To solve this problem, we can use Coulomb's law, which states that the electric force between two point charges is proportional to the product of their charges and inversely proportional to the square of the distance between them.
We can then use the electric force to find the electric field at the location of q3 and the initial acceleration of q3.
a) To find the electric field at the location of q3, we can first find the electric force on q3 due to q1 and q2 and then use the definition of the electric field, which is the electric force per unit charge. The electric force on q³ due to q¹ and q² is:
F1 = k x q¹ x q³/ r1²
F2 = k x q² x q³ / r2²
where r¹ and r² are the distances from q¹ and q² to q³, respectively, and k is Coulomb's constant.
Since q³ is equidistant from q¹ and q², we have r¹ = r² = 0.20 m. Substituting the given values, we get:
F1 = (9.0 x 10⁹ N-m²/C²) x (4.0 x 10⁻⁶ C) x (2.0 x 10⁻⁶C) / (0.20 m)² = 1.8 N
F2 = (9.0 x 10⁹ N-m⁻²/C²) x (-6.0 x 10⁻⁶ C) x (2.0 x 10⁻⁶C) / (0.20 m)² = -5.4 N
The negative sign of F2 indicates that the force on q³ due to q² is in the opposite direction to the force due to q¹.
The net electric force on q3 is the vector sum of the forces due to q1 and q2:
Fnet = F1 + F2 = 1.8 N - 5.4 N = -3.6 N
The electric field at the location of q³ is then:
E = Fnet / q³ = (-3.6 N) / (2.0 x 10⁻⁶ C) = -1.8 x 10⁻⁶N/C
The negative sign of the electric field indicates that the field is directed towards q².
b) To find the initial acceleration of q³, we can use Newton's second law, which states that the net force on an object is equal to its mass times its acceleration:
Fnet = ma
where m is the mass of q³ and a is its initial acceleration.
Substituting the given values, we get:
-3.6 N = (2.0 x 10⁻⁶ kg) x a
Solving for a, we get:
a = -1.8 x 10³ m/s²
The negative sign of the acceleration indicates that it is directed towards q².
c) The direction of the initial acceleration of q³ is towards q².
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The nearest neighboring star to the Sun is about 4 light-years away. If a planet happened to be orbiting this star at an orbital radius equal to that of the Earth-Sun distance, what minimum diameter would an Earth-based telescope's aperture have to be in order to obtain an image that resolved this star-planet system? Assume the light emitted by the star and planet has a wavelength of 550 nm
. The Earth-Sun distance is 149.6×106km
, and 1ly=9.461×1015m
.
To resolve the star-planet system at a distance of 4 light-years, a telescope on Earth would need an aperture with a minimum diameter of 55.88 mm.
What does microscopy's Rayleigh criterion mean?In optical microscopy, the Rayleigh criterion is frequently used to estimate the resolution of the microscope. The resolution limit imposed by this criterion has long been regarded as a roadblock to using an optical microscope to study biological phenomena at the nanoscale.
We can use the Rayleigh criterion,
θ = 1.22 λ / D
θ = angular resolution
λ = wavelength of light
D = diameter of the telescope's aperture
θ = arctan (r / d)
r = radius of the planet's orbit
d = distance to the star
Now, we use the given values,
r = 149.6×106 km = 149.6×109 m
d = 4 × 9.461×1015 m = 3.7844×1016 m
λ = 550 nm = 550×10-9 m
θ = arctan (r / d)
=arctan (149.6×109 / 3.7844×1016) = 0.000012 radians
we can use the Rayleigh criterion,
θ = 1.22 λ / D
D = 1.22 λ / θ
D = 1.22 × 550×10-9 / 0.000012
D = 55.88 mm
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How long does it take for radiation from a cesuim-133 atom to complete 1.5 million cycles
A cesium-133 atom's radiation goes through 1.5 million cycles in around 0.1633 microseconds (or 163.3 nanoseconds).
What frequency does one kind of radiation that cesium-133 emits have?9,192,631,770 hertz (cycles per second) is the frequency of the microwave spectral line that the isotope cesium-133 emits. The basic unit of time is provided by this. Cesium clocks have an accuracy and stability of 1 second in 1.4 million years.
The radiation emitted by cesium-133 has a frequency of 9,192,631,770 cycles per second, or 9.192631770 109 Hz.
The following formula may be used to determine how long 1.5 million radiation cycles take to complete:
Time is equal to the frequency of cycles.
Plugging in the numbers, we get:
time = 1.5 million / 9.192631770 × 10^9 Hz
time = 1.632995101 × 10^-7 seconds
So it takes approximately 0.1633 microseconds (or 163.3 nanoseconds) for radiation from a cesium-133 atom to complete 1.5 million cycles.
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If the sun were more massive, what would happen to Earth’s gravity with the sun?
A. decrease
B. would be infinite
C. would be 0
D. increase
Answer: d. increase
Explanation:
If the sun were more massive, the gravitational force between the sun and Earth would increase. This means that Earth's gravity with the sun would also increase. Therefore, the correct answer is (D) increase.
The gravitational force between two objects is directly proportional to the product of their masses and inversely proportional to the square of the distance between them. So, if the mass of one of the objects increases, the gravitational force between them will also increase. In this case, if the mass of the sun were to increase, the gravitational force between the sun and Earth would become stronger, and hence, Earth's gravity with the sun would also increase.
A .35 kg block at -27.5 ºC is added to .217 kg of water at 25.0 ºC. They come to equilibrium at 16.4 ºC. What is the specific heat of the block?
Answer:
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To solve this problem, we can use the formula for heat transfer:
q = mcΔT
where q is the heat transferred, m is the mass of the object, c is its specific heat capacity, and ΔT is the change in temperature.
We know that the mass of the block is 0.35 kg and that its initial temperature is -27.5 ºC. We also know that the mass of water is 0.217 kg and that its initial temperature is 25.0 ºC.
When they come to equilibrium at 16.4 ºC, we can calculate how much heat was transferred from the water to the block:
q = mcΔT q = (0.217 kg)(4186 J/kg ºC)(25.0 ºC - 16.4 ºC) q = 1825 J
This amount of heat was transferred from the water to the block, so we can set it equal to the amount of heat absorbed by the block:
q = mcΔT 1825 J = (0.35 kg)c(16.4 ºC - (-27.5 ºC)) 1825 J = (0.35 kg)c(43.9 ºC) c = 148 J/kg ºC
Therefore, the specific heat capacity of the block is 148 J/kg ºC.
Explanation:
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A model rocket blast off and moves upward with an acceleration of 12m/s2 until it reaches a height of 26m, at which point its engine shuts off and it continues its flight in free fall.
a) What is the maximum height attained by the rocket?
b) What is the speed of the rocket just before it hits the ground?
c) What is the total duration of the rocket's flight?
can you please tell me where does 1-14 i really need help thanks :) god bless you all
The above has to do with the study of the earth's lithospheric plates. See the attached image and the explanation below.
What are the processes of the movement of lithospheric plates?The movement of lithospheric plates is a geological process that occurs due to the motion of hot, molten material in the Earth's mantle. The lithosphere, which is the rigid outer layer of the Earth's surface, is divided into several large plates that move relative to each other.
These movements are caused by the convection of material in the mantle and the forces that arise at the boundaries between the plates.
There are three main types of plate boundaries: divergent, convergent, and transform. Divergent boundaries occur where plates move apart from each other, creating new oceanic crust. Convergent boundaries arise where plates collide, leading to subduction, volcanic activity, and the formation of mountains. Transform boundaries occur where plates slide past each other.
The movement of lithospheric plates gives rise to various geological phenomena, such as earthquakes, volcanic activity, and the formation of mountain ranges and ocean basins.
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A light ray passing through air strikes the surface of a glass block (n=1.5) and makes 30° angle of incidence. How many degrees will the light ray deviate from its original path after refraction?
The light ray will deviate from its original path with 19.5° after refraction.
How do we calculate?Applying Snell's law to calculate the angle of refraction:
n1 sin θ1 = n2 sin θ2
where n1 and θ1 = the refractive index and the angle of incidence in the first medium (air),
n2 and θ2 = the refractive index and the angle of refraction in the second medium (glass).
In this example,
n1 = 1.00 (refractive index of air), θ1 = 30°, and
n2 = 1.5 (refractive index of glass).
We then calculate for θ2:
n1 sin θ1 = n2 sin θ2
1.00 * sin 30° = 1.5 * sin θ2
0.5 = 1.5 * sin θ2
sin θ2 = 0.5 / 1.5 = 1/3
θ2 = sin^-1(1/3)
θ2 = 19.5°
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franchising why is it the best option for you as an entrepreneur
Answer:
ttrockstars
Explanation:
it's math you to be an expert at math thank you
If the speed of a wave is 400 cm/s with a frequency of 80 Hz, what is the wavelength for this wave?
32,000 cm
32,000 m
5 cm
5m
a wave has a frequency of 40 hertz and a wavelength of 2 meters . what is the wave speed ?
Answer:
[tex]80\; {\rm m\cdot s^{-1}}[/tex].
Explanation:
The frequency [tex]f[/tex] of a wave is the number of cycles completed in unit time ([tex]1\; {\rm s}[/tex] in this example.) In this question, [tex]f = 40\; {\rm s^{-1}}[/tex] ([tex]1\; {\rm Hz} = 1\; {\rm s^{-1}}[/tex]) means that the wave would complete [tex]40[/tex] cycles in every [tex]1\; {\rm s}[/tex].
The wavelength [tex]\lambda[/tex] of a wave is the distance the wave travels in each cycle. It is given that [tex]\lambda = 2\; {\rm m}[/tex].
The goal is to find the wave speed, which is the distance that this wave travels in unit time ([tex]1\; {\rm s}[/tex].)
In this question, it is given that [tex]\lambda = 2\; {\rm m}[/tex] and [tex]f = 40\; {\rm s^{-1}}[/tex]. Thus, this wave would travel a total of [tex]40\, (2\; {\rm m}) = 80\; {\rm m}[/tex] for the [tex]40[/tex] cycles completed in each unit time of [tex]1\; {\rm s}[/tex] ([tex]\lambda = 2\; {\rm m}[/tex] for each cycle.) The speed of this wave would be [tex]80\; {\rm m\cdot s^{-1}}[/tex].
Formally, the speed [tex]v[/tex] of this wave can be found by multiplying the wavelength [tex]\lambda[/tex] of this wave by its frequency [tex]f[/tex]:
[tex]\begin{aligned}v &= \lambda\, f \\ &= (2\; {\rm m})\, (40\; {\rm s^{-1}) \\ &= 80\; {\rm m\cdot s^{-1}}\end{aligned}[/tex].
A 27 g block of ice is cooled to −65 ◦C. It is added to 525 g of water in an 80 g copper calorimeter at a temperature of 25◦C. Find the final temperature. The specific
heat of copper is 387 J/kg ◦C and of ice is 2090 J/kg ◦C . The latent heat of fusion of
water is 3.33 × 105 J/kg and its specific heat is 4186 J/kg ◦C . Answer in units of ◦C.
The final temperature after adding the ice to the water and calorimeter will be approximately 8.37 ◦C.
What is Temperature?
Temperature is a measure of the average kinetic energy of the particles in a substance or system. It is a scalar quantity that indicates how hot or cold an object or medium is. Temperature is commonly measured using various scales, such as Celsius (°C), Fahrenheit (°F), and Kelvin (K), which represent different reference points and units of measurement.
Since energy is conserved, we can set Q_ice equal to Q_water+calorimeter:
m_ice * c_ice * ΔT_ice = (m_water + m_calorimeter) * c_water+calorimeter * ΔT_water+calorimeter
27 g * 2090 J/kg ◦C * (T_f + 65) = (525 g + 80 g) * (4186 J/kg ◦C + 387 J/kg ◦C) * (T_f - 25)
Simplifying and solving for T_f:
27 * 2090 * (T_f + 65) = 605 * (T_f - 25)
56130 T_f + 361350 = 605 T_f - 15125
56130 T_f - 605 T_f = -15125 - 361350
-44,970 T_f = -376475
T_f = (-376475) / (-44,970)
T_f ≈ 8.37 ◦C
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How can you determine the number of neutrons in an atom?
A. Mass number plus number of electrons
B. Atomic number minus mass number
C. Mass number minus atomic number
D. Atomic number plus mass number
Answer:
B. Atomic number minus mass number
Explanation:
30 POINTS!!!! NO CHATGPT OR ANY BOTS_
As you sit in a fishing boat, you notice that 12 waves pass the boat every 45 s
. If the distance from one crest to the next is 9.0 m
, what is the speed of these waves?
Express your answer to two significant figures and include the appropriate units.
The speed of the waves can be expressed to two significant figures as 0.2 m/s. The unit for this expression is meters per second (m/s).
What is wave crest?A wave crest is the highest point of a wave. It is the top of the wave, where the wave is moving most up and away from the equilibrium position. It is the point of highest amplitude (height) of the wave and is followed by a wave trough, which is the lowest point of the wave.
The speed of the waves can be calculated using the formula speed = distance over time.
We know the distance between wave crests is 9.0 m and the time it takes for 12 waves to pass the boat is 45 s. Therefore, the speed of the waves can be calculated as:
Speed = 9.0 m / 45 s
Speed = 0.2 m/s
The speed of the waves can be expressed to two significant figures as 0.2 m/s. The unit for this expression is meters per second (m/s).
This calculation shows that the speed of the waves passing the boat is 0.2 m/s. This speed can be further broken down into how many meters the waves travel in one second if necessary.
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On the water surface, there are two sources of oscillating waves of the same phase located at A and B, emitting two coherent waves of wavelength λ. Let Δ be the line perpendicular to AB at B. On Δ there are 16 interference maxima, the distance between the two closest and farthest interference maxima is 2.71 cm and 229.55 cm, respectively. . Which of the following is the length of line segment AB closest to?
Two or greater sources are said to be coherent if they emit waves that have the identical wavelength (or frequency) and amplitude and which maintain a steady phase difference.
Do two coherent sources have equal wavelength?If two sources have the identical wavelength, frequency, and segment difference, they are said to be coherent. Therefore, we can conclude that coherent sources have the identical wavelength.
Two microwave coherent factor sources emitting waves of wavelenths λare positioned at 5λdistance apart. The interference is being observed on a flat non-reflecting surface alongside a line passing through on sources ,in a course perpendicular to the line joining the two sources
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https://brainly.com/question/12495315#SPJ1A 0.80kg block of carbon (solid) is dropped into 1.4kg of water. If the carbon starts at -20C, the water starts at 92C, and they have equal final temperatures, what is the final temperature of the system?
The system's final temperature is roughly 16.7°C.
What is a system's final temperature?You may determine your substance's final heat by multiplying the temperature change by the initial temperature. Your water's final temperature would be 24 + 6, or 30 degrees Celsius, for instance, if it started off at 24 degrees Celsius.
The following is the formula for energy conservation:
Q1 + Q2 = 0
Q = mcΔT
Q1 + Q2 = 0
568.8
Simplifying and solving for
6394.4 - 106768 = 0
= 16.7°C
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A rock climber stands on top of a 59 m -high cliff overhanging a pool of water. He throws two stones vertically downward 1.0 s apart and observes that they cause a single splash. The initial speed of the first stone was 1.7 m/s . Include value and units.
a) How long after the release of the first stone does the second stone hit the water?
b) What was the initial speed of the second stone?
c) What is the speed of the first stone as it hits the water?
d) What is the speed of the second stone as it hits the water?
a) The time after the release of the first stone that the second stone hits the water is 2.0 s.
b) 15.7 m/s is the initial speed of the second stone.
c) The speed of the first stone as it hits the water is 15.7 m/s.
d) The speed of the second stone as it hits the water is 28.2 m/s.
What is velocity?Velocity is a vector quantity that measures both the speed and direction of an object's motion. It is equal to the rate of change of an object's position with respect to time. Velocity is usually represented by the symbol v and is measured in meters per second (m/s).
a) The time between first and second stone's release is 1.0 s. Since the time of release of first stone and the time of splash of both stones are same, the time between the release of second stone and the splash of both stones is 1.0 s.
Thus, the time after the release of the first stone that the second stone hits the water is 2.0 s.
b) The initial speed of the second stone can be calculated using the equation of motion,
v² = u² + 2as
where v is the final velocity, u is the initial velocity, a is the acceleration due to gravity (9.8 m/s²), and s is the displacement.
Substituting the values,
v² = (1.7)² + 2(9.8) * 59
v = 15.7 m/s
c) The speed of the first stone as it hits the water can be calculated using the equation of motion,
v² = u² + 2as
where v is the final velocity, u is the initial velocity, a is the acceleration due to gravity (9.8 m/s²), and s is the displacement.
Substituting the values,
v² = (1.7)² + 2(9.8) * 59
v = 15.7 m/s
d) The speed of the second stone as it hits the water can be calculated using the equation of motion,
v² = u² + 2as
where v is the final velocity, u is the initial velocity, a is the acceleration due to gravity (9.8 m/s²), and s is the displacement.
Substituting the values,
v² = (15.7)² + 2(9.8) * 59
v = 28.2 m/s
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Which are different forms of an element that have different numbers of neutrons?
ions
isotopes
compounds
molecules
.
.
Answer:A
Explanation:
Isotopes are members of a family of an element that all have the same number of protons but different numbers of neutrons. The number of protons in a nucleus determines the element's atomic number on the Periodic Table.
A ball thrown straight upward returns to its original level in 2.75 seconds. A second ball is thrown at an angle of 40 degrees above the horizontal. What is the initial speed ball if it also returns to its original level in 2.75 seconds?
The initial speed (magnitude of velocity) of the second ball thrown at an angle of 40 degrees above the horizontal is approximately 12.93 m/s.
What is the initial speed ball?Let's consider the motion of the second ball thrown at an angle of 40 degrees above the horizontal. We can break down its motion into horizontal and vertical components.
Given:
Time taken for the ball to return to its original level (time of flight): t = 2.75 seconds
Angle of projection (above the horizontal): θ = 40 degrees
We can use the following equations of motion to find the initial speed (magnitude of velocity) of the ball:
Horizontal motion:
The horizontal velocity of the ball remains constant throughout the motion, and can be given as:
vx = v0 * cos(θ), where v0 is the initial speed.
Vertical motion:
The vertical velocity of the ball changes due to the force of gravity. We can use the following equation:
vy = v0 * sin(θ) - g * t,
where;
g is the acceleration due to gravitySince the ball returns to its original level, the vertical displacement (change in height) is zero:
Δy = 0
We can use the following equation to relate the initial speed, time of flight, and angle of projection:
Δy = v0 * sin(θ) * t - (1/2) * g * t^2 = 0
Plugging in the values and solving for v0:
0 = v0 * sin(40) * 2.75 - (1/2) * 9.8 * (2.75)^2
v0 * sin(40) * 2.75 = (1/2) * 9.8 * (2.75)^2
v0 = (1/2) * 9.8 * (2.75)^2 / (sin(40) * 2.75)
v0 = 12.93 m/s (rounded to two decimal places)
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A 25 kg child plays on a swing having support ropes that are 2.20 m long. A friend pulls her back until the ropes are ăÿÿfrom the vertical and releases her from rest. (a) What is the potential energy for the child just as she is released compared with the potential energy at the bottom of the swing? (b) How fast will she be moving at the bottom of the swing? (c) How much work does the tension in the ropes do as the child swings from the initial position to the bottom?
Answer:
A) P.E = 138.44 J
B) The velocity of swing at bottom, v = 3.33 m/s
C) The work done, W = -138.44 J
Explanation:
Given,
The mass of the child, m = 25 Kg
The length of the swing rope, L = 2.2 m
The angle of the swing to the vertical position, ∅ = 42°
A) The potential energy at the initial position ∅ = 42° is given by the relation
P.E = mgh joule
Considering h = 0 for the vertical position
The h at ∅ = 42° is h = L (1 - cos∅)
P.E = mgL (1 - cos∅)
Substituting the given values in the above equation
P.E = 25 x 9.8 x 2.2 (1 - cos42°)
= 138.44 J
The potential energy for the child just as she is released, compared to the potential energy at the bottom of the swing is, P.E = 138.44 J
B) The velocity of the swing at the bottom.
At bottom of the swing the P.E is completely transformed into the K.E
∴ K.E = P.E
1/2 mv² = 138.44
1/2 x 25 x v² 138.44
v² = 11.0752
v = 3.33 m/s
The velocity of the swing at the bottom is, v = 3.33 m/s
C) The work done by the tension in the rope from initial position to the bottom
Tension on string, T = Force acting on the swing, F
=
= - 2.2 x 25 x 9.8 [cos0 - cos 42°]
= - 138.44 J
The negative sign in the in energy is that the work done is towards the gravitational force of attraction.
The work done by the tension in the ropes as the child swings from the initial position to the bottom of the swing, W = - 138.44 J
The attractive electric force between the point charges q and −2q has a magnitude of 2.2 N when the separation between the charges is 1.4 m . k=8.99×109N⋅m2/C2
What is the magnitude of charge q?
The electric force between two point charges is given by the equation
[tex]F=k*q_1*q_2/r^2[/tex]
What is force?The interaction between two things is measured by the physical quantity known as force. It is a vector quantity, and the sign F is frequently used to denote it. When an object interacts with another object, it feels a push or a pull.
where r is the distance between the charges, q1 and q2 are their magnitudes, and k is the Coulomb constant.
When we enter the problem's specified values, we obtain
[tex]2.2N=8.99*10^9\ N*m^2/C^2*q*-2q/(1.4 m)^2[/tex]
which simplifies to
q = -0.500 N/C.
Thus, the magnitude of charge q is 0.500 N/C.
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How loud in Decibels would a sound be with an intensity of 7.8x10^-4 W/m2? (write your answer to one decimal space)
A sound that is 7.8x10-4 W/m2 in intensity is equal to (10 dB)log3.2106 W/m21012 W/m2=185 dB.
How can you determine the relative volume of a sound?The decibel, often known as the db or 0.1 bel, is the standard measurement unit. Hence, b = 10 log10 (I/I0) can be used to express the relationship between relative intensities, or b, in decibels. This equation can be used to determine that one decibel equals a 26 percent intensity variations.
What does physics mean by relative intensity?The "decibel level" of a sound is a less formal term for relative intensity level. It is not the same as energy; relative intensity level reflects loudness more faithfully by using a logarithmic scale.
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According to this graph, the acceleration
is approximately:
A. 12 m/s²
C. 4 m/s²
Velocity (m/s)
14
12
10
12 2 3 4
Time t (s)
B. 1.5 m/s2
D. 3 m/s2
Help please
Answer:
Explanation:
Because you have velocity along the y axis and time along the x axis, this is a velocity v time graph which is an acceleration graph. The slope of the line in this graph IS the acceleration. We can use 2 points and the slope formula to solve for the acceleration:
(0, 0) and (1, 3):
[tex]m=\frac{3-0}{1-0}=3[/tex] m/s squared, choice D.
Please help me in this question
The lift is the force created by the airplane's passage through the air. Lift is an aerodynamic force. ("aero" stands for the air, and "dynamic" denotes motion).
Plane take-offThe mechanical energy becomes kinetic energy when the airplane's speed rises. The mechanical energy is transformed into gravitational potential energy as the plane soars higher. Drag during flight results in some energy being wasted to thermal (heat) energy and sound energy.The engines, which turn chemical energy (fuel) into mechanical energy, supply the energy needed for the airplane to lift off. (the spinning of fan blades, or, in some cases, propellers). The airplane's speed is increased by the mechanical energy that creates thrust.For more information on aero plane take-off kindly visit to
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an election of mass 9.1 × 10^31kg moves with a velocity of 4.2 × 10^7mJs between the cathode and anode of an X-ray tube. Calculate the wavelength.( take Planck's constant, h= 6.6 × 10^ 34 J's)
The wavelength of the electron is 1.724 × 10^-12 m.
How do we calculate?The wavelength of the electron is found using the de Broglie wavelength formula:
λ = h / p
where λ = wavelength,
h= Planck's constant, a
p = momentum of the electron.
we find the momentum of the electron,
p = m * v
p = (9.1 × 10^-31 kg) * (4.2 × 10^7 m/s)
p = 3.822 × 10^-22 kg m/s
Therefore, wavelength ;
λ = h / p
λ = (6.6 × 10^-34 J s) / (3.822 × 10^-22 kg m/s)
λ = 1.724 × 10^-12 m
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For every baryon in the Universe, there are about 109 photons. The ratio of photons to baryons has been
constant since a few seconds after the big bang. This is a crucial number that sets the stage for much of
the future evolution of the Universe. If the number were just a little different, the Universe would be a
very different place, and life could possibly not exist. In this question we will use the photon-to-baryon
ratio to work out the redshift at which the Universe becomes dominated by matter, instead of by
radiation.
Assume that most of the photons in the present Universe are cosmic microwave radiation photons that
are a relic of the big bang. (It turns out that this is not a bad assumption). For simplicity, also assume
that all the photons have the energy corresponding to the wavelength of the peak of a 2.73K black-body
radiation curve. At approximately what redshift will the energy density in radiation be equal to the
energy density in matter?
The Universe became dominated by matter instead of radiation at a redshift of around 3300.
To determine at what redshift the Universe became dominated by matter, we need to find the redshift at which the energy density of matter becomes equal to the energy density of radiation.
Let's start with the energy density of radiation, which can be calculated using the Stefan-Boltzmann law:
$[tex]u_{rad} = \frac{4\sigma}{c}T^4$[/tex]
where $\sigma$ is the Stefan-Boltzmann constant, $c$ is the speed of light, and $T$ is the temperature of the radiation. Since we are assuming that the cosmic microwave radiation is a black-body radiation, we can use the temperature of 2.73 K, which corresponds to the peak of the radiation curve:
[tex]$u_{rad} = \frac{4\sigma}{c}(2.73K)^4 \approx 0.261 \text{ eV/cm}^3$[/tex]
Next, let's calculate the energy density of matter. We know that the number density of baryons is [tex]$n_b \approx \frac{1}{10^9}n_{\gamma}$, where $n_{\gamma}$[/tex] is the number density of photons. Since we are assuming that the photon-to-baryon ratio is constant, we can write:
[tex]$\frac{\rho_b}{\rho_{\gamma}} = \frac{m_b n_b}{\frac{4}{3}\sigma T^4} = \frac{3m_b}{4\sigma T^3 n_{\gamma}} \approx \frac{3m_b}{4\sigma T^3}\frac{1}{n_{\gamma}}$[/tex]
where $m_b$ is the mass of a baryon. Substituting the values, we get:
[tex]$\frac{\rho_b}{\rho_{\gamma}} \approx 4.15 \times 10^{-10}$[/tex]
Since the total energy density of the Universe is given by:
[tex]$\rho_{tot} = \rho_b + \rho_{\gamma}$[/tex]
we can write:
[tex]$\frac{\rho_b}{\rho_{tot}} = \frac{\rho_b}{\rho_b + \rho_{\gamma}} \approx \frac{\rho_b}{\rho_{\gamma}} = 4.15 \times 10^{-10}$[/tex]
At the redshift $z$, the energy density of radiation will be diluted by a factor of $[tex](1+z)^4[/tex]$, while the energy density of matter will be diluted by a factor of $[tex](1+z)^3[/tex]$. Thus, at some redshift $z$, we will have:
$ [tex]\frac{\rho_b}{\rho_{tot}} = \frac{\rho_b}{\rho_b + \rho_{\gamma}} = \frac{1}{1+z}\frac{3m_b}{4\sigma T^3 n_{\gamma}}[/tex] $
Setting this equal to the value we calculated above, we can solve for $z$:
$ [tex]\frac{1}{1+z}\frac{3m_b}{4\sigma T^3 n_{\gamma}} \approx 4.15 \times 10^{-10}[/tex] $
$ [tex]1+z \approx \frac{3m_b}{4\sigma T^3 n_{\gamma}}\frac{1}{4.15 \times 10^{-10}}[/tex] $
$ [tex]z \approx 3300[/tex] $
Therefore, the Universe became dominated by matter instead of radiation at a redshift of around 3300.
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5. Two equal charges are situated in a vacuum 10.0cm apart, if they repel each other with a force of 0.5N, calculate the value of the charge on each. [4π)¹ = 9.0 x 10⁹ I
The value of the charge on each particle is [tex]1.05 x 10^-8 C[/tex].
What is Coulomb's law?Coulomb's law is a fundamental principle of electrostatics that describes the interaction between electric charges. It states that the force between two point charges is directly proportional to the product of their charges and inversely proportional to the square of the distance between them. We can use Coulomb's law to solve this problem. Mathematically,
[tex]F = k(q1q2)/r^2[/tex]
where F is the force of attraction or repulsion between the two charged particles,[tex]q1[/tex] and [tex]q2[/tex] are the magnitudes of the charges on the two particles, r is the distance between them, and k is Coulomb's constant, which has a value of [tex]9.0 x 10^9 Nm^2/C^2.[/tex]
In this problem, we know that the charges are equal and the distance between them is 10.0 cm. We also know that the force between them is 0.5 N. Therefore,
[tex]0.5 N = k(q^2)/(0.1 m)^2[/tex]
Solving for q, we get:
[tex]q = \sqrt{[(0.5 N)(0.1 m)^2/k]}[/tex]
[tex]q = \sqrt{(0.5 N)(0.01 m)/(9.0 x 10^9 Nm^2/C^2)}[/tex]
[tex]q = 1.05 x 10^-8 C[/tex]
Therefore, the value of the charge on each particle is [tex]1.05 x 10^-8 C.[/tex]
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Which of the following best describes the relationship between the two variables?
Answer:
correlation is defined as the statistical association between two variables
Explanation:
a correction exits between two variables when one of them is related to the other in some way
As a 5.00-kg sample of liquid mercury is cooled into a solid, it liberates 157 kJ of energy. What is the original temperature of the mercury? For mercury, the melting point is 234 K, the heat of fusion is 11.3 kJ/kg,
and the specific heat is 140 J/kg . K.
378 K
690 K
157 K
410 K
The original temperature of the mercury is 260.6K
Here is how to arrive at temperature of the mercuryTo solve this problem, we can use the formula for the heat released during the solidification of a substance:
Q = m * Lf
where Q is the heat released, m is the mass of the substance, and Lf is the heat of fusion of the substance.
In this case, Q = 157 kJ, m = 5.00 kg, and Lf = 11.3 kJ/kg.
We also need to use the formula for the heat absorbed or released during a temperature change:
Q = m * c * ΔT
where Q is the heat absorbed or released, m is the mass of the substance, c is the specific heat of the substance, and ΔT is the change in temperature.
We can use this formula to calculate the heat released as the mercury cools from its original temperature to its melting point, and then use the formula for solidification to calculate the heat released as the mercury solidifies.
Let T be the original temperature of the mercury.
The heat released as the mercury cools from its original temperature to its melting point is:
Q1 = m * c * (T - 234)
The heat released as the mercury solidifies is:
Q2 = m * Lf
The total heat released is:
Q = Q1 + Q2 = m * c * (T - 234) + m * Lf
Substituting the values given in the problem, we get:
157 kJ = 5.00 kg * 140 J/kg . K * (T - 234) + 5.00 kg * 11.3 kJ/kg
Simplifying and solving for T, we get:
T = 260.6 K
Therefore, the original temperature of the mercury was 260.6 K.
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Within the living area of the colony, what atmospheric gases must be present on Venus?
Humans would need a breathable environment like that on Earth in the living section of a colony on Venus in order to survive. Nitrogen, oxygen, and trace amounts of other gases, such as carbon dioxide, make up the majority of the atmosphere on Earth.
What gases are present in Venus' atmosphere?The clouds are made of sulfuric acid, and the atmosphere is primarily carbon dioxide, the same gas that causes the greenhouse effect on Venus and Earth. And the heated, high-pressure carbon dioxide acts corrosively at the surface.
What gases are found in Mars' and Venus' atmospheres?For instance, compared to Earth, which has 99% nitrogen and oxygen in its atmosphere, Venus and Mars both contain more than 98% carbon dioxide and nitrogen.
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A Carnot Engine operates between two heat reservoirs. The cold reservoir is maintained at 20.0 °C. What temperature must the hot reservoir be at in order for the efficiency of the engine to be 20.0 %?
A heat engine with a 65.0% Carnot efficiency is currently being developed. Between a reservoir that is 25.00C and one that is 3750C, a heat engine is operational.
What is the formula for Carnot efficiency ?The equation is: Carnot efficiency is equal to 1 - Tc/Th, wherein Tc is the cycle's cold end temperature and Th is its hot end temperature. In other words, efficiency is equal to one minus the difference between the hot and cold temperatures.
Explanation: The cold reservoir's temperature is TL=20C=20+273=293K. T L = 20 ∘ C = 20 + 273 = 293 K .
A Carnot cycle running between both of these two reservoirs has a thermal efficiency of = 1 TC/TH. This value exceeds the value of the Otto cycle, which is operating between similar reservoirs by a large margin.
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