The formula for the EMF induced in the wire as it grows is: EMF = -πG(Do2 + 2DoGt + (Gt)2)/4
The EMF induced in the wire is given by Faraday's law of induction, which states that EMF induced in a circuit is equal to the negative rate of change of magnetic flux through the circuit. Therefore, the EMF induced in the wire can be expressed as:
EMF = -dΦ/dt
where Φ is the magnetic flux through the wire loop. Since the magnetic flux through the wire loop is proportional to the area of the wire loop, we can express this as:
EMF = -d(πD2/4)/dt
Substituting in the expression for D(t), we get:
EMF = -πG(Do + Gt)2/4
Therefore, the formula for the EMF induced in the wire as it grows is:
EMF = -πG(Do2 + 2DoGt + (Gt)2)/4
b. The resistance of the wire is given by Ohm's law as:
R = ρL/A
where ρ is the resistivity of the wire, L is the length of the wire, and A is the cross-sectional area of the wire. Since the wire is a loop, the length is equal to the circumference of the loop, and the cross-sectional area is equal to the area of the wire loop. Therefore, the resistance can be expressed as:
R = ρ(πD/To)/(πD2/4)
Substituting in the expression for D(t), we get:
R = ρTo/(π(Do + Gt)2/4)
The current in the wire is given by Ohm's law as:
I = V/R
where V is the voltage across the wire. Since the voltage across the wire is equal to the EMF induced in the wire, we can substitute the expression for the EMF in the equation above to get:
I = (πG(Do2 + 2DoGt + (Gt)2)/4)/(ρTo/(π(Do + Gt)2/4))
Therefore, the formula for the current in the wire as a function of time is:
I = (Do2 + 2DoGt + (Gt)2)/(Toρ)
c. The graph of I(t) would be a parabola that is increasing as t increases. The graph will start at I(0) = Do2/(Toρ) and will rise as t increases. The rate of increase will depend on the value of G; the higher the value of G, the faster the current increases. The graph will reach a maximum value at t = (Do/G) and will then decrease as t continues to increase. The maximum value of the current is given by I = (Do2 + 2Do2/G + (Do/G)2)/(Toρ). Beyond t = (Do/G), the graph will decrease, eventually reaching I(∞) = 0.
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what is climate change?
What Is Climate Change?
Climate change refers to long-term shifts in temperatures and weather patterns. These shifts may be natural, such as through variations in the solar cycle. But since the 1800s, human activities have been the main driver of climate change, primarily due to burning fossil fuels like coal, oil and gas.
Burning fossil fuels generates greenhouse gas emissions that act like a blanket wrapped around the Earth, trapping the sun’s heat and raising temperatures.
Examples of greenhouse gas emissions that are causing climate change include carbon dioxide and methane. These come from using gasoline for driving a car or coal for heating a building, for example. Clearing land and forests can also release carbon dioxide. Landfills for garbage are a major source of methane emissions. Energy, industry, transport, buildings, agriculture and land use are among the main emitters.
The Earth is feeling the heat.
Greenhouse gas concentrations are at their highest levels in 2 million years
And emissions continue to rise. As a result, the Earth is now about 1.1°C warmer than it was in the late 1800s. The last decade (2011-2020) was the warmest on record.
Many people think climate change mainly means warmer temperatures. But temperature rise is only the beginning of the story. Because the Earth is a system, where everything is connected, changes in one area can influence changes in all others.
The consequences of climate change now include, among others, intense droughts, water scarcity, severe fires, rising sea levels, flooding, melting polar ice, catastrophic storms and declining biodiversity.
The Earth is asking for help.
People are experiencing climate change in diverse ways
Climate change can affect our health, ability to grow food, housing, safety and work. Some of us are already more vulnerable to climate impacts, such as people living in small island nations and other developing countries. Conditions like sea-level rise and saltwater intrusion have advanced to the point where whole communities have had to relocate, and protracted droughts are putting people at risk of famine. In the future, the number of “climate refugees” is expected to rise.
Every increase in global warming matters
In a series of UN reports, thousands of scientists and government reviewers agreed that limiting global temperature rise to no more than 1.5°C would help us avoid the worst climate impacts and maintain a livable climate. Yet policies currently in place point to a 2.8°C temperature rise by the end of the century.
The emissions that cause climate change come from every part of the world and affect everyone, but some countries produce much more than others. The 100 least-emitting countries generate 3 per cent of total emissions. The 10 countries with the largest emissions contribute 68 per cent. Everyone must take climate action, but people and countries creating more of the problem have a greater responsibility to act first.
Photocomposition: an image of the world globe looking worried to a thermometer with raising temperatures
We face a huge challenge but already know many solutions
Many climate change solutions can deliver economic benefits while improving our lives and protecting the environment. We also have global frameworks and agreements to guide progress, such as the Sustainable Development Goals, the UN Framework Convention on Climate Change and the Paris Agreement. Three broad categories of action are: cutting emissions, adapting to climate impacts and financing required adjustments.
Switching energy systems from fossil fuels to renewables like solar or wind will reduce the emissions driving climate change. But we have to start right now. While a growing coalition of countries is committing to net zero emissions by 2050, about half of emissions cuts must be in place by 2030 to keep warming below 1.5°C. Fossil fuel production must decline by roughly 6 per cent per year between 2020 and 2030.
Growing coalition
Adapting to climate consequences protects people, homes, businesses, livelihoods, infrastructure and natural ecosystems. It covers current impacts and those likely in the future. Adaptation will be required everywhere, but must be prioritized now for the most vulnerable people with the fewest resources to cope with climate hazards. The rate of return can be high. Early warning systems for disasters, for instance, save lives and property, and can deliver benefits up to 10 times the initial cost.
We can pay the bill now, or pay dearly in the future
Climate action requires significant financial investments by governments and businesses. But climate inaction is vastly more expensive. One critical step is for industrialized countries to fulfil their commitment to provide $100 billion a year to developing countries so they can adapt and move towards greener economies.
Climate finance
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A cannon is to fire up to 500 m horizontally. What should be the angle of projection, if the shells are fired with a velocity of 100 m/s? (g=10 m/s^2 )
The 15 ° is the the angle of projection, if the shells are fired with a velocity of 100 m/s.
What is angle of projection ?
Angle of projection: The angle created between the projection's direction and the horizontal line drawn there.
What is velocity ?
The velocity of the body or object determines its direction of motion. Speed is frequently a scalar number. In its most basic form, velocity is a vector quantity. It gauges how rapidly a distance changes. It is the pace at which displacement is altering.
Given V=100ms and Range R=500m and g=10m/s²
Let the angle of projection is θ with the horizontal.
Horizontal velocity Vh =Vcosθ=100cosθ
Vertical velocity Vv =Vsinθ=100sinθ
∴ Time of flight = 2Vv/g = 2×100sinθ/g
⇒ Range =Vh ×Time of flight
⇒ 100cosθ×2×100sinθ/g =500 ⇒sin2θ=1/2
⇒2θ=30° ⇒θ=15 °
Therefore, 15 ° is the the angle of projection, if the shells are fired with a velocity of 100 m/s.
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10. A 40 Kg crate (rubber chickens, perhaps?) is pulled across the ice with a rope. A force of 100 N is applied at an angle of 30 degrees with the horizontal to a rope attached to the crate, as shown above. Neglecting friction, calculate the acceleration of the crate. Calculate the upward force the ice exerts on the crate as it is pulled. (2.17m/s/s, 342N)
The acceleration of the crate is 1.82m/s2 and the upward force the ice exerts on the crate as it is pulled is 339.5N
How do you calculate the acceleration and the upward force?The force Fx causing the acceleration is the horizontal component of the pull force F=90 Non the mass m=kg for the angle θ=36∘ to the horizontal.
Fx = F cos36 ∘
=90cos36∘
≈72.81N
According to Newton's second Law, the acceleration a due to the net force Fx=72.81N equals the force divided by the mass m of the crate, i.e.
a = F / m
=72.81 / 40kg
≈1.82m/s2
The upward force mentioned in the question is the normal reaction
N of the ice. It is equal to the weight of the crate mg minus the vertical component Fy of the pull force F i.e.
N = mg − Fy
= mg − F sin36∘
= 40kg*9.81m/s2 − 90sin36∘N
≈339.5N
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a rectangular coil of n turns and of length a and width b is rotated at frequency f in a uniform magnetic field , as indicated in fig. 30-40. the coil is connected to co-rotating cylinders, against which metal brushes slide to make contact. (a) show that the emf induced in the coil is given (as a function of time t) by 2pfnabb sin(2pft) 0 sin(2pft).
ε = 2πfNabB sin2πft = εsin2πft this is the proved equation for the emf induced in the coil as a function of time t.
What does an EMF mean?Electromagnetic radiation-induced electric and magnetic forces. Researchers are examining whether the electromagnetic fields (EMFs) produced by electrical equipment, wireless and cellular cellphones, and power lines might result in cancer or other negative health effects. likewise known as electromagnetic field.
How to prove that emf induced in the coil as a function of time t ?Since, the coil of conducting wire is placed in a magnetic field,
number of turns = N
frequency = f
area = A
now, angular velocity of coil, ω = 2πf
in time t coil is rotated by θ angle, θ = ωt
Magnetic field through coil, φ = ΦB. dA = ΦB.dAcosθ
dA = area of N turns = NA
φ = NABcosθ
After putting value of θ, φ = NABcosωt
ε = dφ/dt
ε = d/dt×NABcosωt
= -NAB [-ωsinωt]
= NABωsinωt
ε = NAB2πft
area of rectangular coil, A = a×b
ε = Nab2πfsin2πft
sin2πft = 1, emf will be maximum
εmax = ε' = NabB2πf
ε = ε'sin2πft
ε = 2πfNabB sin2πft = εsin2πft
Hence proved that the emf induced in the coil is given as a function of time t.
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The diagram shows 2.0-kilgram cart traveling at a constant speed in a horizontal circle of radius 3.0 meters. The magnitude of the centripetal force of the cart is 24 newtons Use this information t0 answer the following question(s). 2.0-kg Cart A What is the speed of the cart shown in the diagram? 3.0 m
The linear speed of the cart is determined as 6 m/s.
What is the speed of the cart?
The speed of the cart is calculated by applying the formula for centripetal acceleration as shown below;
Mathematically, the formula for centripetal acceleration is given as;
a = v² / r
where;
v is the speed of the cartr is the radius of the carta is the centripetal acceleration of the cartv² = ar
v = √ ( ar )
F = ma
a = F / m
a = 24 N / 2 kg
a = 12 m/s²
Substitute the given parameters and solve for the speed of the cart as shown below;
v = √ ( ar )
v = √ ( 12 x 3 )
v = 6 m/s
Thus, the speed of the cart is a function of centripetal acceleration and the radius of the circular path.
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a bottle has a mass of 36.00 gg when empty and 95.94 gg when filled with water. when filled with another fluid, the mass is 89.22 g. Determine the specific gravity of the other fluid.
The specific gravity of the other fluid in the bottle with a mass of 53.22 g is determined to be 0.8879.
The ratio of a material's density to a predetermined reference substance is the substance's specific gravity. If anything has a specific gravity, it will either float or sink. When tested against water, the specific gravity of a solid or liquid is compared; if it is less than one, it will float, and if it is greater than one, it will sink. Then, the specific gravity of a material is given by, [tex]RD = \frac{\rho_{\text{substance}}}{\rho_{\text{reference}}}[/tex].
The mass of water in the bottle is 95.94 g - 36.00 g = 59.94 g. And the mass of another fluid in the bottle is 89.22 g - 36.00 g = 53.22 g. Then,
[tex]\begin{aligned}\text{specific gravity of other fluid}&=\frac{\rho_{\text{fluid}}}{\rho_{\text{water}}}\\&=\frac{\frac{m_f}{V}}{\frac{m_w}{V}}\\&=\frac{m_f}{m_w}\\&=\frac{53.22}{59.94}\\&=0.8879\end{aligned}[/tex]
The answer is 0.8879.
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the speed of light is the fastest anything in the universe can go if it is traveling through space.________ can break that speed limit.
The speed of light is the fastest anything in the universe can go if it is traveling through space. Much faster than light can break that speed limit.
How quickly must you go in order to surpass the speed of light?We can never go faster than light. Or, to be more precise, in a vacuum, we can never travel at the speed of light. In other words, the 299,792,458 m/s upper limit of the universe's speed is the speed at which all other particles must move in order to exist.
What is the light's 3x10 8 speed?In a vacuum, light travels at a speed of 3 108 m/s. About 8 minutes pass before sunlight reaches Earth.
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On a loop the loop a ball of mass m starts from rest a distance 6 R above the table, where R is the radius of the loop. When the ball rolls without friction, at some instant it is right at the top of the loop, a distance of 2 R above the table. At this instant, with what force is it press ing against the track? 1. Zero 2. Because the ball is rolling, it can't exert a force on anything. 3. m g 4. The ball will not be in contact with the track at this point, since it does not have quite enough speed to reach it 5. 3 mg 6. 7m g 7. 2m g 8. 5 m g 9. 6 mg 10. 4 mg
The force with which it pressing against the track is F= r^(−2cr+4er³ ) .
By energy conservation:
[tex]\frac{1}{2}mv_a^2 + mgH = \frac{1}{2}mv_b^2 + mgh[/tex]
[tex]\frac{1}{2}m*0^2 + mg*6R = \frac{1}{2}mv_b^2 + mg*2R[/tex]
[tex]4gR = \frac{1}{2}v_b^2[/tex]
[tex]\sqrt{8gR }=v_b[/tex]
Now by force balance at the top point
[tex]mg + F_N = \frac{mv_b^2}{R}[/tex]
[tex]mg + F_N = \frac{m*8gR}{R}[/tex]
[tex]F_N = \frac{8mgR}{R} - mg[/tex]
[tex]F_N = 7 mg[/tex]
2. [tex]U =cr^2 - er^4[/tex]
Force and potential energy is related by the following equation
[tex]F = - \frac{dU}{dr}[/tex]
[tex]F = - \frac{d}{dr}cr^2 - er^4[/tex]
[tex]F = \hat r (- 2cr + 4er^3)[/tex].
Forces are influences that can change the movement of an object. A force can change the velocity of an object with mass accelerating it. Forces can also be described intuitively by pushing or pulling. A force has both magnitude and direction and is a vector quantity. The word force has a precise meaning.
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which of the following experiments best supports the idea that a transcriptional regulatory sequence can be located in an intron of a gene?
The experiment which best supports the idea that a transcriptional regulatory sequence can be located in an intron of a gene is: The intron of a gene is deleted, the gene is introduced into mouse cells, and the mRNA levels are measured. These mRNA levels are compared to a normal gene which is also introduced into mouse cells. The mutated gene shows no mRNA transcription, whereas the normal one does.
What is an intron of a gene?An intron is a region which resides within a gene but does not remain in the final mature mRNA molecule following transcription of the gene and does not code for amino acids which make up the protein encoded by the gene. Most protein-coding genes in the human genome consist of exons and introns.
Introns are crucial because the protein repertoire or variety is greatly enhanced by alternative splicing in which introns take partly important roles. Alternative splicing is a controlled molecular mechanism producing multiple variant proteins from a single gene in a eukaryotic cell.
Although part of your question is missing, you might be referring to this full question: Which of the following experiments best supports the idea that a transcriptional regulatory sequence can be located in an intron of a gene?
The intron of a gene is deleted, the gene is introduced into mouse cells, and the mRNA levels are measured. These mRNA levels are compared to a normal gene which is also introduced into mouse cells. The mutated gene shows no mRNA transcription, whereas the normal one does.The deleted intron that acts as a transcriptional regulatory element would result in a lack of mRNA, whereas the mouse cells with the normal gene would show mRNA transcription, thus serving as a positive control.Learn more about introns at: https://brainly.com/question/14317818
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A bowling ball of mass 7.22 kg and radius 10.2 cm rolls without slipping down a lane at 3.20 m/s . Calculate its total kinetic energy.
The total kinetic energy of the bowling ball is 51.75 Joules.
The mass of the bowling ball is 7.22 Kg and the radius of the ball is 10.2cm.
The radius in meter is 0.102 m.
The ball is rolling without slipping with a speed of 3.20m/s.
The total kinetic energy of the bowling ball is given by,
KE = 1/2Mv²(1+k²/r²)
where,
M is the mass of the ball,
v is the speed of the ball on the lane,
k is the radius of gyration,
r is the radius of the ball.
Putting values,
KE = 0.5 x 7.22 x 3.2 x3.2 x 1.4
KE = 51.75 Joules.
The total kinetic energy of the ball is 51.75 Joules.
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Suppose that a woman weighing 130 lb and wearing high heeled shoes momentarily places all her weight on the heel of one foot. If the area of the heel is 0.50 in.2, calculate the pressure exerted on the underlying surface in (a) pounds per square inch, (b) kilopascals, and (c) atmospheres.
The pressure exerted on a 130 lb woman wearing high heels to momentarily place her entire body weight on the heel with an area of 0.50 in 2 on either foot is:
a. 260 lb/in².
b. 1,794 KPa
c. 17.69 atm
PressurePressure is a strong pushing force. Physics explains that the unit of pressure is symbolized by the letter P.
In addition to N/M², the pressure formula has another unit of measurement, namely Pascal (Pa).
The pressure formula used is:
P = F/A.
Where,
P = pressure (N/m²or Pa)
F = compressive force (N).
A = surface area (m²)
If you have the mass of the object:
P = (m.g)/A
m = object mass (kg)
g = acceleration due to gravity (m/s²)
A = surface area (m²)
We have,
Mass of the woman = 130 lb ⇒ 58.97 kg
The area of the heel = 0.50 in² ⇒ 3.21 m²
So, the pressure exerted on the underlying surface:
a. P = F/A
= 130 lb/0.50 in²
= 260 lb/in²
b. P = (58.97) (9.8) / 3.22
= 179.4 x 10⁴ Pa = 1,794 KPa
c. 1 KPa = 0.0098692329 atm
So, 1,794 KPa = 17.69 atm
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In an experiment, a student measured the volume of a substance while the mass was changed. The student measured up to five kilograms. The graph of the data is plotted below.
A volume versus mass graph is shown with mass on the vertical axes from 1 to 10 kilograms and volume on the horizontal axis from 1 to 5 milliliters. A line from the origin through all points and beyond.
Which of the following is an error the student made in creating an accurate graph?
The axes and graph are based only on measured values.
The axes are labeled with the incorrect variables.
The plotted points do not show all data collected.
The title has the incorrect order for the variables.
The graph is incorrect because; the title has the incorrect order for the variables. Option D
What is a graph?We know that a graph is made up of two parts. It has two axes and these are what we call the parts of the graph. It is common that we would have the independent variable on the x axis and then we have the dependent variable on the y axis.
With this said, we would now have to look at the graph that has been attached so that we can be able to see what the error in the graph that has been plotted as shown is and how the error that is in the graph can be able to be correct as the student is trying to pass information by the use of a graph system.
The title of the graph can be seen to show that the volume rather than the mass is plotted on the y axis.
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WILL MAKE BRAINLIEST:
A 100 kg object takes one MINUTE to travel 300 m east. It began travelling at 240 m/s and came to a stop (0 m/s) at the end. What was its acceleration?
240
0.8
-4
-2.4
Answer:
To find the acceleration of the object, we can use the formula: acceleration = (final velocity - initial velocity)/time.
Plugging in the given values, we get: acceleration = (0 m/s - 240 m/s)/1 minute.
Since 1 minute is equal to 60 seconds, we can convert the time to seconds to get: acceleration = (0 m/s - 240 m/s)/60 seconds.
Simplifying this equation gives us: acceleration = -4 m/s^2.
Therefore, the acceleration of the object is -4 m/s^2. The correct answer is therefore (-4).
While visiting the Albert Michelson exhibit at Clark University, you notice that a chandelier (which looks remarkably like a simple pendulum) swings back and forth in the breeze once every T = 6.1 seconds.
a) Calculate the frequency of oscillation (in Hertz) of the chandelier.
b) Calculate the angular frequency ω of the chandelier in radians/second.
c) Determine the length L in meters of the chandelier.
d) That evening, while hanging out in J.J. Thompson's House O' Blues, you notice that (coincidentally) there is a chandelier identical in every way to the one at the Michelson exhibit except this one swings back and forth 0.11 seconds slower, so the period is T + 0.11 seconds. Determine the acceleration due to gravity in m/s2 at the club.
The acceleration an object experiences as a result of gravitational force is known as acceleration due to gravity. M/s2 is its SI unit. Its vector nature—which includes both magnitude and direction—makes it a quantity. The unit g stands for gravitational acceleration. At sea level, the standard value of g on earth's surface is 9.8 m/s2.
How do we calculate the gravitational acceleration?
The formula for calculating acceleration due to gravity is given below in its most practical form by these two laws: Where g is the acceleration brought on by gravity, G is the gravitational constant of the universe, M represents mass, and R is distance, g = G*M/R2.
Describe 9.8 m s2?
Lowercase g indicates the gravity acceleration's magnitude, which is 9.8 m/s2. g = 9.8 m/s2. This means that gravity will increase an object's velocity by 9.8 m/s for every second it is in free fall. Following one second, the item is moving at a speed of 9.8 m/s.
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g a uniform electric field has magnitude e and is directed in the negative x direction. the potential difference between point a (at x= 0.60 m) and point b (at x= 0.90 m) is 310 v. Part A Which point, a or b, is at the higher potential? Part B Calculate the value of E. Express your answer using two significant figures. Part C A negative point charge q = -0.200 mu C is moved from b to a. Calculate the work done on the point charge by the electric field. Express your answer using two significant figures.
A) Point A is the one with the highest potential.
B) The uniform electric field's magnitude E is equal to 1033.33 V/m.
Given that,
Potential difference at point A ( at x ) = 0.6 m
Potential difference at point B ( at x ) = 0.9 m
Potential difference = 310 volts
Point charge is -0.200 μC = - 0.2 * 10⁻⁶ C
A) The point with a larger potential is point A because the uniform electric field of magnitude (E) is not close to the positive charge and is farther away from point B by 0.9 m. This is because the uniform electric field is directed in the negative x direction. Additionally, the square of the distance from a point charge has an inverse relationship with the potential difference of an electric field.
B) In order to determine the size (E) of the uniform electric field:
The equation Vab = E* d determines the magnitude (E) of this electric field at a constant potential difference.
Where Vab is the potential difference between points A and B, and E is the uniform electric field's magnitude
E is the electric field's strength, and d is the separation between points A and B.
Let us determine the distance (d),
d = db - da
⇒ 0.9 - 0.6 = 0.3 m
By changing the values in the formula above, we arrive at
310 = 0.3 E
E = 1033.33 V/m
Therefore, the uniform electric field has a magnitude of 1033.33 V/m.
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FILL IN THE BLANK If we add fresh water and salt water to raw iron in the first two test tubes, respectively, then we will observe: ________and if we omit oxygen or water from the iron in the 3rd and 4th test tubes, respectively, then we will observe: _________
Raw iron will rust more quickly in salt water when we add it to the first two test tubes, which will be filled with fresh and salt water, respectively.
The iron in the third and fourth test tubes will rust more quickly if oxygen or water are removed from them, respectively. Iron is susceptible to rusting, a form of corrosion. When iron is exposed to oxygen and water, rusting happens because hydrated iron(III) oxide is created. This means that any action we take to keep iron away from oxygen or water will delay the rusting process. When iron is exposed to salts or a low pH, the rusting process is also sped up. There is no water in a tube with simply air, but the nail is exposed to the air. Since air contains some water vapour, water will eventually find its way inside the tube. In tap water, there is always a little amount of dissolved oxygen gas. This indicates that the tube already contains water and oxygen.
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13. A child throws a 6.9 kg package horizontally from a boat with a speed of 10.0 m/s. Calculate the resulting recoil velocity of the boat if assuming it was initially at rest. The mass of the child is 25 kg and that of the boat is 55 kg. (.863m/s)
Answer:
0.863 m/s
Explanation:
This is a conservation of momentum problem.
Momentum = p = mv
(6.9 kg)(10 m/s) = (25 kg + 55 Kg)(v)
69 kg·m/s = (80 kg)v
v = (69 kg·m/s)/(80 kg) = 0.863 m/s
At an intersection of hospital hallways, a convex spherical mirror is mounted high on a wall to help people avoid collisions. The magnitude of the mirror's radius of curvature is0.560m.
(a) Locate the image of a patient10.6m from the mirror. (Use the correct sign conventions.)
cm (from the mirror)
(b) Indicate whether the image is upright or inverted.
upright
inverted
(c) Determine the magnification of the image.
At an intersection of hospital hallways, a convex spherical mirror is mounted high on a wall to help people avoid collisions. The magnitude of the mirror's radius of curvature is0.560m. The image of a patient Located at -0.2877m. The image is an upright and a virtual image. The magnification of the image is 0.0271.
The image location can be calculate as follows:
The values of the image distance and focal length for a convex mirror are negative. using the mirror formula
1 = 1/u + 1/v
f u v
where,
f is the focal length = Radius of curvature/2 = 0.560/2 = 0.28m
u is the object distance = 10.6m
v is the position of the image
1 = 1 + 1
f u v
1 = 1 + 1
0.28 10.6m v
3.57 = 0.094 - 1/v
3.57 - 0.094 = -1/v
3.476 = -1/v
v = -1/3.476
v = -0.2877m
B) The fact that the image distance is negative indicates that the image is virtual and upright. Every upright image has a negative image distance.
C) Magnification: image/object distance
Magnification = 0.2877/10.6
Magnification= 0.0271.
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Monochromatic light from a distant source is incident on a slit 0.750 mm wide. On a screen 2.00m away, the distance from the central maximum of the diffraction pattern to the first minimum is measured to be 1.35mm
Calculate the wavelength of the light (answer in nm)
The wavelength of the light if a monochromatic light from a distant source is incident on a slit 0.750 mm wide. On a screen 2.00m away, the distance from the central maximum of the diffraction pattern to the first minimum is measured to be 1.35mm is 506.25 nm
When a wave is bent by an obstruction whose dimensions are close to the wavelength, diffraction is noticed. We can disregard the effects of extremes because the Fraunhofer diffraction is the simplest scenario and the impediment is a long, narrow slit.
This is a simple situation where the Fraunhofer single slit diffraction equation can be applied:
y = mλ D
α
where,
y = displacement from the centerline for minimum intensity = 1.35 mm
m = order number = 1
λ = light wave length
α = witdh of the slit = 0.750 mm
D = distance between the screen and the slit = 2m
so
λ = yα
mD
λ = (1.35 x 10⁻³)( 0.750 x 10⁻³) = 5.0625 x 10⁻⁷m = 506.25 nm
1x2
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hans decides to test an idea that the atom is made of a soft positive substance with hard specks of negative substance (the electrons) embedded in it. he sets up an in which heavy positive particles will be fired into some gold atoms. hans will monitor how much these positive particles are deflected passing through the gold atoms.
He sets up experiment an in which heavy positive particles will be fired into some gold atoms.
The electron is a subatomic particle with a bad one standard electric charge. Electrons belong to the primary technology of the lepton particle own family, and are typically thought to be fundamental particles because they have no recognized additives or substructure.
For most realistic purposes, an electron is a structureless particle with an intrinsic angular momentum, or spin. simply two numbers — the electron's mass and its electric price — gasoline the equations that describe its behaviour.
By using the best values for the wave-length and the scattering by matter of tough X-rays and ?-rays, the radius of the electron is anticipated as approximately 2 × 10-10 cm.
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A very long insulating cylinder of charge of radius2.40 cm carries a uniform linear density of 13.0 nC/m.
If you put one probe of a voltmeter at the surface, how far fromthe surface must the other probe be placed so that the voltmeterreads 200 V?
The distance at which the probe should be placed so that the voltmeter reads 200 V is equal to 0.216 cm.
To find the distance at which the voltmeter reads 200 V, we need to use the equation for the electric potential at a point due to a continuous distribution of charge:
V = k * ∫λ(r')/r' dr'
where V is the electric potential at a distance r from the center of the cylinder, k is the Coulomb constant (8.99 x 10^9 N*m^2/C^2), λ is the linear charge density (13.0 nC/m in this case), and r' is a dummy variable of integration.
To find the electric potential at a distance r from the surface of the cylinder, we can split the integral into two parts: one from the surface of the cylinder (r') to the point where the probe is placed (r), and one from r to the center of the cylinder (which will be a negative value since the charge density is negative):
V = k * [∫λ(r')/r' dr' from r'=r to r'=2.4 cm] + k * [∫λ(r')/r' dr' from r'=2.4 cm to r'=0]
The first term on the right hand side represents the potential at the point where the probe is placed, and the second term represents the potential at the surface of the cylinder. We are given that the potential at the surface is 200 V, so we can set the equation equal to 200 V and solve for r:
200 V = k * [∫λ(r')/r' dr' from r'=r to r'=2.4 cm] + k * [∫λ(r')/r' dr' from r'=2.4 cm to r'=0]
To solve this equation, we need to evaluate the integrals on the right hand side. The first integral is easy to evaluate:
∫λ(r')/r' dr' from r'=r to r'=2.4 cm = λ * ln(2.4 cm/r)
The second integral is a little more tricky, but we can use the fact that the charge density is uniform to simplify it:
∫λ(r')/r' dr' from r'=2.4 cm to r'=0 = λ * ∫1/r' dr' from r'=2.4 cm to r'=0
= λ * [ln(r')] from r'=2.4 cm to r'=0
= λ * [-ln(2.4 cm)]
Substituting these values back into the original equation and solving for r, we find that the distance at which the voltmeter reads 200 V is:
r = 2.4 cm * exp(-200 V / (k * λ))
r = 0.216 cm
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Of the first exoplanets found, most were detected by:
A) noting the drop in the star's light as the planet transits its disk.
B) imaging them with the HST in the infrared, where they are easier to stop.
C) noting the Doppler shifts of the star as the planet orbits it from side to side.
D) receiving radio transmissions from them, much like Jupiter emits.
E) detecting the oxygen in their atmospheres spectroscopically.
Of the first exoplanets found, most were detected by: C) noting the Doppler shifts of the star as the planet orbits it from side to side.
The first exoplanets were found in what way?Instead, the first extraterrestrial planets were found by tracking the star's movement. It's a tiny white lie that kids are taught that planets rotate around the sun. In fact, the entire solar system's mass center revolves around the sun and the planets.
What and when was the first planet discovered?Uranus was the first planet to be found by the use of a telescope; it was identified as a planet in 1781 as a result of observations made using a telescope by Sir William Hershel (UK) and others. On March 13, 1781, Sir William Herschel performed the observations that proved Uranus was not a typical star.
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turn on the supply of fig 13.4 and measure the voltage vab. then calculate the current il using the measured value of the 47 resistor
At the junction of two resistors, a voltage (V1) proportional to the measured voltage will be shown. The Arduino's analogue pin can then be attached to this junction.
This formula can be used to determine the voltage. Vm = (R2/(R1+R2)) * V1 The Arduino then measures the voltage V1. A voltage divider circuit that consists of two resistors linked in series as shown can be used to solve this problem. The voltage to be measured (Vm) is linked to one end of this series connection, and the ground is attached to the other end.
Vab can be determined visually to be 14 volts. First, use your eyes. Write down the following values for the voltages and currents specified by Ohm's law using just your eyes: Your biggest error, in my opinion, was failing to realise that the ground (shown in green) is connected to both the 6 volt supply and the 5 ohm resistor.
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What is the largest atom of period 4
The largest atom of period 4 is Potassium (K).
What are the elements of period 4?
One of the chemical elements in the fourth row (or period) of the periodic table of the elements is known as element of period 4. The periodic table is organized into rows to show recurrent (periodic) tendencies in the chemical behavior of the elements as their atomic number rises.
One element is present in each of the eighteen groups, making up the fourth period's 18 elements, which start with potassium and end with krypton. d-block, which includes transition metals, makes its first appearance in the table.
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Antoine burns some charcoal, and a very small diamond (!), and makes the ____________ that the only product of both reactions is a heavy gas (carbon dioxide).
Antoine burns some charcoal, and a very small diamond, and makes the observation that the only product of both reactions is a heavy gas (carbon dioxide).
The descriptions of scientists engaging in activities that are part of the scientific method.
When Antoine burns charcoal and a small amount of diamond, then in that case, each Carbon atom will form a tetrahedral bond with the other four carbon atoms which are present in a Diamond.
Due to the formation of the tetrahedral bond the structure becomes more and more compact and rigid.
Hence, the missing word is given below.
Antoine burns some charcoal, and a very small diamond (l) and makes the observation that the only product of both reactions is a heavy gas.
Missing word:- Observation
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A copper wire loop is constructed so that its radius r can change. It is held near a solenoid that has a constant current through it.
a. Suppose that the radius of the loop were increasing. Use Lenz's law to explain why there would be an induced current through the wire. Indicate the direction of current.
b. Check your answer regarding the direction of the induced current by considering the magnetic force that is exerted on the charge in the wire of the loop.
c. Find the direction of the magnetic moment of the loop and the direction of force exerted on the loop by the solenoid.
The top page will receive the current in the loop, and the bottom page will receive it out of the loop.
(a) Because B is constant and there is a constant magnetic Feld, we may recast the change in flux as shown above. Since A is positive, the loop will have a negative emf, which corresponds to an induced magnetic moment on the page that points to the left. The loop's current will flow into and out of the page in opposite directions. V=-Δφ/ Δt = -B·ΔA/ Δt
(b) Individual electrons in the wire loop can be imagined travelling radially outward as the loop's radius grows. We'll take into account one at the top of the loop (which is moving up the page). The Lorentz force Law is F=q(v)=qvB(yx)=-qvB.
(c) Circular orbits will emerge from constant forces pointing into the center of the loop (around the wire). We can tell we have positive current there since the force is pointing into the middle of the loop (into the page).
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in the overhead view of fig. 15-48, a long uniform rod of mass 0.600 kg is free to rotate in a horizontal plane about a vertical axis through its center. a spring with force constant k
The period of the small oscillations that result when the rod is rotated slightly and released is 0.0653s.
Harmonic motion, where the damping force is proportional to the velocity, which is a realistic damping force for a body moving through a fluid is called damped harmonic motion.
If τ=−Cθ, where τ is the torque, θ is the angle of rotation, and C is a constant of proportionality, then the angular frequency of oscillation is ω= sqrtC/I and the period is T=2π/ω=2π sqrtI/C.
where, I is the rotational inertia of the rod. The plan is to find the torque as a function of θ and identify the constant C in terms of identies given in question.
Now using T=2π sqrtI/C, we get
T= 2π sqrtm/3K
putting given quantities,
T= 0.0653s.
The question is incomplete, the complete question is
In the overhead view of above figure, a long uniform rod of mass 0.600kg is free to rotate in a horizontal plane about a vertical axis through its center. A spring with force constant k=1850N/m is connected horizontally between one end of the rod and a fixed wall. When the rod is in equilibrium, it is parallel to the wall. What is the period of the small oscillations that result when the rod is rotated slightly and released?
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When a bar magnet is thrust into a coil of copper wire, the coil tends toA) repel the magnet as it enters. B) attract the magnet as it enters. C) both of these D) neither of these
A) repel the magnet as it enters.
When a bar magnet is thrust into a coil of copper wire the coil tends to repel the magnet as it enters. Option A.
For example, passing the poles of a permanent bar magnet through a coil of wire induces a current in the coil. The current creates a magnetic field around the coil, turning it into a magnet. Lenz's law indicates the direction of the induced current.
When a magnet moves in a coil of wire the magnetic field and flux through the coil change, creating a voltage in the coil according to Faraday's law. In the example shown below, as the magnet moves into the coil, the galvanometer deflects to the left in response to the increasing magnetic field.
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during a solar eclipse, the moon, earth, and sun all lie on the same line, with the moon between the earth and the sun.
The negative sign means the Moon is being pulled by the Sun more than it is being pulled by the Earth. Net force on Moon is -2.237×10^26 N
F = G * (M1 * M2) / R^2
G = 6.67×10^-11 m^3/(kg*s)
M = Mass of object
R = Distance between objects
F = force
Force between Moon and Earth
G * (7.35×10^22 kg * 5.97×10^24 kg) / (3.84×10^5 km)^2 = 1.98×10^26 N
Force between Moon and Sun
G * (7.35×10^22 kg * 1.99×10^30 kg) / (1.50×10^8 km - 3.84×10^5 km)^2 = 4.36×10^26 N
Net force on Moon
1.98×10^26 N - 4.36×10^26 N = -2.237×10^26 N
The negative sign means the Moon is being pulled by the Sun more than it is being pulled by the Earth.
Only the Moon orbits Earth naturally. With a diameter around one-fourth that of Earth, it is the largest and most massive satellite in relation to its home planet and the fifth largest satellite in the Solar System overall[f] (comparable to the width of Australia). [16] According to geophysical definitions of the term, the Moon qualifies as a satellite planet and is larger than other known dwarf planets of the Solar System because it is a planetary-mass object with a differentiated rocky body. [17] It has no major magnetic field, atmosphere, or hydrosphere. The only satellite in the Solar System known to have a higher surface gravity and density is Jupiter's moon Io, which has a gravity and density around one-sixth that of Earth (0.1654 g).
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Question is attached below
(a) the shell's horizontal range = 285839 m.
(b) the amount of time the shell is in motion is: 273.11 sec.
What is horizontal range?The length of the horizontal axis is a projectile's horizontal range. In addition, it would move before returning to the original vertical position.
Horizontal range is equal to Initial Speed in the horizontal direction, multiplied by the time the shell is in motion. Therefore, both questions can be solved at the same time.
Step 1. Find Velocity in the Horizontal direction by:
Vx = (1.70 x 10³) × cos(52°)
Vx = 1046.6 m/sec
Step 2. Find Velocity in the Vertical direction by:
Vy = (1.70 x 10³) × sin (52°)
Vy = 1339.6 m/sec
Step 3. Find the amount of time the shell is in motion by:
t= (2 × Vy)/gravity
t = (2 × 1339.6) / 9.81 [ Gravity = 9.81m/s²]
t = 273.11 sec
Step 4. Find the shell's horizontal range:
Distance = Vx × t
or, distance = (1046.6 × 273.11)
or, distance = 285839 m
Thus, (a) the shell's horizontal range = 285839 m.
(b) the amount of time the shell is in motion is: 273.11 sec.
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