The electric field due to a charged rod of length 2a with total charge q uniformly distributed along its length, placed along the z axis with its center at the origin.
To find the electric field everywhere due to the charged rod, we can use Coulomb's law and the principle of superposition. The electric field due to a small segment of the rod at a point P in space is given by:
dE = k dq / r^2
where k is Coulomb's constant, dq is the charge on the segment, r is the distance from the segment to the point P, and dE is the electric field due to the segment. To find the total electric field at P, we integrate this expression over the entire length of the rod, from -a to +a, as follows:
E = ∫ dE = k ∫ dq / r^2
where the integral is taken over the length of the rod. We can express dq in terms of the charge density λ, which is the charge per unit length of the rod, as dq = λ ds, where ds is an infinitesimal length element along the rod. We can also express r in terms of the distance s from the origin to the segment, as r = √(s^2 + z^2), where z is the distance from the segment to the z axis.
Substituting these expressions into the integral, we obtain:
E = k ∫ dq / r^2 = k ∫ λ ds / (s^2 + z^2)
To evaluate this integral, we use a trigonometric substitution, letting s = z tan θ. Then, ds = z sec^2 θ dθ, and the limits of integration become -arctan(a/z) and arctan(a/z). Substituting these expressions into the integral, we obtain:
E = k λ z ∫_{-arctan(a/z)}^{arctan(a/z)} dθ / (1 + (a/z)^2 tan^2 θ)
This integral can be evaluated using the substitution u = tan θ, which gives:
E = k λ z / (2πε_0) ∫_{-a/z}^{a/z} du / (1 + u^2)
where ε_0 is the permittivity of free space. This integral can be evaluated using the inverse tangent function, giving:
E = k λ z / (2πε_0) [arctan(a/z) - arctan(-a/z)]
Simplifying this expression using the identity arctan(-x) = -arctan(x), we obtain:
E = k λ a / (2πε_0 z√(a^2 + z^2))
This is the expression for the electric field due to a charged rod of length 2a with total charge q uniformly distributed along its length, placed along the z axis with its center at the origin. The electric field points radially away from the rod, and its magnitude decreases as 1/r^2 with distance from the rod
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A transport plane takes off from a level landing field with two gliders in tow, one behind the other. The mass of each glider is 700 , and the total resistance (air drag plus friction with the runway) on each may be assumed constant and equal to 2800 . The tension in the towrope between the transport plane and the first glider is not to exceed 12000 . Part A If a speed of 40 is required for takeoff, what minimum length of runway is needed? Express your answer using two significant figures. Part B What is the tension in the towrope between the two gliders while they are accelerating for the takeoff? Express your answer using two significant figures. Please try to explain how you get to the answer. Don't just give the answer alone. Thank you!
The maximum length of runway needed and tension in the towrope will be 175.05 m and 5999N.
For solving this question we will use the laws of Kinematics as well as the Newton's Laws of Motion. According to the third law of Kinematics
v² = u² + 2aS ; where v is the final velocity, u is the initial velocity, a is the acceleration and S is the displacement.
According to Newton's Laws of Motion we know that the net force is equal to product of mass and acceleration that is
F = ma ; where F is net force, m is mass of the body and a is the acceleration.
Now, form the free body diagram of the gliders, we balance the forces by Newton's law of motion as:
For glider 1 the forces in x axis will be:
T₁ - T₂ - f = ma ......(1)
where T₁ and T₂ are tensions on glider 1 and 2 respectively and f is the frictional force.
In y axis the forces will be:
N₁ - W = 0 ; where N₁ is the normal on first glider and W is the weight due to gravity.
For glider 2 the forces in x axis will be:
T₂ - f = ma ......(2)
where T₂ is tensions on glider 2 and f is the frictional force.
In y axis the forces will be:
N₂ - W = 0 ; where N₂ is the normal on second glider and W is the weight due to gravity.
From equation (1) and (2) we get
T₁ - 2f = 2ma
a = T₁ - 2f/2m
a = 12000 - 2(2800)/2(700)
a = 6400/1400
a = 4.57 m/s²
Now from laws of Kinematics we have
v² = u² + 2aS; here the initial velocity is zero so u = 0 and v = 40 m/s
(40)² = 0 + 2 × 4.57 × S
S = 1600/9.14
S = 175.05 m
Now for the tension in the second rope of glider we use equation (2) that is
T₂ - f = ma
T₂ = ma + f
T₂ = 700 × 4.57 + 2800
T₂ = 3199 + 2800
T₂ = 5999 N
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watch the tsunami arrival topic of the tsunami initiation animation, and pay close attention to see what happens along the beach just before the wave hits.
1. As the Tsunami wave approaches the beach, water levels will start to rise, and the ocean may appear to recede away from the shoreline.
2. The ocean may become very calm, and the surface may appear glassy.
3. Strong currents may be felt, and debris such as seaweed, branches, and shells may be seen rushing away from the shoreline.
4. Animals such as birds may be seen fleeing from the shoreline, and a loud roar may be heard as the wave approaches.
5. The wave will eventually reach the beach, and the water levels will quickly rise to a high level. The wave will then crash into the shore, causing destruction and flooding.
What is a Tsunami?A Tsunami is a powerful series of ocean waves caused by an underwater disturbance, such as an earthquake, volcano, or landslide. These waves travel across the ocean at high speeds and can reach up to hundreds of feet in height when they reach coastlines, causing severe flooding and destruction. Tsunamis are also known as seismic sea waves, and they can occur anywhere in the world.As the wave energy travels, it causes the sea level to rise and creates a “wave” that can travel up to 500 miles per hour. Tsunamis can reach heights of up to 100 feet and can cause extensive damage to coastal areas. The strength of the wave depends on the intensity of the earthquake or eruption that caused it.
Tsunamis usually arrive onshore suddenly and without warning, leaving little time for people to evacuate to safety and are often accompanied by strong currents and large amounts of debris, making them even more destructive.
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Consider the two vectors A and B. You know the magnitudes of these vectors (lmand 10 m respectively), but you do not know anything about their directions ca ment Status here for 9 H a vector is defined to be the sum of these two vectors CHA+B) which of the following are true about the magnitude of C7 Choose all that apply C. cannot be determined Grade Summary Cain
A. The magnitude of C can be determined.
D. The magnitude of C is between 1m and 10m.
When two vectors are added, the magnitude of the resulting vector can be found using the law of cosines. For the vectors A and B, the magnitude of their sum C is given by:
|C|² = |A|² + |B|² + 2|A||B|cosθ,
where θ is the angle between the vectors A and B. Since the directions of A and B are unknown, θ could take any value between 0 and 180 degrees. However, the minimum value of cosθ is -1, which occurs when θ = 180 degrees. Therefore, the minimum magnitude of C is:
|C|min = |A| - |B| = 1 m - 10 m = 9 m.
The maximum value of cosθ is 1, which occurs when θ = 0 degrees. Therefore, the maximum magnitude of C is:
|C|max = |A| + |B| = 1 m + 10 m = 11 m.
Therefore, the magnitude of C is between 1m and 10m, and it can be determined.
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correct question
Which of the following statements are true about the magnitude of the vector C, which is defined as the sum of two given vectors A and B with magnitudes 1m and 10m respectively, but unknown directions? (Choose all that apply.)
A. The magnitude of C can be determined.
B. The magnitude of C is less than 10m.
C. The magnitude of C is less than 1m.
D. The magnitude of C is between 1m and 10m.
E. The magnitude of C is greater than 11m.
A SOLID OF MASS 1.3KG Suspended by a spring Is Completely Immersed in H₂0. If the tension in the spring is 6N. Calculate: a. upthrust on the solid b. the volume of the solid c. Density (take g=10m/s², density of H₂0= 1000kg/m³)
a. Upthrust on the solid:
[tex]Upthrust = volume of solid * density of fluid * g = 1000 kg/m^3 * volume of solid * 10 m/s^2[/tex]
b. Volume of the solid:
[tex]volume = mass/density = 1.3 kg / (1000 kg/m^3) = 1.3 x 10^-3 m^3[/tex]
c. Density of the solid:
So,[tex]density = mass/volume = 1.3 kg / (1.3 x 10^-3 m^3) = 1000 kg/m^3[/tex]
What is upthrust?Upthrust is the upward force exerted on an object immersed in a fluid. It is equal to the weight of the fluid displaced by the object and acts in the opposite direction to gravity. Upthrust helps to counteract the weight of the object and keep it afloat.
a. The upthrust on an object immersed in a fluid is equal to the weight of fluid displaced by the object. The weight of fluid displaced can be calculated using the formula:
Weight of fluid = volume of fluid * density of fluid * g
Since the solid is completely immersed in water, the volume of the fluid displaced is equal to the volume of the solid. The density of water is given as 1000 kg/m^3, and the acceleration due to gravity is given as[tex]10 m/s^2.[/tex]
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HELPPP A wave with an amplitude of 0.25m intereferes with a wave with an amplitude of 1m. What
is the resulting amplitude? Draw the waves before the interference and after the
interference in the show your work section.
The resulting amplitude of the two waves is 1.25 m
What happens when two waves of different amplitudes interfere?When two waves of different amplitudes interfere, the resulting wave pattern is determined by the relative phase and amplitude of the two waves. If the two waves are in phase, meaning that their peaks and troughs line up, they will reinforce each other and produce a wave with a larger amplitude. This is known as constructive interference.
In this case the amplitude of the resulting wave would be a combination of two amplitudes of the waves and that would be 1.25 m
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Derive the expression for the RMS pressure of a square wave and a triangular wave. Compare the value of the RMS pressure for sinusoidal, square and triangular waves. Assume all three waves have the same period and amplitude and all have zero mean values
Answer:
Explanation:
The Root Mean Square (RMS) pressure of a waveform can be defined as the square root of the average of the square of the pressure values over one period of the wave. The RMS pressure provides a measure of the effective pressure of a waveform and is often used to compare the strength of different waveforms.
For a square wave, the RMS pressure can be found as follows
P_RMS = sqrt((1/T) * ∫_0^T (P_square(t))^2 dt)
Where T is the period of the waveform and P_square(t) is the pressure value of the square wave at time t. The integral is taken over one period of the waveform.
For a triangular wave, the RMS pressure can be found as follows:
P_RMS = sqrt((1/T) * ∫_0^T (P_triangular(t))^2 dt)
Where T is the period of the waveform and P_triangular(t) is the pressure value of the triangular wave at time t. The integral is taken over one period of the waveform.
The RMS pressure of a sinusoidal wave is given by the equation:
P_RMS = (A/sqrt(2))
Where A is the amplitude of the waveform.
Comparing the RMS pressures of the three waveforms, it can be seen that the RMS pressure of a sinusoidal wave is (A/sqrt(2)) which is smaller than the RMS pressure of a square wave or a triangular wave. This is because the square wave and triangular wave have sharper transitions from positive to negative values compared to the sinusoidal wave, which results in higher peak pressure values and hence a higher RMS pressure.
It is worth noting that while the RMS pressures of the three waveforms are different, they provide a measure of the effective pressure of the waveforms and can be used to compare their strengths.
Here is a definition of each variable used in the equation:
P_RMS: The Root Mean Square (RMS) pressure of the waveform. It is a measure of the effective pressure of the waveform.
T: The period of the waveform. It is the time it takes for the waveform to repeat itself.
P_square(t): The pressure value of the square wave at time t.
P_triangular(t): The pressure value of the triangular wave at time t.
∫_0^T: The integral symbol. It represents the sum of the pressure values over one period of the waveform, from time t = 0 to time t = T.
A: The amplitude of the waveform. It is the maximum positive or negative deviation from the zero line of the waveform.
sqrt: The square root symbol. It is used to find the square root of a value.
(A/sqrt(2)): The RMS pressure of a sinusoidal wave. It is calculated as the amplitude divided by the square root of 2.
the bolts on the cylinder head of an engine require tightening to a torque of 84 m n. if a wrench is 28 cm long, what force perpendicular to the wrench must the mechanic exert at its end
300 N of force must be applied by the mechanic perpendicular to the end of the wrench.
The SI unit of force is what?The SI unit of force is the newton, denoted by the letter N. Base units that are pertinent to force are: The symbol for the length unit of a metre is m. the kilogramme (kg), a unit of mass. S represents the second, a measure of time.
The following formula can be used to resolve this issue:
Torque equals force times distance times sin (angle), where:
Torque is the 84 mN desired torque.
Force is the unknowable force that we must discover.
Distance is the length of the wrench in meters, which is 0.28 m
Angle is the angle between the wrench and the direction of the force, which is 90 degrees for a perpendicular force (sin(90) = 1)
Plugging in the values, we get:
84 mN = Force x 0.28 m x 1
Solving for Force, we get:
Force = 84 mN / 0.28 m
Force = 300 N
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true/false. living cells contribute to the turbidity of a culture, but cells also contribute to the turbidity of a culture, which is a disadvantage of the indirect spectrophotometer method.
The given statement " Living cells contribute to the turbidity of a culture, and this contribution can be a disadvantage of the indirect spectrophotometer method, is True.
The indirect spectrophotometer method, which measures the turbidity of a culture to estimate cell density, assumes that the only contributor to turbidity is the cells themselves. However, other factors such as debris, bubbles, and extracellular materials can also contribute to the turbidity, leading to inaccuracies in cell density measurements. In microbiology, turbidity is a measure of the cloudiness or haziness of a liquid culture, and it is often used as an indirect measure of cell density. The more cells there are in the culture, the more turbid it will appear.
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Two metal spheres are connected by a metal wire that has a switch in the middle. Initially the switch is open. Sphere 1, with the larger radius, is given a positive charge Sphere 2, with the smaller radius, is neutral. Then the switch is closed. Afterward, Sphere 1 has charge Qi, is at potential Vi, and the electric field strength at its surface İs E1-The values for Sphere 2 are Q2. V2, and E2. a) Is Vi larger than, smaller than, or equal to V2? Explain b) Is Qi larger than, smaller than, or equal to Qa? Explain. c) Is Ei larger than, smaller than, or equal to E2? Explain.
(1) The potential difference between the two spheres will cause charges to flow from Sphere 1 to Sphere 2 until their potentials are equal.(2) Since the total charge is conserved, the total charge on both spheres after the switch is closed will be equal to the charge on Sphere 1 before the switch is closed.
a) The potential difference between the two spheres will cause charges to flow from Sphere 1 to Sphere 2 until their potentials are equal. Since Sphere 1 has a positive charge, electrons will flow from Sphere 2 to Sphere 1 until their potentials are equal. This means that Sphere 1 will end up with a lower potential than its initial potential and Sphere 2 will end up with a higher potential than its initial potential. Therefore, Vi is smaller than V2.
b) Since the total charge is conserved, the total charge on both spheres after the switch is closed will be equal to the charge on Sphere 1 before the switch is closed. Therefore, the final charge on Sphere 2, Q2, will be equal to the initial charge on Sphere 1. Hence, Qi is equal to Q2.
c) The electric field strength at the surface of a charged conductor is proportional to the surface charge density. Since Sphere 1 has a larger radius than Sphere 2, it has a larger surface area and therefore a lower surface charge density. This means that E1 will be smaller than E2. Additionally, as charges move from Sphere 1 to Sphere 2, the surface charge density on Sphere 1 decreases, leading to a decrease in E1. Therefore, E1 will be smaller than E2 after the switch is closed.
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1)Depending on the amount of water in the lake, the salinity of an ocean is 34.5 0/00, If this were the case, 1000g of this would consist of____ grams of water and ____grams of salt.
2)Describe how salinity and temperature effect the density of sea water:
(1) If this were the case, 1000g of this would consist of 965.5 grams of water and 34.5 grams of salt.
(2) Increase in either salinity or temperature leads to an increase in the density of seawater and vice versa.
What is the amount of water and salt contained?The salinity of seawater is typically measured in "parts per thousand" (ppt), which means that for every 1000 parts (by weight) of seawater, 34.5 parts are salt.
So it implies that in 1000g of seawater with a salinity of 34.5 ppt, there would be 34.5g of salt and 965.5g of water.
Salinity has a direct effect on the density of seawater because the dissolved salts in seawater increase its mass, which in turn increases its density.
Temperature also affects the density of seawater because as the temperature increases, the water molecules move faster and the spaces between them increase, leading to a decrease in the density of the water.
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A box slides down an inclined plane 37° above the horizontal. The mass of the block, m, is 35 kg, the coefficient of kinetic friction is 0.3 and the length of the ramp, d, is 8 m. (a) How much work is done by gravity? (b) How much work is done by the normal force? (c) How much work is done by friction? (d) What is the total work done?(1690J; 0; -671J; 1019J)
part a.
the work done by gravity is approximately 1690 J.
part b.
the work done by the normal force is 0.
part c.
the work done by friction is approximately -671 J
part d.
the total work done is approximately 1019 J
What is work done?work done is described as the multiplication of magnitude of displacement d and the component of the force that is in the direction of displacement.
For part a, the work done by gravity can be found using the formula:
W_gravity = mgh
h = dsin(37°) = 8sin(37°) = 4.83 m
W_gravity = (35 kg) * (9.81 m/s^2) * (4.83 m) ≈= 1690 J
In conclusion, the same pattern can be followed to calculate for b, c and d.
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. HELP
Which are characteristics of bryophytes? (Select all that apply.)
Most of them are vascular plants.
Most of them grow tall.
Most of them need water to help reproduce.
Most of them live in shady, moist, or humid areas.
Answer: Most of them need water to help reproduce & Most of them live in shady, moist, or humid areas.
Explanation:
Bryophytes are non-vascular plants, meaning they do not have specialized tissue for transporting water and nutrients throughout their bodies. Instead, they absorb nutrients and water from the environment. Bryophytes are usually short-lived and don't grow tall, and they prefer to live in shady, moist, or humid areas because they require water to help them reproduce.
suppose that earth's spin would suddenly reverse direction, but the direction of earth's motion around the sun was preserved. which of the following changes would you expect to observe?
The east would be the location of the Sun's rising and setting are the changes would you anticipate seeing.
Annual motion is the term used to describe variations in the position of the stars in the sky.Annual motion, which is a direct result of the Earth's rotation around the sun, is the visible yearly move of the stars as seen from Earth. The ecliptic is a line on the surface of a sphere around which the revolves around the sun 360 degrees each year.
The stars seem to rise with in east as set in the west, but why is that so?We, the watchers on Earth, whirl past this foreground of far-off stars as the planet rotates on its axis. The stars seem to travel throughout our darkness of space from east to west as Earth spins for the same reason.
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Can anyone solve this
Answer:
sorry I'm not smart
Explanation:
A car drives straight off the edge of a cliff that is 58 m high. The police at the scene of the accident note that the point of impact is 0.136 km from the base of the cliff. How long did it take to hit the ground?
It will take the car 3.2 seconds to hit the ground.
Using the kinematic equation,
y = yo + vot + 1/2a*t^2
where y is the displacement (in this case, y = -58 m), yo is the initial displacement (yo = 0), vo is the initial velocity (vo = 0), a is the acceleration due to gravity (a = -9.81 m/s^2), and t is the time we want to find.
We can solve for t by rearranging the equation:
t = sqrt(2*y/a)
t = sqrt(2*(-58)/(-9.81))
t = 3.2 seconds (to two significant figures)
Time taken is 3.2 seconds.
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What part of acceleration formula represents the time has passed?
The general formula for acceleration is:
[tex]a = (v_f - v_i) / t[/tex]
where a is the acceleration, [tex]v_f[/tex] is the final velocity[tex], v_i[/tex] is the initial velocity, and t is the time interval during which the change in velocity occurs.
What is acceleration?Acceleration is the rate of change of an object's velocity over time. It is a vector quantity that is defined as the change in velocity divided by the time interval during which the change occurs. Acceleration can be positive, negative, or zero, and it is measured in units of meters per second squared [tex](m/s^2).[/tex]
To find the time that has passed given the acceleration formula, we would need to rearrange the formula to solve for time "t" in terms of the other variables. For example, if we know the initial velocity, final velocity, and acceleration, we can use the formula to find the time interval during which the velocity changes.
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physics conclusion question:explain why the reading on a scale would be less after leaving the top floor and heading downward.
The reading on a scale could be less after leaving the top floor and heading downward due to the effect of gravity on the body.
What is gravity ?Gravity is a fundamental force of nature that exists between all objects that have mass or energy. It is the force that pulls two objects towards each other, and it is what keeps objects like planets, stars, and galaxies in their orbits.
The force of gravity is directly proportional to the masses of the objects and inversely proportional to the square of the distance between them. This means that the greater the mass of the objects and the closer they are to each other, the greater the force of gravity between them.
Gravity is responsible for many phenomena that we observe in our daily lives, such as keeping us and other objects on the surface of the Earth, causing tides in the ocean, and making objects fall to the ground when we drop them. It is also a key concept in the fields of astronomy and astrophysics, as it is what allows us to understand the motion and behavior of celestial objects in the universe.
Hence, The reading on a scale could be less after leaving the top floor and heading downward due to the effect of gravity on the body.
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space station consists of three modules, connected to form an equilateral triangle of side length 82.0 m. Suppose 100 people, with an average mass of 75.0 kg each, live in each capsule and the mass of the modules is negligible compared to the mass of the people. At the current rotational rate the effec- tive acceleration of gravity is g/2. (a) What angular momentum of the system? (b) If the modules are pulled closer what should happen to the rota- tional rate? Explain. (c) What distance between the modules would give an effective acceler- ation of gravity equal to g? A
The angular momentum of the system is 225,540 kg [tex]m^{2} /s[/tex] and the distance between the modules that would give an effective acceleration of gravity equal to g is 24.8 m.
(a) The angular momentum of the system is given by L = Iω.
The moment of inertia of an equilateral triangle of mass M and side length a is I = (1/6)M[tex]a^{2}[/tex]
The mass of each capsule is 100 people × 75.0 kg/person = 7,500 kg.
Therefore, the total mass of the system is M = 3 × 7,500 kg = 22,500 kg.
The radius of the circle is half the side length of the equilateral triangle, so r = 41.0 m.
Therefore, the angular velocity of rotation is given by ω = (g/2)/r = 0.120 rad/s.
Using these values, the angular momentum of the system is L = (1/6)M[tex]a^{2}[/tex]ω = (1/6) × 22,500 kg × (82.0 [tex]m^{2}[/tex]) × 0.120 rad/s = 225,540 kg[tex]m^{2} /s[/tex]
(b) If the modules are pulled closer together, the moment of inertia of the system will decrease, because the mass of the system will be closer to the axis of rotation. According to the conservation of angular momentum, if the moment of inertia decreases, the angular velocity of rotation must increase in order to keep the angular momentum constant. Therefore, pulling the modules closer together would increase the rotational rate of the space station.
(c) The effective acceleration of gravity is given by g_eff = (g/2) + ([tex]v^{2}[/tex]/r), where v is the linear velocity of the space station. At the current rotational rate, the linear velocity of the space station is v = rω = 41.0 m × 0.120 rad/s = 4.92 m/s.
g.eff = (g/2) + ([tex]v^{2}[/tex]/r) = g
([tex]v^{2}[/tex]/r) = (g/2)
r = (2[tex]v^{2}[/tex])/g
Substituting the values for v and g, we get:
r = (2 × [tex]4.92m/s ^{2}[/tex])/9.81 [tex]m/s^{2}[/tex] = 24.8 m
Therefore, the distance between the modules that would give an effective acceleration of gravity equal to g is 24.8 m.
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If a lining is ciliated, what is it covered in?
mucous
O
Oskin
Ogrooves
hair
If a lining is ciliated, then it is covered in hair. Thus, the correct option is D.
What is Ciliated lining?Cilia are the small, slender, hair-like structures which are present on the surface of all the mammalian cells. They are primitive in nature and could be single or many types.
Cilia play a major role in the locomotion of body parts. Cilia are also involved in the mechanoreception. The organisms which possess the cilia are known as ciliates.
The bronchus present in the lungs are lined with the hair-like projections called cilia which move the microbes and debris up and out of the airways in the respiratory tract. Scattered throughout the cilia are the goblet cells which secrete mucus that helps in protection of the lining of the bronchus and trapping the microorganisms.
Therefore, the correct option is D.
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Answer:
It's hair!
Explanation:
I got it right on me test~
What is the average force of gravitation between Mercury and the Sun?
Answer:
The gravitational force between the Sun (mass = 1.99 × 1030 kg) and Mercury (mass = 3.30 × 1023 kg) is 8.99 × 1021 N
Explanation:
Answer:
Average force of gravitation between Mercury and the Sun is approximately 3.54 x 10^20 N.
Explanation:
The following equation determines the gravitational force between two objects:
F = G * (m1 * m2) / d^2
In this equation, F is the gravitational force, G is the gravitational constant (G = 6.67 x 10-11 Nm2/kg2), m1 and m2 are the objects' masses, and d is the space between their centres.
We need the masses of Mercury and the Sun as well as their typical separation in order to compute the average gravitational force between them.
The Sun's mass is roughly 1.989 x 1030 kg, while Mercury's mass is roughly 3.285 x 1023 kg. Mercury and the Sun are typically separated by around 57.9 million kilometres (0.39 astronomical units).
With these values entered into the formula, we obtain:
F is equal to G * (3.285 x 1023 kg) * (1.989 x 1030 kg) * (57.9 x 106 m) * 2
F is equal to G * (3.285 x 1023 kg) * (1.989 x 1030 kg) * (57.9 x 106 m) * 2
F = 3.54 x 10^20 N
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An 8.90-kg block of ice, released from rest at the top of a 1.15-meter long frictionless ramp, slides downhill, reaching a speed of 2.87 m/s at the bottom.
What would be the speed of the ice at the bottom if the motion were opposed by a constant friction force of 11.0 N parallel to the surface of the ramp?
I have already solved the angle of the ramp, it is 21.4 degrees.
Answer:
2.32 m/s
Explanation:
If an 8.90 kg block of ice slides down a 1.15 m frictionless ramp to reach a speed of 2.87 m/s, you want to know its final speed if there were friction opposing the motion with a force of 11.0 N.
EnergyThe kinetic energy at the bottom of the frictionless ramp is ...
KE = 1/2mv²
KE = 1/2(8.90 kg)(2.87 m/s)² = 36.654205 J
FrictionWhen friction is introduced, the work done to oppose the friction is ...
W = Fd
W = (11 N)(1.15 m) = 12.65 J
Hence the remaining energy of the block at the bottom of the ramp with friction is ...
KE' = 36.654205 -12.65 J = 24.004205 J
This corresponds to a speed of ...
v = √(2·KE/m) = √(2·24.004205/8.9) ≈ 2.32 . . . . m/s
The speed at the bottom of the ramp with friction is about 2.32 m/s.
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Additional comment
We can find the slope of the ramp by equating the ending kinetic energy to the beginning potential energy. As you can see, that is not relevant to the problem, since the opposing force is parallel to the ramp.
Adults are not born knowing what they like to do.
A. True
B. False
estimate the radiation pressure due to a 75-w bulb at a distance of 8.0 cm from the center of the bulb. estimate the force exerted on your fingertip if you place it at this point.
At a height of 8.0 cm from the bulb's center, the radiation pressure caused by a 75-w bulb is calculated as current=watts divided by voltage=75/120=0.625 amperes.
How do you define radiation pressure class?The mechanical stress that is applied to any surface as a result of the electrical waves and the object exchanging momentum is known as radiation pressure. When photons hit the object's surface in this instance, momentum is transferred.
What does radiation pressure look like in practice?The development of cometary tail, in which dust particles ejected by cometary nuclei are driven by solar radiation into distinctive trailing patterns, is another visually striking example of radiation pressure. With the development of, it became possible to apply radiation pressure to terrestrial environments.
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what is a biotic animal that lives in two terrestrial ecosystems
Answer: A bear
Explanation:
I think it is a bear because in the North pole it swims to get food and walks in land to hide.
Sally was removing her nail polish to get ready for a dance. She was also drinking a bottle of water. The doorbell rang and she rushed to answer it, leaving the open bottle of nail polish remover (acetone) and the bottle of water open. Sally forgot about them until the next morning and when she checked, the nail polish remover (acetone) was empty and the water looked untouched.
Sally believes the particles in water stick together more. In terms of your knowledge of the strength of electrical forces and the structure of substances, explain Sally's statement.
The visible part of the electromagnetic spectrum can be divided into seven color bands of Red, Orange, Yellow, Green, Blue, Indigo, and Violet (from long to short wavelength). A single photon of which of these colors has the greatest amount of energy?
*e. Violet mnemonic: "ROY" G "BIV"
A single photon of violet color has the greatest amount of energy among the visible colors of the electromagnetic spectrum. This is because violet light has the shortest wavelength and the highest frequency among the visible colors.
According to the equation E = hf, where E is the energy of a photon, h is Planck's constant, and f is the frequency of the radiation ,Because the wavelengths of electromagnetic radiation are inversely proportional to their frequencies, according to the equation c = λf, where c is the speed of light, λ is the wavelength of the radiation, and f is its frequency. Therefore, photons of violet light, having the highest frequency, also have the highest energy.
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You and your best buddy have to carry two crates up a flight of stairs. Your crate is twice as heavy as your buddy's. Your buddy is doing ______________ work as you are doing.
half I think that's just a guess though
Which of the following sets of quantum numbers represents the highest energy of an atom?A. n = 3, l = 0, m = 0, s = +1/2B. n = 3, l = 1, m = 1, s = +1/2C. n = 3, l = 2, m = 1, s = +1/2D. n = 4, l = 0, m = 0, s = +1/2
(c) n=3,1=2,m=1,s=+1/2 this set of quantum number represents the highest energy of atom
Correct option is C)
The sets of the quantum numbers and the corresponding orbitals are as shown below.
a)n=3,l=0 means 3s− orbital
b)n=3,l=1 means 3p− orbital
c)n=4,l=2 means 4d− orbital
d)n=4,l=0 means 4s− orbital
Increasing order of energy among three orbitals is 3s<3p<4s<4d
∴4d has highest energy.
Hence, the set c of quantum numbers (n=4,l=2,m=1,s=+1/2) represents the highest energy of an atom.
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a 1.2 kg pebble is stuck in a tread of a .76 m
Answer:
Fc=mv2/r v=√(Fcr/m) v=√[(3.6 N)(0.38 m)/(0.0012kg)] v=33.76388603 m/s v=38 m/s
Explanation:
Given that the human body is mostly made of water, estimate the total amount of positive charge in a 70 kg person. Express your answer to two significant figures and include the appropriate units.
The estimated total amount of positive charge in a 70 kg person is 5.88 Coulombs (C).
Since the human body is mostly made of water, we can assume that the total amount of positive charge is equal to the total amount of sodium ions (Na+) and other positively charged ions in the body.
The concentration of sodium ions in the human body is approximately 140 milliequivalents per liter (mEq/L), which is equivalent to 0.140 moles per liter (mol/L).
Assuming that the total volume of water in a 70 kg person is approximately 42 liters, we can estimate the total amount of sodium ions in the body as follows:
Total amount of sodium ions = concentration x volume of water
Total amount of sodium ions = 0.140 mol/L x 42 L
Total amount of sodium ions = 5.88 mol
Since each sodium ion has a charge of +1, the total amount of positive charge in a 70 kg person is also 5.88 C.
Therefore, the estimated total amount of positive charge in a 70 kg person is 5.88 Coulombs (C).
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