The roller coaster possesses only potential energy when it begins motion from rest at its greatest point, which is equal to 21.2ms2 (rounded to the next decimal point).
What is the definition of potential energy?Potential radiation is a term that stored energy that depends on the interactions between various system elements. A spring's potential energy rises when it is stretched or squeezed. A steel ball does have more potential energy if it is lifted just above ground аѕ opposed to dropping to the ground.
What three types of potential energy are there?Stones perched on a cliff's edge have potential energy. If the stones fall, the potential energy would be transformed into kinetic energy. Because they have the ability to fall to the ground, tree branches high in the tree carry potential energy. We consume chemical potential energy in our food.
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Why more physicists are starting to think space and time are ‘illusions’ ?
Some physicists are starting to question the traditional view of space and time as fundamental and unchanging entities because of the strange and counterintuitive behaviour of the universe at very small scales, as described by quantum mechanics.
What does quantum physics suggest?It suggests that the concepts of definite position and definite momentum cannot both be precisely known at the same time and that the position and velocity of particles are inherently uncertain.
What does general relativity theory predict?General relativity predicts that spacetime itself can be affected by matter and energy and that it can bend, stretch, and curve.
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a business jet of mass 36000 kg takes off when the thrust for each of two engines is 22000 n . part a find its acceleration.
A business jet of mass 36000 kg takes off when the thrust for each of two engines is 22000 N .its acceleration is 1.22 m/s^2.
The acceleration (a) can be calculated as follows:
a = (F_net) / m
Where F_net is the net force acting on the jet and m is its mass.
The net force can be calculated as the sum of the thrusts produced by each engine:
F_net = 2 * 22000 N = 44000 N
Finally, substituting the values of F_net and m into the equation above:
a = 44000 N / 36000 kg = 1.22 m/s^2
Thrust is a type of force that propels an object in a specific direction. It is the push or pull that moves an aircraft, a rocket, or any other type of vehicle through the air or through space. Thrust is created by the action of a engine or motor, which generates energy that is then transformed into movement. This movement can take various forms, such as the spinning of a fan, the burning of fuel in a combustion engine, or the explosion of a rocket.
Thrust is an essential component of flight, as it provides the energy needed to overcome the forces of gravity, air resistance, and friction. The amount of thrust generated by an engine is measured in units of force, such as pounds or newtons, and is dependent on factors such as the engine design, the fuel being used, and the speed of the vehicle.
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in the bohr theory of the hydrogen atom, an elec-tron moves in a circular orbit about a proton, where the radius of the orbit is 5.29 3 10211 m. (a) find the magni-tude of the electric force exerted on each particle. (b) if this force causes the centripetal acceleration of the electron, what is the speed of the electron?
The magnitude of the electric force exerted on each particle is F=[tex]8.22 \times 10^{-8}[/tex] N and the the speed of the electron is v = [tex]2.19\times 10^{6}\: m/s[/tex]
The nucleus and electrons are drawn to one another by the electric force. The void created by a positive or negative charge is referred to as an electric field since it generates a field there. If you had a positive charge just here, it would have an electric field surrounding it and affect the area in which it was located. The same applies for a negative charge; it too has an electric field surrounding it. Now, opposite charges attract each other while like charges repel one another. A positive charge here and a positive charge here, for example, would resist one another since they are similar charges.
a) - F=[tex]K_e\frac{e^2}{r}[/tex]'
F=[tex](8.99\times10^9Nm^2/C^2)\frac{(1.60\times10^{-19})^{2} }{(0.529\times10^{-10} )^2}[/tex]
F=[tex]8.22 \times 10^{-8}[/tex] N
b)- [tex]v=\sqrt\frac{Fr}{m}[/tex]
[tex]v=\sqrt\frac{8.22\times 10^{-8}\times0.529\times 10^{-10}}{9.11\times 10^{-31}}[/tex]
v = [tex]2.19\times 10^{6}\: m/s[/tex]
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which combination represents the si base units of force? which combination represents the si base units of force? kg m m/s2 kg m/s kg m/s2 kg
The metre, a measure of length denoted by the sign m, is the fundamental unit of force. The symbol for the kilogramme is a unit of mass The newton (sign N) is the SI unit of force.
The metre, a measure of length denoted by the sign m, is the fundamental unit of force. The symbol for the kilogramme is a unit of mass.
In mechanics, force is any action that tends to maintain or alter a body's motion or distort it. The concept of force is frequently explained in terms of Isaac Newton's three laws of motion, as stated in his Principia Mathematica (1687). A body that is at rest or moving at a uniform rate in a straight line will remain in that state until some force is applied to it, according to Newton's first principle. According to the second law, when an external force acts on a body, it causes the body to accelerate (change in velocity) in the direction of the force.
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efficient estimation of word representations in vector space
A set that is closed under finite scalar and vector addition is known as a vector space, or V.
What is vector space?The fundamental illustration is an n-dimensional Euclidean space Rn where each element is represented by a list of n real numbers, scalars are real numbers, addition is componentwise, and scalar multiplication is multiplication on each term individually.
Scalars are constituents of a field F in a general vector space, in which case V is referred to as a vector space over F.
A set whose elements, frequently termed vectors, can be added to and multiplied ("scaled") by figures known as scalars is referred to as a vector space (also known as a linear space).
Therefore, A set that is closed under finite scalar and vector addition is known as a vector space, or V.
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which of the following are considered alternative sources of energy? (select three) a. wind power b. gas power c. nuclear power d. geothermal power e. coal-based power
When nuclear reactions are used to generate energy, this is known as nuclear power. Currently, nuclear power plants use uranium and plutonium fission to generate the great majority of the world's electricity from this source.
What is the issue with nuclear energy?The creation of radioactive wastes such spent (spent) enriched uranium, uranium mill tailings, and other nuclear waste is a substantial environmental risk connected to nuclear power. These materials could stay radioactive and dangerous to human health for millions of years.
How do you refer to nuclear energy?The energy released in large quantities during activities that have an impact on atomic nuclei, or the dense centers of atoms, is known as nuclear energy, also known as atomic energy.
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if a bird flies 30 degrees north of east at 20 m/s relative to the air, and if there is a wind towards the south at 10 m/s relative to the ground, what is the bird's speed relative to the ground in m/s?
The required speed of the bird relative to the ground is calculated to be 11.18 m/s.
The speed of the bird relative to air is given as 20 m/s.
The speed of air with respect to the ground is given as 10 m/s.
The speed of the bird relative to the ground in m/s is to be calculated.
The angle at which the bird flies is 30° north of east.
The equation of velocity of the bird relative to the ground can be written as,
V bg = V ba + V ag
where,
V bg is the velocity of bird with respect to ground
V ba is the velocity of the bird with respect to air
V ag is the velocity of air with respect to ground
Putting the values into the above equation, we have,
V bg = V ba + V ag = 20 sin30° i + 10 sin30° j = 20 × 1/2 i + 10 × 1/2 j = 10 i + 5 j
The magnitude of the velocity of bird with respect to ground is,
V bg = √(10² + 5²) = √(100 + 25) = √125 = 11.18 m/s
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how far must you walk toward speaker b to move to reach the first point of destructive interference? take the speed of sound to be 344 m/s . express your answer in meters.
0.2425 m you walk toward speaker b to move to reach the first point of destructive interference.
Calculating the problem:The following formula can be used to determine the wavelength:
λ = v/f, where f is the frequency of the sound wave and v is the speed of sound.
When we change the values, we get: λ = 344 m/s / 708 Hz = 0.485 m
The distance between the two points of constructive and destructive interference is equal to half the wavelength, or λ/2,
d = λ/2 = 0.485 m / 2 = 0.2425 m = 243.5 cm
We need to walk 243.5 cm in the direction of speaker B in order to reach the first point of destructive interference, as d = λ/2 = 0.485 m / 2 = 0.2425 m.
How does wavelength work?A wavelength is the distance between two identical points (adjacent crests) in consecutive cycles of a waveform signal that travels through space or down a wire. In wireless systems, this length is typically measured in meters (m), centimeters (cm), or millimeters (mm). The relationship between frequency and wavelength .
The wavelength of a signal decreases with increasing frequency. For gamma radiation (), visible light (UV), infrared (IR), and ultraviolet (UV) (nm), the wavelength is more frequently mentioned in nanometers.
For instance, a water wave is one that combines transverse and longitudinal motions. An electromagnetic wave is produced when an electric field and a magnetic field vibrate together.
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g a copper wire that is 3.14 m long with a diameter of 2 cm has an electrical resistance of 10 ohms. if this wire is cut exactly in half (equal length), what is the electrical resistance of each wire piece?
The resistance of the copper wire when the length of the wire is halved is 5 ohms
The length of the copper wire = 3.14 m
The diameter of the wire = 2 x 10⁻² m
The resistance of the wire = 10 ohms
The electrical resistance of the wire if the length of the wire is cut in half is
R = ρ L / A
where R is the resistance of the copper wire
ρ is the resistivity
L is the length of the copper wire
A is the area of the copper wire
We can see that the resistance is directly proportional to the length of the copper wire in the above equation.
Thus, if the length of the wire is cut in half, then the resistance of the wire will also be reduced by half the value.
Resistance = 10 ohms / 2
= 5 ohms
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Neglecting air resistance, if a brick is dropped, a
baseball is hurled horizontally, and a bullet is fired
horizontally all at the same height, which object
hits ground first? Explain.
for the bulbs connected in parallel: how does the current through each bulb compare to the total current leaving/entering the battery? what do you think is the underlying reason for this?
The current through each bulb in a parallel circuit is equal to the total current leaving/entering the battery, and this is because in a parallel circuit, the voltage across each component is the same, and the total current is equal to the sum of the currents through each component.
When bulbs are connected in parallel circuit, each bulb has the same voltage across it, which is equal to the voltage of the battery. This means that the current through each bulb depends only on the resistance of that bulb and is independent of the other bulbs in the circuit. Therefore, the total current flowing into the parallel circuit is equal to the sum of the currents flowing through each bulb.
This is in contrast to a series circuit, where the total current is shared by all the components and is the same at any point in the circuit. The reason for this difference is the different ways in which current and voltage are distributed in parallel and series circuits.
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an automobile travels on a straight road for 18km at 31 km/h. it then continues in the same direction for another 18km at 62 km/h. what is the average velocity of the car during this 36 km trip?
The average velocity of the car during this 36 km trip was 41.1 km/h.
The average velocity of an object over a certain distance is given by the total distance traveled divided by the total time taken to travel that distance.
In this case, the first part of the trip took 18 km / 31 km/h = 0.581 hours. The second part of the trip took 18 km / 62 km/h = 0.290 hours. The total time taken for the entire trip was 0.581 + 0.290 = 0.871 hours.
The total distance traveled was 18 km + 18 km = 36 km.
Therefore, the average velocity of the car during this 36 km trip was 36 km / 0.871 hours = 41.1 km/h.
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a spring does 800 j of work on a marble to launch it across a horizontal floor. it applies 200 n of force. how far does the marble travel?
Use the formula work = force x distance to calculate the marble's travel distance. Distance in rearranging equals work / force. Distance = 800 J / 200 N = 4 m after plugging in the values.
What pressure does the spring exert on the marble?
The spring exerts a 200 Newton force on the marble. This is a gauge of the force being exerted on the marble and is based on how much work the spring is putting in.
The spring is exerting 800 Joules of energy in this instance to propel the marble across a horizontal floor. The forcethe spring applies is directly proportional to the amount of work it is doing, so as the amount of work increases, the force
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What is accurate about seismic waves moving through the Earth?S-waves (also called shear-waves) move through neither solids nor liquids.S-waves (also called shear-waves) move through solids and all liquids except Diet Pepsi.Correct!S-waves (also called shear-waves) move through solids but not liquids.S-waves (also called shear-waves) move through liquids but not solids.S-waves (also called shear-waves) move through both solids and liquids.
S-waves, also known as shear waves, flow through liquids but not solids, which is correct information regarding seismic waves travelling through the earth.
What are seismic waves?Seismic waves are created when materials unexpectedly move inside the Earth, such as when they slide down a fault when in an earthquake.. Seismic waves can also be produced by volcanic eruptions, explosions, landslide, avalanches, or even swiftly flowing rivers. An acoustic wave that passes through the Planet or the other planetary body is called a seismic wave. Large landslides, volcanic eruptions, magma movement, earthquakes, and man-made explosions that release a lot of low-frequency acoustic energy can all cause it.
What causes seismic?Sudden movement along Earth's fault lines causes earthquakes. The motion releases "elastic strain" energy that has been accumulated inside the form of seismic waves, that travel through the Earth & cause the earth to tremble. Seismic wave research is crucial for understanding and forecasting earthquakes and tsunamis, but it also provides details on the structure and properties of the Earth, much like it did for the discovery the Mohorovicic's discontinuity.
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if the airspeed of the plane (its speed in still air) is 450.0 km/h , in which direction should the pilot head?
The plane's speed relative to the ground when airspeed of the plane is given is calculated to be 329.64 km/h and the direction is 79.74° West or North.
Airspeed of the plane = 450 km/h
Wind speed is 80 km/h in a south direction.
The pilot should head in the direction,
OA = AB × cos θ
cos θ = OA/AB = 80/450 = 0.178
θ = 79.74°
When the airspeed is 450 km/h the pilot must head 79.74° West or North.
The speed of the plane in relation to the ground is,
OB = AB × sin θ
OB = 335 × sin (79.74°)
OB = 329.64
Therefore, the plane's speed relative to the ground is 329.64 km/h.
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(i) describe one advantage of using hydroelectric power plants over using coal-fired power plants. (ii) describe one potential disadvantage of hydroelectric power plants.
As they can immediately supply power to the system, hydropower facilities provide essential backup power during large electrical outages or disturbances.
What advantages do hydroelectric power facilities offer over those that burn coal?Hydropower is more environmentally benign when compared to other large fossil fuel-based sources of energy. Hydroelectric generators don't emit the extra energy and gases that fossil fuel-powered facilities do, which are major causes of acid rain, global warming, and air pollution.
What are the disadvantages of using hydroelectric power plants rather than coal-fired ones?Hydropower can generate electricity without emitting any greenhouse gases into the atmosphere. However, it can also result in risks to society and the environment, such as deteriorated water quality, hampered fish migration, and harmed habitat for wildlife.
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please help me! Fill in all the blanks using the highlighted words. All 23 please. Thank you!!
Blood travels throughout the body as follows:
oxygen inhale red blood cellsblood vena cavaright atriumright ventriclelungs pulmonary deoxygenated lungs Gas exchangecapillaries oxygenated pulmonaryleft oxygenated heart left atrium ventricle aortaupper lowerHow does circulation work?Circulation is the continuous movement of blood throughout the body by the circulatory system. It consists of the heart, blood vessels (arteries, veins, and capillaries), and blood. The heart acts as a pump, sending oxygen-rich blood through the arteries to the body's cells, and then returning oxygen-depleted blood through the veins back to the heart.
The exchange of oxygen, nutrients, and waste products between the blood and cells occurs through the capillaries. This continuous flow of blood helps to maintain the body's functions and overall health.
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choose the correct definition of precession, and the correct explanation how does it affect what we see in our sky?
Precession is the slow and continuous change in the orientation of the rotational axis of a spinning body, such as a spinning top or the Earth.
When compared to its orbital plane around the sun, the Earth's rotational axis tilts at an inclination of about 23.5 degrees.
The Earth's rotational axis travels in a round pattern in space as a result of precession; one full cycle takes about 26,000 years to complete. The celestial poles, which are the spots in the sky where the Earth's rotational axis crosses the celestial sphere, are impacted by this movement of the rotational axis.
The Earth's spinning axis points in a different direction over time as a result of precession, which affects the position of the celestial poles. The position of the stars as seen from Earth is then impacted by this.
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if the wire has a diameter of 0.7 in. , determine how much it stretches when a horizontal force of 2.5 kip acts on the pole.
A horizontal force is one that moves in a direction perpendicular to the horizon.
If we exert a horizontal force, when?Apply the equilibrium equation at C.ΣΜ =025x4-7, sin 30°x7=010-3.57=0 TR₁ = 2.857 kipCalculate the length of the steel wire (1)7cos 30° = 8.083 ftCalculate the stretch/elongation in the wire, using the following for AE2.857x(8.083×12 (022 * 29000-0.3042 inusing this and it is constantly perpendicular to the contact area.
What kind of thing is horizontal?A line going form left to right is referred to as a horizontal line. The sunrise is seen across a horizontal line when it appears over the horizon. A perfect example of the a horizontal line is the x-axis.
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How are physical quantities classified as scalars and vectors?
Physical quantities can be classified as scalars or vectors based on their ability to describe magnitude and direction. Scalar quantities solely have magnitude and do not have direction. Vector quantities are the quantities that have both magnitude and direction.
What are some examples of vectoir quantities?Vector quantities are physical quantities that include both magnitude and direction. Some common examples of vector quantities include: Velocity, Displacement, acceleration, Electric field, etc.
Is force a vector quantity?Yes, force is a vector quantity. Force is a quantity that describes the interaction between two bodies, with a direction that indicates the direction of the interaction.
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a merry-go-round rotates at the rate of 0.1 rev/s with an 97 kg man standing at a point 1.6 m from the axis of rotation. what is the new angular speed when the man walks to a point 0 m from the center? consider the merry-go-round is a solid 72 kg cylinder of radius of 1.6 m. answer in units of rad/s.
The new angular speed when the man walks to a point 0m from the center is ω = 0.369 rev/s.
What Is Angular Speed?The definition of angular speed is the rate at which angular displacement changes, and it is expressed as,
ω=θ/t
where t is the period of time, is the angular speed, and ω is the angular displacement.
Angular Speed UnitRadian per second is used to measure angular speed. Both angular velocity and angular speed are represented using the same formula.
Now for the given question,
Since there is no external torque, angular momentum of the system is conserved. Then, the angular momentum when the man is at x = 1.6 m, it is equal to that of x = 0 m.
[tex]L_1=L_2\\I_1ω_1=I_1ω_2[/tex]
where I is the moment of inertia of the system. Here we consider the merry-go-round which is a solid cylinder and the man which can be regarded as a point object.
Total moment of inertia in first case is
[tex]I_1=I_{cylinder}+ I_{man}= 1/2 m_{cylinder}R^2_{cylinder}+m_{man}d^2\\ = 1/2 (72)(1.6)^2+(97)(1.6)^2=340.48[/tex]
moment of inertia in second case is
[tex]I_2=1/2 m_{cylinder}R^2_{cylinder}+ m_{man}(0)\\=1/2(72)(1.6)^2=92.16[/tex]
In the second case, the man shows no contribution to the moment of inertia of the system, since he stands on the center.
Finally,
[tex]I_1ω_1=I_2ω_2\\(340.48)(0.1)=(92.16)ω_2\\ω_2=0.369 rev/sec.[/tex]
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A figure skater begins spinning counterclockwise at an angular speed of 4.1 π rad/s. During a 4.5 s interval, she slowly pulls her arms
inward and finally spins at 7.1 π rad/s.
What is her average angular acceleration
during this time interval?
Answer in units of rad/s^2.
The average angular acceleration of the skater is 2.1 rad/s².
What is the average angular acceleration of the skater?
The average angular acceleration of the skater is calculated by applying the following formula.
a = Δω / Δt
where;
Δω is change in angular speedΔt is change in time of motiona = ( ω₂- ω₁ ) / ( t₂ - t₁ )
where;
ω₁ is the initial angular speedω₂ is the final angular speedt₁ is initial timet₂ is final timea = ( 7.1π - 4.1π ) / ( 4.5 )
a = 2.1 rad/s²
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merits and demerits of dimensional equations
Answer:
Explanation:
Merits of Dimensional Equations:
Simplification of physical laws: Dimensional analysis allows us to simplify complex physical laws into simpler, dimensionally homogeneous equations.
Prediction of unknown quantities: Dimensional analysis can be used to predict unknown physical quantities by using only the dimensional information of known quantities.
Unit conversion: Dimensional analysis can be used to convert units of physical quantities from one system to another.
Detection of errors: Dimensional analysis helps in detecting errors in mathematical expressions, as the dimensions of the different terms in an equation must match for the equation to be physically meaningful.
Demerits of Dimensional Equations:
Limited applicability: Dimensional analysis is only applicable to problems where the dimensions of the physical quantities involved are well-defined.
Assumptions required: Dimensional analysis requires certain assumptions to be made about the physical system being studied, and these assumptions may not always be valid.
Approximations involved: Dimensional analysis often involves approximations and simplifications, which can lead to errors in the final results.
Limitations in complex systems: Dimensional analysis can be difficult to apply in complex systems, where multiple physical phenomena are interacting and where the dimensions of the physical quantities involved are not well-defined.
if you wanted to determine the scaled size (radius or diameters) of the planets in your scaled model, what would you need to do?
If you wanted to determine the scaled size of the planets in your scaled model, you would need to know the actual size of the planets and the scale factor you are using for your model.
What is needed to determine the scaled size (radius or diameters) of the planets in your scaled model?To determine the scaled size (radius or diameter) of the planets in your scaled model, you need to know the actual size of the planets and the scale factor you are using for your model. Then, you can calculate the scaled size by multiplying the actual size by the scale factor.
For example, if the actual diameter of a planet is 10,000 kilometers and your scale factor is 1:10,000,000, the scaled diameter of the planet in your model would be 0.1 millimeters.
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Why are electromagnets the strongest of all magnets?
what tracking system did the u.s. department of defense create that uses satellites to support navigation?
The U.S. Department of Defense created a satellite-based navigation system called the Global Positioning System (GPS). The GPS system provides positioning accuracy to within a few meters, making it a crucial tool for navigation and positioning in many different applications.
What is a GPS system?GPS is a worldwide navigation system that uses a network of satellites to provide precise positioning, velocity, and time information to users on the ground, in the air, or at sea. The system was originally developed for military use, but today it is widely used.
How does a GPS work?GPS uses a constellation of satellites orbiting the Earth that transmit signals to GPS receivers on the ground. The receiver calculates its position by determining the time delay between the signals from different satellites .
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a nuclear of 208pb has 82 protons with a sphere of radius 6.34 * 10^-15m. calculate the electric field at the surface of the nucleus
A nuclear of 208pb has 82 protons with a sphere of radius 6.34 * [tex]10^{-15}[/tex]m. The electric field at the surface of the nucleus is 2.24 x [tex]10^{11}[/tex] N/C.
The electric field at the surface of a nucleus can be calculated using Coulomb's law, which states that the electric field produced by a point charge is proportional to the charge and inversely proportional to the square of the distance from the point charge.
E = k * q / [tex]r^{2}[/tex]
where,
E = the electric field in N/C
k = the Coulomb constant, equal to 8.99 x [tex]10^{9}[/tex] N [tex]m^{2}[/tex] / [tex]C^{2}[/tex]
q = the charge on the nucleus, equal to 82 times the charge on a proton, or 82 * 1.60 x [tex]10^{-19}[/tex] C
r is the radius of the nucleus, equal to 6.34 x [tex]10^{-15}[/tex]m
Plugging in these values, we get:
E = 8.99 x [tex]10^{9}[/tex] N [tex]m^{2}[/tex] / [tex]C^{2}[/tex] * 82 * 1.60 x [tex]10^{-19}[/tex] C / 6.34 x [tex]10^{-15}[/tex]m ^2
E = 2.24 x [tex]10^{11}[/tex] N/C.
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which of the following quantities is a displacement? question 7 options: a) 32 ft, vertically downward b) 120 in c) 9.8 m/s2, downward d) -120 m/s e) 9.8 m/s2, upward f) 40 km
From the given options, (f) 40km is representing displacement as it is a vector quantity but has a scalar value that represents the change in position of an object over a given distance, and is expressed in kilometers.
Displacement is a vector quantity that represents the change in position of an object with respect to its initial position. It is defined as the shortest distance between the initial and final points, and is denoted by a straight line connecting the two points. Displacement is always a scalar value and is measured in units of distance, such as meters or kilometers.
In the given options, the only quantity that represents a displacement is "40 km". It is a scalar value that represents the change in position of an object over a given distance, and is expressed in kilometers. The other options are not displacements, but represent other physical quantities such as distance (32 ft), length (120 in), acceleration (9.8 m/s2), or velocity (-120 m/s).
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charge is at charge is at charge is at at what point in the (x, y) plane is the electric field zero?
The electric field is defined as the force experienced by a unit positive test charge placed at a particular point in space.The electric field is zero at a point in the (x, y) plane if there is no net force experienced by the test charge at that point.
This can occur if the test charge is placed at a point of symmetry in the charge distribution, such as the center of a spherical distribution of charges or the midpoint between two equal and opposite charges.
Additionally, the electric field can also be zero at a point if the charges are arranged in such a way that the electric field vectors at that point cancel each other out. To determine the exact location of the point(s) where the electric field is zero, one must perform a vector analysis of the electric field due to the individual charges in the distribution.
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the capacitor has a plate area of 10.0cm2 and a plate spacing of 2.00mm . the dielectric constant for the inserted material is 3.00 . if the potential between the plates exceeds 150.0v , the capacitor discharges and fails. what is the maximum charge that the capacitor can have after the dielectric is inserted?
The required maximum charge that the capacitor can have after the dielectric is inserted Q ≈ 1.98 x 10^-8 C
How to use formula of capacitance to find charge?The capacitance of a parallel-plate capacitor is given by:
C = ε * ε0 * A / d
where
C is the capacitance (in Farads)
ε is the dielectric constant of the material between the plates
ε0 is the vacuum permittivity (8.854 x 10^-12 C^2/Nm^2)
A is the plate area (in m^2)
d is the plate spacing (in meters)
The maximum charge that can be stored in a capacitor without exceeding a given voltage V is given by:
Q = C * V
where Q is the charge (in Coulombs).
According to data:So, first we need to convert the plate area and plate spacing to SI units:
A = 10.0 cm^2 = 10.0 x 10^-4 m^2
d = 2.00 mm = 2.00 x 10^-3 m
Next, we can find the capacitance:
C = ε * ε0 * A / d
C = 3.00 * 8.854 x 10^-12 * 10.0 x 10^-4 / 2.00 x 10^-3
C ≈ 1.32 x 10^-10 F
Finally, we can find the maximum charge:
Q = C * V
Q = 1.32 x 10^-10 * 150.0
Q ≈ 1.98 x 10^-8 C
So, the maximum charge that the capacitor can have after the dielectric is inserted is approximately 1.98 x 10^-8 Coulombs.]
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