlegde
Starting from rest, an object rolls freely down a 10. -meter long incline in 2. 0 seconds. The acceleration of the object is.
The acceleration of this object is 5 m/s².
Initial velocity = 0 m/s (since the object starts from rest).
Distance = 10 meters
Time = 2 seconds.
To find the acceleration of the object, we would use the second equation of motion:
Mathematically, the second equation of motion is given by the formula;
= s = ut + (1/2)at²
Where;
S represents the distance covered.
u is the initial velocity.
a represents the acceleration.
t is the time measured in seconds.
Substituting the parameters into the formula, we have;
= 10 = 0 + (1/2)a(2)²
= a = 10/2
= a = 5 m/s²
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1. suppose a spaceship which is traveling at c/2 passes a light source. what is the velocity of light from the source in the reference frame of the spaceship?
The speed of light from the source in the spacecraft's frame of reference is given by the formula Ux = Ux+v/C2+2Uxv/C2. The pace at which an object's position changes in relation to a frame of reference.
And is a result of time. An object's speed and direction of motion are specified by its velocity. A crucial idea in kinematics is velocity. Two different categories of frame of reference are as follows: An object that is fixed or moving at a constant speed is said to have an inertial frame of reference. The First Law of Motion of Newton is directly relevant in this frame. The frame of reference refers to the context in which an observer is placed when recording data.
Ux = Ux+v/C^2+Uxv/C^2
here, c =c/2
Ux = Ux+v/C^2+2Uxv/C^2
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the range of visible light wavelengths is between 3.9 x 10 -7 m and 7.0 x 10 -7 m. what is the corresponding range of frequencies for visible light?
The range of visible light is from 7.69 * 10¹⁴ Hz.
Frequency is defined as the number of complete cycles a wave can complete in one second. We know that, the SI unit of frequency is Hertz (Hz).
We know the relation between speed of light, wavelength and frequency as
v = f * λ ----(1)
where, v is the speed of light in air
f is the frequency of visible light
λ is the wavelength of visible light
Making ' f ' as subject in the above equation as,
f = v / λ ----(2)
We know that speed of light in air is 3 * 10⁸ m/s
λ = from 3.9 * 10⁻⁷ m
Substituting the values in the above equation (2), we have
f = v / λ = (3 * 10⁸)/(3.9 * 10⁻⁷) = 0.769 * 10¹⁵ Hz = 7.69 * 10¹⁴ Hz
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If a 65-kilogram astronaut exerts a force with a magnitude of 50. Newtons on a satellite that she is repairing, the magnitude of the force that the satellite exerts on her is.
The magnitude of force ( 50 N ) which satellite exerts on her but in opposite direction.
We will apply the Newton's Third Law of motion for solving this problem, which says that, "To each activity, there is an equivalent and inverse response". And that implies if any article (say object 1) apply some power on another article (say object 2), then, at that point, the item 2 will likewise apply same greatness of power on object 1, yet it will be in inverse heading.
So, we have amount of force exerted by a 65-kg astronaut on satellite which is 50N.
To balance that force, satellite will apply same amount of force on astronaut but in just opposite direction .
F' = - F
or F' = - 50 N.
Here, negative sign shows that the direction of force is opposite.
Hence, required value of force is 50N.
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The magnitude, m, of an earthquake is represented by the equation m=23logee0 where e is the amount of energy released by the earthquake in joules and e0=104.4 is the assigned minimal measure released by an earthquake. which equation could be used to find the amount of energy released by an earthquake with a magnitude of 2.7?
An earthquake's energy output when it has a magnitude of 2.7 is 4.5 × [tex]10^{12}[/tex].
The magnitude of an earthquake is the most common indicator of its size. It serves as a barometer for the size of an earthquake's single source. Because it is the same no matter where and how you see it, the following calculation may be done:
magnitude, M = 2 ÷ 3 log(E ÷ [tex]E_{0}[/tex])
Where E is the power generated in Joules and M is the lowest magnitude emitted by such an earthquake, [tex]E_{0} = 10^{4.4}[/tex].
Assuming 5.5, the same magnitude is provided when the preceding equation is used:
M = 2 ÷ 3 log(E ÷ [tex]E_{0}[/tex])
5.5 = 2 ÷ 3 log(E ÷ [tex]E_{0}[/tex])
8.25 = [tex]log(\frac{E}{10^{4.4}})[/tex]
[tex]10^{8.25}[/tex] = [tex]\frac{E}{10^{4.4}}[/tex]
E = [tex]10^{4.4}[/tex] × [tex]10^{8.25}[/tex]
E = 4.5 × [tex]10^{12}[/tex]
Therefore the final answer is 4.5 × [tex]10^{12}[/tex].
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What is energy associated with motion called?
The energy associated with motion is called kinetic energy.
Your body doesn't just have energy when you're in motion. When an object is in motion it has a finite amount of kinetic energy. However, when not in motion, the body can store energy in the form of potential energy.
The body can also have a certain internal energy. This can be explained as follows. Energy is basically the ability of any body to do work. Suppose you are sitting ideally in your room and suddenly you realize that someone has changed the position of your study desk and you want to change it. So I pushed the table and moved it to where it suited me. This means that we have applied a finite force that causes displacement, i.e. we have done some work. So you had the ability to work properly. This means that you had energy in the form of internal energy.
[tex]mgh+\frac{mV^2}{2}=Energy \\\\m[gh+V^2/2]=E[/tex]
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question what would cause a backpack sitting on the floor of the school bus to suddenly fly forward? responses the bus makes a hard turn to the left. the bus makes a hard turn to the left. the bus is going forward and suddenly stops. the bus is going forward and suddenly stops. the bus is going backward and suddenly stops. the bus is going backward and suddenly stops. the bus makes a hard turn to the right.
Answer:
Below
Explanation:
Going forward and stops .....the backpack wants to keep going forward due to its inertia.
Kara less was applying her makeup when she drove into south's busy parking lot last friday morning. Unaware that lisa ford was stopped in her lane 30 feet ahead, kara rear-ended lisa's rented taurus. Kara's 1300-kg car was moving at 11 m/s and stopped in 0. 14 seconds.
The momentum of Kara's car before the collision, given that it was moving with a velocity of 11 m/s is 14300 Kg.m/s
Momentum of an object is simply defined as the product of mass and velocity. Mathematically it is expressed as:
Momentum = mass × velocity
Using the above formula, we can obtain the momentum of Kara's car before the collision as follow::
Mass of Kara's car = 1300 Kg
Velocity of Kara's car = 11 m/s
Momentum of Kara's car =?
Momentum = mass × velocity
= 1300 Kg × 11 m/s
= 14300 Kg.m/s
Thus, the momentum of Kara's car is 14300 Kg.m/s
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what is the band gap energy in kilojoules per mole if blue diamonds absorb orange light with a wavelength of 675 nm?
Based on the wavelength of the light, the energy of the photons emitted by a sodium lamp is 17.74 X 10² kJ/mol.
The energy is given by the formula;
E = hv
where,
h is Planck's constant = 6.63 X 10⁻³⁴ Js
f is frequency of light
Also, f = c/λ
where,
c is velocity of light = 3.0 X 10⁸ m/s
λ is wavelength of light = 589 nm = 6.75 X 10⁻⁷ m
1 mole of sodium atom will emit 6.02 X 10²³ photons,
N = 6.02 X 10²³ photons,
Thus,
= E = Nhc/λ
= E = (6.02 X 10²³ X 6.63 X 10⁻³⁴ J.s X 3.0 X 10⁸ m/s)/6.75 X 10⁻⁷ m
= E = 119.74 X 10⁻³ / 6.75 X 10⁻⁷
= E = 17.74 X 10⁵ J/mol
= E = 17.74 X 10² kJ/mol
Therefore, the energy of the photons emitted by a sodium lamp is 17.74 X 10² kJ/mol.
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Some students were on a tour exploring the inside of a cave. While the students were in the cave, they realized they heard an echo every time that they spoke. Which MOST likely caused the echo to occur?
A. the accumulation of the sound waves
B. the diffraction of the sound waves
C. the refraction of the sound waves
D. the reflection of the sound waves
A group of kids were taking a tour and looking inside a cave. The pupils in the cave soon learned that every time they spoke, there was an echo. i.e. (D). the reflection of the sound waves is correct option.
Acoustic waves are reflected by solid surfaces like walls and fences as well as by mountains. Reflection can be attributed to a break in the propagation medium. This can be heard when the reflection returns with sufficient magnitude and lag to be audible. The term "reverberation" refers to an echo that has experienced many reflections from various surfaces.The human ear cannot distinguish between the echo and the original direct sound if the delay is less than 1/10 of a second. The sound speed in dry air is approximately 343 m/s at 25 °C.As a result, the reflecting object must be farther away for an echo to be audible to someone standing close to the sound source.
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radio waves travel at a speed of 1.7x10^8 m/s through ice. A radio wave pulse sent into antarctic ice reflects off earth at the bottom and returns to the surface in 32.9x10^-6 s. how deep is the ice?
Then the depth of the ice is 26.55 x 10¹² m
Let speed of the radio wave be represented as 'v'
Let frequency of the radio wave be represented as 'f'
Let distance of the radio wave be represented as 's'
Let time period of the radio wave be represented as 't'
From the formula for distance:
v=s/t
v= s x 1/t
Frequency is the inverse of time period. So, 1/t in the above formula can be replaced by f.
v = s x f
putting values in the above equation
t = 32.9 x 10⁻⁶ s
v = 1.7 x 10⁸ m/s
The, f = 1/t
f = 1/3.2 x 10⁻⁶ s⁻,
So,
s = 1.7 x 10⁸ x 1/3.2 x 10⁻⁶
= 1.7/3.2 x 10⁸⁺⁶
= 0.531 x 10¹⁴
= 53.1 x 10¹²
Then the depth of the ice would be s/2 as the distance is covered twice by the wave in the given time frame.
Depth of ice = 53.1 x 10¹²/2
Depth of ice = 26.55 x 10¹² m
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suppose that you want to take a photograph of yourself as you look at your image in a mirror 3.1 m away. for what distance should the camera lens be focused?
The camera should be focused for 6.2 m.
In addition, we already know that the main use of plane mirrors is to observe an object's reflection. Periscopes and kaleidoscopes, vehicles, shaving mirrors, dental mirrors, torch lights, solar cookers, and security-related uses are just a few of the many functions and applications of a plane mirror.
As we're standing 3.1 m away from the mirror so our image is also formed 3.1 away from the mirror as the mirrors used for this purpose are plane mirrors. So the camera should be focused for twice the distance at which we're standing from the mirror i.e 3.1 * 2 = 6.2 m
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what is the total number of unique ways to distribute two identical objects in three separate containers when there is no limit on the number of objects that can be in a container?
There are 6 unique ways to distribute two identical objects in three separate containers.
Unique ways are the different ways in which the objects can be separately placed in the containers.
Number of ways are:
Container 1: both Object ; Container 2: 0 object ; Container 3: 0 objectContainer 1: 0 Object ; Container 2: both object ; Container 3: 0 objectContainer 1: 0 Object ; Container 2: 0 object ; Container 3: both objectContainer 1: 1 Object ; Container 2: 1 object ; Container 3: 0 objectContainer 1: 0 Object ; Container 2: 1 object ; Container 3: 1 objectContainer 1: 1 Object ; Container 2: 0 object ; Container 3: 1 objectThese are the 6 ways to distribute two identical objects in three separate containers.
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what pressure does light emitted uniformly in all directions from a 200-w incandescent light bulb exert on a mirror at a distance of 5.0 m?
The pressure exerted on the mirror by the light emitted from the 200-w incandescent light bulb is negligible. This is because the pressure exerted by light is proportional to the intensity of the light .
and the intensity of the light drops off as the square of the distance. At a distance of 5.0 m, the intensity of the light is extremely low, and thus the pressure is practically zero.
Step 1: Calculate the intensity of light:
We know that the power of the light bulb is 200 W, so the intensity of light is given by:
I = P/4πd2
Where P is the power of the light and d is the distance from the light to the mirror.
In this case, we have:
I = 200 W / 4π(5.0 m)2
I = 0.0025 W/m2
Step 2: Calculate the pressure exerted by the light on the mirror:
We know that the pressure exerted by the light on the mirror is given by:
P = I/c
Where I is the intensity of the light and c is the speed of light.
In this case, we have:
P = 0.0025 W/m2/3.00 x 108 m/s
P = 8.3 x 10-10 N/m2
Therefore, the pressure exerted by the light emitted from the 200-w incandescent light bulb on a mirror at a distance of 5.0 m is 8.3 x 10-10 N/m2.
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Element x has two isotopes. If 72. 0% of the element has an isotopic mass of 84. 9 amu and 28. 0% has an isotopic mass of 87. 0 amu, the average atomic mass of element x is numerically equal to.
The average atomic mass of element X is numerically equal to 85.48 amu.
Isotopes can be defined as the variants of chemical elements that possess the same number of protons and electrons, but a different number of neutrons. In other words, isotopes are variants of elements that differ in their nucleon ( The total number of protons and neutrons) numbers due to a difference in the total number of neutrons in their respective nuclei. i.e. same atomic number but different masses.Given , Percentage of isotope 1 = 72%
Percentage of isotope 2 = 28%
Mass of isotope 1 = 84.9 amu
Mass of isotope 2 = 87 amu
i.e.
Average atomic mass = (0.72 * 84.9) + (0.28 * 87) = 85.48 amu
So the average atomic mass of element X is numerically equal to 85.48 amu.
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If a muon is traveling at 70% the speed of light, how long will it take to decay in the observer's rest frame (i. E. , what is the observed lifetime)?.
A muon takes to decay in the observer's rest frame is 3.08 μs.
A muon is an unstable subatomic particle that decays into other particles with a mean lifetime of 2.20 μs. This is in the muon reference frame.
The formula for the relativistic factor
[tex]\gamma \:=\: \frac{1}{\sqrt{1 \:-\: (\frac{v}{c})^2}}[/tex]
v = muon's speed = 70% c = 0.7cc = the speed of lightγ = the relativistic factor[tex]\gamma \:=\: \frac{1}{\sqrt{1 \:-\: (\frac{0.7c}{c})^2}}[/tex]
[tex]\gamma \:=\: \frac{1}{\sqrt{1 \:-\: 0.7^2}}[/tex]
[tex]\gamma \:=\: \frac{1}{\sqrt{1 \:-\: 0.49}}[/tex]
[tex]\gamma \:=\: \frac{1}{\sqrt{0.51}}[/tex]
[tex]\gamma \:=\: \frac{1}{\sqrt{1 \:-\: 0.7^2}}[/tex]
[tex]\gamma \:=\: \frac{1}{0.714}[/tex]
γ = 1.4
Relativistic time interval formula
t = γ t₀
t₀ = the time according muon reference frame = 2.20 μst = the time according to the observer's rest framet = 1.4 × 2.2
t = 3.08 μs
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20 kj of heat is added to a cup containing 1-kg of water at 20 c. what is the final temperature of the water? answer in c, and assume water has a specific heat of 4186 j/(kg c). answer in celsius.
The final temperature of the water is equal to 24.77 °C.
What is the specific heat capacity?The specific heat capacity can be explained as the amount of heat needed to increase the temperature of one unit of material by one degree Celsius. The specific heat capacity depends upon the nature of the material.
The mathematical equation is used to calculate the specific heat is equal to:
Q = mCΔT
Given, the mass of the water, m = 1 Kg
The initial temperature of the water, T₁ = 20°C
The specific heat capacity of water, C = 4186 J/(kg °C)
The heat added to the cup, Q = 20,000 J
The final temperature of the water can be determined as:
20000 = 4186 × 1 × (T₂ - 20)
T₂ - 20 = 4.77
T₂ = 24.77 °C
Therefore, the final temperature of the water is 24.77 °C.
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