a) The energy stored in the capacitor is 5.10 × 10⁻¹⁰ J.
b) The energy stored in the capacitor with the dielectric inserted is 1.04 × 10⁻⁹ J.
c) The energy stored in the capacitor with the dielectric inserted and the battery disconnected is 2.14 × 10⁻¹⁰ J.
The energy stored in a parallel-plate capacitor is given by the formula:
U = [tex]\frac{1}{2}CV^2[/tex]
where U is the energy stored, C is the capacitance, and V is the voltage across the capacitor.
(a) The capacitance of a parallel-plate capacitor is given by the formula:
C = [tex]\frac{\epsilon_0A}{d}[/tex]
where [tex]\epsilon_0[/tex] is the permittivity of free space, A is the area of the plates, and d is the distance between them.
Substituting the given values, we have:
C =[tex]\frac{(8.85 \times 10^{-12} \textrm{ F/m})(2.00 \times 10^{-4} \textrm{ m}^2)}{5.00 \times 10^{-3} \textrm{ m}} = 7.08 \times 10^{-12} \textrm{ F}[/tex]
The voltage across the capacitor is given by the battery voltage, which is 12.0 V. Substituting these values into the formula for energy, we have:
U = [tex]\frac{1}{2}(7.08 \times 10^{-12} \textrm{ F})(12.0 \textrm{ V})^2 = 5.10 \times 10^{-10} \textrm{ J}[/tex]
(b) When a dielectric is inserted between the plates, the capacitance increases. The new capacitance is given by the formula:
[tex]C' = \kappa C[/tex]
where [tex]\kappa[/tex] is the dielectric constant of the material.
Substituting the given values, we have:
[tex]C' = (2.56)(7.08 \times 10^{-12} \textrm{ F}) = 1.82 \times 10^{-11} \textrm{ F}[/tex]
The voltage across the capacitor remains the same, so the energy stored in the capacitor becomes:
[tex]U' = \frac{1}{2}(1.82 \times 10^{-11} \textrm{ F})(12.0 \textrm{ V})^2 = 1.04 \times 10^{-9} \textrm{ J}[/tex]
(c) If the battery is disconnected before the dielectric is inserted, the charge on the plates remains the same. However, the voltage across the capacitor decreases due to the increased capacitance. The new voltage is given by the formula:
[tex]V' = \frac{V}{\kappa}[/tex]
Substituting the given values, we have:
[tex]V' = \frac{12.0 \textrm{ V}}{2.56} = 4.69 \textrm{ V}[/tex]
The energy stored in the capacitor becomes:
[tex]U' = \frac{1}{2}(1.82 \times 10^{-11} \textrm{ F})(4.69 \textrm{ V})^2 = 2.14 \times 10^{-10} \textrm{ J}[/tex]
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the wheelbase on a truck is 2.4 m wide and the truck's center of mass is located along the vertical centerline of the truck and 2.0 m above the bottom of the tires. the truck is going around a banked turn, when it is forced to stop. what is the maximum slope that the bank can have such that the truck will not tip over?
As center of mass is located along the vertical centerline of the truck, The maximum slope that the bank can have such that the truck will not tip over is 16.7°.
To calculate the maximum slope that the bank can have such that the truck will not tip over, we need to consider the forces acting on the truck and the torque due to these forces. The forces acting on the truck are the weight of the truck and the normal force of the road, and the torque is due to the fact that these forces do not act through the center of mass of the truck. The maximum slope can be calculated by finding the angle at which the normal force is reduced to zero, causing the truck to tip over. At this point, the weight of the truck will provide the only force acting on the truck, and it will act through the edge of the tires.
Let θ be the angle of the bank, and let W be the weight of the truck. The normal force acting on the truck:-
N = W cosθ
The weight of the truck acts through the center of mass, which is located 2.0 m above the bottom of the tires. The torque due to the weight:-
τ W = W * 2.0 * sinθ
The normal force acts through the center of the tires, which are located 1.2 m apart. The torque due to the normal force:-
τ N = N * 1.2/2 * sinθ
For the truck not to tip over, the torque due to the normal force must be greater than or equal to the torque due to the weight:
τ N ≥ τ W
Reserving the expressions for N and the torques:-
W cosθ * 0.6 * sinθ ≥ W * 2.0 * sinθ
Simplifying:-
tanθ ≥ 0.6/2.0
θ ≥ arctan0.3
θ ≥ 16.7°
Therefore, the maximum slope that the bank can have such that the truck will not tip over is 16.7°.
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Two large, charged plates with charge density ±30µC/m^2 face each other with a separation of 5.0 mm. The negative plate is grounded, and defined as 0 potential. Find the electric potential at a location 8.0mm from the negative plate, 3.0mm from the positive plate.
V=3.39×10⁶ ×d for 0≤d≤0.005 m, 7.73x10⁷ m/s is the electric potential at a location 8.0mm from the negative plate, 3.0mm from the positive plate
a. Identify the unknown:
The potential everywhere
List the Knowns:
Charge density of the two plates: σ = ±30×10⁻⁶ C/m²
Distance between the two plates: d=5×10⁻³ m
Permittivity of free space: ε₀=8.85×10⁻¹² C²/N⋅m²
Set Up the Problem:
Since the σ are equal and opposite, this means that in the region outside of the two plates, the electric fields cancel each other out to zero: E = 0 The electric field between the plates is this strong:
E = σ/ε₀ = 30×10⁻⁶/8.85×10⁻¹² = 3.39x10⁶N/C
Possible variations between the positive plate and the negative plate include:
ΔV=Ed=3.39×10⁶ ×0.005=1.7×10⁴ V
Assuming the negatively charged plate is at the origin (d=0) and has no potential, the electric field is directed away from the positively charged plate and towards the negatively charged plate, the positive plate is at (d=+0.005 m) and have 1.7×10⁴ V
Solve the Problem:
V=0 for d<0
V=3.39×10⁶×d for 0≤d≤0.005 m
V=1.7×10⁴ V for d>0.005m
b. Identify the unknown:
when an electron leaves a state of rest at the negative plate and strikes the positive plate, how quickly it moves
List the Knowns:
Electron charge: e=1.6×10⁻¹⁹ C
Electron mass: m=9.11×10⁻³¹ kg
Set Up the Problem:
Potential and electric potential energy have the following relationships: = U/q
U=qV
To move the drop, this potential energy is converted to kinetic energy:
1/2mv²=qV
v = √2qV/m
Solve the Problem:
v = √(2×1.6×10⁻¹⁹×1.7×10⁴/9.11×10⁻³¹) = 7.73x10⁷ m/s
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what is the purpose of the rheostat in this experiment? 1) to limit the current in the circuit. 2) to overheat. 3) as an aid to adjusting the current in the circuit. 4) it is the resistor whose resistance is to going to be determined. group of answer choices 3 and 4 1 and 2 1 and 3 2 and 3 4 only
The purpose of the rheostat in this experiment is It limits the current in the circuit and as an aid to adjusting the current in the circuit. Option C.
A rheostat is defined as,
A variable resistor which is used for controlling the inflow of electric current either by accelerating or dropping the resistance.
The term rheostat was chased by the English scientist Sir Charles Wheatstone and is concluded from the Greek word “ rheos ” and “ statis ” which means current controlling device.
All electrical circuit has three fundamental components, and they are
The circuit's applied voltage
through the circuit current
the circuit's resistance offering
A rheostat is a variable resistor that's used to control the inflow of electrical current in a circuit. By conforming the resistance of the rheostat, it's possible to acclimate the quantum of current flowing through the circuit.
This can be useful in a variety of electrical trials and operations, similar as testing the current- voltage relationship of a circuit or regulating the quantum of power supplied to a cargo.
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The stored energy that can be used to do work is called ______ energy, while the energy of motion used to do work is called ________ energy.
The stored energy that can be used to do work is called Potential energy
while the energy of motion used to do work is called kinetic energy.
Potential energy is simply stored energy that, depending on its surroundings or circumstances, a thing may use. Potential energy is the energy that is held inside a system of physically interacting things, to use terminology more closely related to physics.
Kinetic energy, often known as the energy of motion, may be seen in the motion of things and subatomic particles. Kinetic energy may be found in all particles and moving objects. Examples of kinetic energy in action include a person walking, a baseball flying through the air, food tumbling off a table, and a charged particle in an electric field. Everything contains kinetic and potential energy. Kinetic energy is the ability to move anything (KE). Energy is a potential form of energy (PE).
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What is the activation energy of a reaction if it has the following rate constants?
Rate Constant Temperature
6.20 x 10^-4 s^-1 700 K
2.39 x 10^-2 s^-1 760 K
The activation energy of a reaction if it has the following rate constants is calculated to be 126.8 kJ/mol.
To calculate the activation energy of a reaction, we can use the Arrhenius equation:
k = A × e^(-Ea/RT)
where,
k is the rate constant
A is the pre-exponential factor
Ea is the activation energy
R is the gas constant
T is the temperature in Kelvin
We have two rate constants at different temperatures, so we can set up two equations:
k₁ = A × e^(-Ea/RT₁)
k₂ = A × e^(-Ea/RT₂)
We want to solve for Ea, so we can take the natural logarithm of both sides of each equation:
ln(k₁) = ln(A) - Ea/RT₁
ln(k₂) = ln(A) - Ea/RT₂
We can subtract the second equation from the first to eliminate ln(A):
ln(k₁) - ln(k₂) = Ea/R × (1/T₂ - 1/T₁)
Now we can solve for Ea:
Ea = -R × (ln(k₁) - ln(k₂)) / (1/T₂ - 1/T₁)
Plugging in the given values, we get:
Ea = -8.314 J/mol/K × (ln(6.20 × 10⁻⁴) - ln(2.39 × 10⁻²)) / (1/760 K - 1/700 K)
Ea ≈ 126.8 kJ/mol
Therefore, the activation energy of the reaction is approximately 126.8 kJ/mol.
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5. Express the following quantities in their basic dimensions: a) Electric resistance (2), (R = V = q = 1xt) b) Universal Gas constant (J/K mol) 1
Answer:
a) Electric resistance: The basic dimensions of electric resistance are resistance (R) which has the dimension of [mass] x [length]^2 / [time]^3.
b) Universal Gas Constant: The basic dimensions of the Universal Gas constant (R) are [energy]/[temperature x amount of substance]. These dimensions can be expressed as [mass] x [length]^2 / [time]^2 / [temperature] x [amount of substance].
Explanation:
acceleration is a vector and has direction. when the object moves to the right and speeds up, what is the direction of the acceleration? group of answer choices to the right. to the left. up. down. in the direction of the force that is causing the change of speed. in the direction of the gravitational force.
An object that is travelling to the right would accelerate in the same direction as its motion, which would be to the right. This is so because acceleration, which encompasses both speed and direction of motion, is the rate at which velocity changes.
If an object is going to the right and then accelerates, the acceleration would also be moving to the right, following the motion. This is so because acceleration, which encompasses both speed and direction of motion, is the rate at which velocity changes. While the item in this instance is moving faster, its velocity is rising in the same direction as its motion, and consequently, the acceleration is likewise moving faster. The other possible solutions don't work in this case.The rate at which velocity changes is known as the acceleration, which is a vector quantity. The speed and direction of motion of an object are described by a vector called velocity.
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how is the second law demonstrated in the experiment when we use a single fixed mass? group of answer choices the experiment demonstrates the acceleration as being proportional to the force. the experiment shows that that the net force is the sum of forces acting on the object. the experiment shows that the motion of the object stops when the force stops. the experiment shows that the application of force causes the object to acquire a constant speed. that the net force applied is zero. the experiment shows that when a constant force is applied the acceleration increases continuously. the experiment shows that when a force is applied the mass changes inversely with it.
Experiment demonstrates second law of motion, where acceleration is directly proportional to force and inversely proportional to object's mass.
The second law of motion states that the acceleration of an object is directly proportional to the force applied to it and inversely proportional to its mass. In an experiment where a single fixed mass is used, the second law is demonstrated by the acceleration being proportional to the force applied to the object. As the force acting on the object is increased, the acceleration also increases proportionally. This is because the mass remains constant and the force acting on the object is the net force, which is the sum of all the forces acting on it.
Furthermore, the experiment also shows that the motion of the object stops when the force acting on it stops, and the application of a constant force causes the object to acquire a constant speed. This is because, according to the second law, the object will continue to move with a constant velocity when there is no net force acting on it.
Therefore, the experiment with a single fixed mass is an excellent way to demonstrate the second law of motion, which states that the acceleration is directly proportional to the force applied and inversely proportional to the mass of the object.
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what is the electric field vector ~e(r) for r < a, where r is the distance from the center of the shell? explain your answer
Assuming you are referring to a uniformly charged spherical shell with radius "a", the electric field inside the shell (i.e., for r < a) is zero.
This can be explained by the fact that the shell has a symmetrical charge distribution, and hence, for any point inside the shell, the electric field due to all charges on the shell cancel out exactly. This is a consequence of the superposition principle of electric fields, which states that the total electric field at any point in space is the vector sum of the individual electric fields due to all the charges present. To see why the electric field inside the shell is zero, consider an arbitrary point P inside the shell at a distance "r" from the center of the shell. We can imagine dividing the shell into small elemental areas dA, each of which contains a small amount of charge dQ. The electric field vector due to each of these small charges at point P can be calculated using Coulomb's law as:
[tex]dE = (1 / 4\pi\epsilon _0) (dQ / r^2)r[/tex]
Since the shell is uniformly charged, we can assume that the magnitude of the electric field due to each elemental charge is the same. Also, since the direction of ȓ is different for each elemental charge, the direction of the electric field vector dE varies as we move around the shell. However, due to the symmetry of the charge distribution, the magnitude of the electric field at point P due to all the elemental charges on the shell is the same, and hence the electric field due to all elemental charges is perfectly cancelled out at point P, resulting in a net electric field of zero.
Therefore, we can conclude that the electric field vector ~e(r) for r < a, where r is the distance from the center of the shell, is zero.
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a 2-khz sound wave traveling through a bar of iron has a wavelength of 2.56 meters. what is the velocity of sound in iron?
From the information provided, the velocity of sound in iron is approximately 5120 m/s.
Velocity is a vector quantity that describes the rate of change of an object's position with respect to time. It is defined as the displacement of an object divided by the time interval over which the displacement occurred, and it has both magnitude and direction.
We can use the formula for the velocity of a sound wave:
v = fλ
where v is the velocity of the sound wave, f is the frequency of the wave, and λ is the wavelength of the wave.
Substituting the given values, we get:
v = (2 kHz)(2.56 m) = 5120 m/s
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3. The electric field at a point 27 cm from a charged particle is 105 N
C
toward the particle.
What is the charge on the particle?
The particle has a charge of 2.44 x 10-8 C. when electric field at a point 27 cm from a charged particle is 105 N
What is charge?The electrical properties of particles like electrons and protons are described by charge, a fundamental property of matter. Particles with the same electric charge repel one another while those with the opposite charge attract one another. Electric charge can be positive or negative. The Coulomb (C) is the charge measurement unit, and particles' charges are typically measured in Coulombs.
E is equal to kQ/r₂, where k is the Coulomb constant, r is the distance from the particle to the point where the electric field is being measured, Q is the charge on the particle, and E is the electric field.
The electric field at a distance of 27 cm from the particle is calculated to be 105 N/C in the particle's direction. We now have:
By substituting these values into the equation for the electric field, we obtain: E = 105 N/C r = 27 cm = 0.27 m
105 N/C = (8.99 x 10⁹ N m²/C²) × Q / (0.27 m)²
Solving for Q, we get:
Q = (105 N/C) × (0.27 m)² / (8.99 x 10⁹ N m²/C²)
Q = 2.44 x 10⁻⁸ C
Therefore, the charge on the particle is 2.44 x 10⁻⁸ C.
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according to the kinetic theory, collisions between molecules in a gas_____
According to the kinetic theory of gases, collisions between the molecules in a gas are perfectly elastic.
It means that the total kinetic energy of the colliding molecules is conserved. This means that during a collision, the molecules may exchange energy and momentum with one another, but the total amount of energy and momentum remains constant.
In addition, according to the kinetic theory, the molecules in a gas are in constant random motion and travel in straight lines until they with each other or with the walls of their container.
The average kinetic energy of the molecules is proportional to the temperature of the gas, and the pressure of the gas is proportional to the number of collisions the molecules make with the walls of the container in a given amount of time. The kinetic theory provides a useful framework for understanding the behavior of gases at the molecular level.
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A car speeds up from 13. 5 m/s to 34. 4 m/s in 4. 8 seconds. What is the average speed during this time? round your answer to 2 decimal places
The average speed during the acceleration is 23.95 m/s.
The average speed of the car during the time it takes to accelerate can be calculated as the average of the initial and final speeds.
Speed is equal to the total distance covered by the car divided by the time required to cover the distance.
As per the given information,
The initial speed of the car is 13.5 m/s, and
the final speed is 34.4 m/s.
Therefore, the average speed can be calculated as:
Average speed = (initial speed + final speed) / 2
Average speed = (13.5 m/s + 34.4 m/s) / 2
Average speed = 23.95 m/s
Rounding to two decimal places, the average speed during the acceleration is 23.95 m/s.
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a proton and an electron are fixed in space with a separation of 821 nm. calculate the electric potential at the midpoint between the two particles.
The electric potential at the midpoint between the two particles a proton and an electron is 2.95*10⁻³ V.
You employ the following to determine the two protons' combined electric potential at their midpoint:
[tex]V = V1 + V2 =k\frac{q}{r} +k\frac{q}{r} = 2\frac{kq}{r}[/tex]
where you have considered how each proton contributes to the overall electric potential.
k: Coulomb's constant = 8.98*10^9 Nm^2/C^2
q: charge of the proton = 1.6*10^{-19}C
r: distance from the point (at the midway distance between the protons) to one proton = 821nm = 821nm/2 = 410.5nm = 410.5*10⁻⁹m
You replace the values of the parameters in the equation (1):
[tex]V =2\frac{(8.98*10^-^9 Nm^2/C^2)(1.6*10^-^1^9)}{410.5*10^-^9 m} \\\\V = 2.95*10^-^3 V[/tex]
The electric potential is 2.95*10⁻³ V
Because each proton generates an electric field with a same magnitude but an opposite direction, there is no electric field at the halfway between the protons.
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Nichrome is used as a heating element in electric iron. give reason
Nichrome is used as a heating element in electric irons
High resistanceCorrosion resistanceGood temperature stabilityWhy Nichrome is used as a heating element?High resistance: Nichrome has a high electrical resistance, which means that it converts electrical energy into heat energy efficiently. This makes it ideal for use in heating elements where heat generation is the primary requirement.
Good temperature stability: Nichrome has a high melting point and a low coefficient of thermal expansion. This means that it can maintain its structural integrity even at high temperatures and does not deform or break easily.
Corrosion resistance: Nichrome is resistant to corrosion, which makes it suitable for use in electrical appliances that are exposed to moisture, such as electric irons.
Long lifespan: Nichrome has a long lifespan and does not degrade easily even with repeated use. This makes it a reliable and durable choice for heating elements.
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Assertion - Rainbow is a natural phenomenon showing dispersion.
Reason - Splitting light is known as dispersion of light
Rainbow is a natural phenomenon showing dispersion. Splitting light is known as dispersion of light. The reason is correct for the given assertion.
What is Dispersion of light?Dispersion is the phenomenon in which the phase velocity of a light wave depends on its frequency. It is sometimes also termed as chromatic dispersion, which is used for the specificity to optics in particular. A medium having this common property may be termed as a dispersive medium.
A rainbow is a meteorological phenomenon which is caused by the reflection, refraction and dispersion of light in the water droplets resulting in a spectrum of light appearing in the sky. This takes the form of a multicolored circular arc. Rainbows are caused by the sunlight which always appear in the section of sky directly opposite the Sun.
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Your question is incomplete, most probably the complete question is:
Assertion - Rainbow is a natural phenomenon showing dispersion.
Reason - Splitting light is known as dispersion of light
What is right answer?
What happens to the time period of a simple pendulum if the amplitude is doubled?
When producing modest swings, the amplitude frequently has no impact at all on the pendulum's period. There is a tiny but insignificant rise in the period when the pendulum's amplitude is greater.
What alter on time period pendulum if amplitude changed?The distance to travel increases as the amplitude rises, but when the restoring force rises as well, the acceleration rises correspondingly.
This implies that the mass can move faster and cover a bigger distance. Since these qualities cancel one another, amplitude has no bearing on period.
A straightforward harmonic oscillator's period is independent of its amplitude. with the graphs of acceleration and velocity produced by the time derivatives. These oscillators also show how kinetic and potential energy can be transferred.
Therefore, the length of time is unrelated to the vibration's magnitude. Time period is unchanged by doubling the oscillation's amplitude.
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the length of the vibrating part of a string on a musical instrument is 0.65 m. when plucked, that string has a fundamental frequency of 110 hz. the string is plucked after the instrument is placed in a room filled with helium gas. what is the wavelength of the sound wave that propagates in the room?
The wavelength of the sound wave in the room is approximately 3.118 meters, given the frequency and assumed speed of sound.
The speed of sound in a gas relies upon the properties of the gas, and specifically on its temperature, pressure, and sub-atomic weight. Since the issue doesn't give data on these properties, we will accept that the speed of sound in helium is equivalent to in air at room temperature and tension, which is roughly 343 meters each second.
To find the frequency of the sound wave in the room, we can utilize the recipe:
frequency = speed of sound/recurrence
Connecting the qualities we know, we get:
frequency = 343 m/s/110 Hz = 3.118 m
At long last, we can utilize the recipe frequency = speed of sound/recurrence to track down the frequency of the sound wave in the room. The frequency is the distance between two sequential focuses on the wave that are in stage with one another, i.e., that have a similar plentifulness and bearing of movement. For this situation, the frequency ends up being around 3.118 meters.
Subsequently, the frequency of the sound wave in the room is roughly 3.118 meters.
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An object traveling in the negative direction and accelerating in the negative direction will slow down. Group of answer choices
True
False
False. An object traveling in the negative direction and accelerating in the negative direction will not slow down, but will actually speed up.
Acceleration is the rate of change of velocity, and if an object is accelerating in the negative direction, it means that its velocity is decreasing in the positive direction and increasing in the negative direction. Therefore, the object will continue to move in the negative direction at a faster speed.
It is important to consider that acceleration is a magnitude that can cause the velocity of a body to increase or decrease.
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you're flying a cessna 182 skylane, n935fa, on a cross-country vfr flight with flight following. during a handoff, the ideal call sign to use when contacting the new controller is .
You're flying a Cessna 182 Skylane, N935FA, on a cross-country VFR flight with flight following. During a handoff, the ideal call sign to use when contacting the new controller is Skylane 935FA.
Flight following is a relatively simple concept as it’s an aircraft flying under VFR that is taking use of Air Traffic Control (ATC) services. Practically, it indicates that several advisories may be available from the controller and the flight is radar identified by ATC.
The service is given on a workload-permitting basis and involves multiple layers of service, there’s not entirely uniform delivery among Center or Approach control facilities. The fusion of these realities has resulted in misinformation, misunderstandings, and even no awareness of its existence.
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Negative charge particle located in the electron cloud is called?
The negative charge particle located in the electron cloud of an atom is called an electron.
define electron ?
An electron is a subatomic particle that carries a negative electric charge. It is one of the fundamental particles that make up atoms, along with protons and neutrons.
Electrons are extremely lightweight, having a mass of approximately 9.11 x 10^-31 kilograms. They are found in shells or energy levels surrounding the nucleus of an atom and participate in chemical reactions and the flow of electrical current.
The negative charge particle located in the electron cloud of an atom is called an electron.
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a car moving a constant 7.0 m / s turns a corner with a radius of 20 m . what is the acceleration of the car?
The acceleration of the car as it turns the corner is 2.45 m/s^2, and it is directed towards the center of the turn.
What is Acceleration?
When an object changes its velocity, either by increasing or decreasing its speed or by changing its direction of motion, it experiences acceleration.
The formula for acceleration is:
a = (v2 - v1) / t
where a is the acceleration, v2 is the final velocity, v1 is the initial velocity, and t is the time taken for the change in velocity to occur.
To find the acceleration of the car as it turns the corner, we can use the centripetal acceleration formula:
a = v^2 / r
where a is the acceleration, v is the velocity of the car, and r is the radius of the turn.
In this case, the velocity of the car is constant at 7.0 m/s, and the radius of the turn is 20 m.
a = (7.0 m/s)^2 / 20 m
a = 2.45 m/s^2
Therefore, the acceleration of the car as it turns the corner is 2.45 m/s^2, and it is directed towards the center of the turn.
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consider a cold canned (typically cylindrical in shape) drink left on a table. would the heat transfer be steady or transient? would you model the heat transfer as one-, two-, or three-dimensional? also, which coordinate system would you use to analyze this heat transfer problem?
The heat transfer in this situation would be transient, as the temperature of the room, the can, and the drink inside the can are all changing over time.
The heat transfer can be modeled as a two-dimensional problem, since the can is cylindrical in shape and the temperature of the can and the drink inside the can will only depend on the vertical and horizontal components of heat transfer. The coordinate system used to analyze the heat transfer problem would be cylindrical, since it is the most appropriate for modeling a cylindrical object. In this system, the radial direction is along the circular circumference of the can, and the axial direction is along the length of the can. The temperature of the can and the drink inside the can can then be calculated using the two-dimensional equations of heat transfer, which consider both the radial and axial components of heat transfer.
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A toy rocket is launched from a 5.6 m high platform in such a way that its height, h (in meters), after t seconds is given by the equation h= - 4.97t^2+ 38.5t + 5.6. How long will it take for the rocket to hit the ground?
The time it will take the rocket to hit the ground is 7.92 seconds
What is the time of motion of the rocket?
The rocket will hit the ground when its height, h, is equal to zero. To find the time, t, when this happens, we can set h equal to zero and solve for t:
-4.97t^2 + 38.5t + 5.6 = 0
We can use the quadratic formula to solve for t:
t = (-b ± √(b^2 - 4ac)) / 2a
where
a = -4.97,
b = 38.5, and
c = 5.6
Plugging in these values, we solve for time of motion:
t = (-38.5 ± √(38.5^2 - 4(-4.97)(5.6))) / 2(-4.97)
t = (-38.5 ± √(1486.25 + 94.544)) / -9.94
t = (-38.5 ± √(1580.794)) / -9.94
t = (-38.5 ± 39.939) / -9.94
t = (-38.5 - 39.939) / -9.94
t = (78.439) / -9.94
t = 7.92 seconds
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. a common statistic in car tests is the standing (starting from rest) quarter-mile performance. a modern sports car can achieve a terminal speed (speed at the end of the quarter-mile) of 120 mph (193 km/h). how does the average acceleration compare to g? (0.25 mile
The required acceleration of the car compared to g is 0.36 times the value of g.
The velocity v of the car is given as 193 mph = 193× 18/5 = 53.61 m/s.
The distance covered = 0.25 miles = 0.25× 1609 m/ 1 mile = 402.336 m
Initial velocity u = 0
Let us find the acceleration of the car using the equation of motion.
v² - u² = 2 a s
where,
v is final velocity
u is initial velocity
a is acceleration
s is distance
Entering values in the above equation, we have,
53.61² - 0 = 2 a (402.336)
804.672 a = 2874.03
a = 3.57 m/s²
Let us compare it with the value of 'g',
a/g = 3.57/9.8 = 0.36
So, a = 0.36 g
Thus, the acceleration of the car is 0.36 times the value of g.
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You kick a soccer ball with an initial vertical velocity of 14 m/s and a horizontal velocity of 18 m/s. What is the initial resultant velocity of the soccer ball?
Answer:
Explanation:
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electrical activity is started at the sa node, which causes an action potential to spread through the heart through the ______.
eight 7 w christmas tree lights are connected in series to each other and to a 120v source. what is the resistance of each bulb
From the information provided, each christmas tree bulb has a resistance of approximately 257.4 Ω.
To determine the resistance of each bulb, we first need to find the total resistance of the circuit. We can use Ohm's law to do this:
V = IR
where V is the voltage (120 V), I is the current, and R is the total resistance. Since the lights are connected in series, the current is the same through each bulb. We can use the power of each bulb (7 W) and the voltage to find the current:
P = IV
I = P/V = 7 W / 120 V = 0.0583 A
Now we can use Ohm's law to find the total resistance:
R = V/I = 120 V / 0.0583 A = 2059.5 Ω
Since there are eight bulbs, each bulb has the same resistance. We can find the resistance of each bulb by dividing the total resistance by the number of bulbs:
R_each = R_total / number of bulbs = 2059.5 Ω / 8 = 257.4 Ω
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if the field changes in value from -0.100 t to 0.150 t in an interval of 0.500 s, what is the magnitude of the average voltage induced in the coil?
The magnitude of the average voltage induced in the coil if the field changes in value from -0.100 t to 0.150 t in an interval of 0.500 s is 125000 V.
The "pressure" that pushes electricity is referred to as voltage. A voltage is measured in volts (V), and greater voltages result in more electricity flowing to an electronic equipment. Yet, electronic gadgets must work within a range of voltages since too much voltage might harm their circuitry.
Change in magnetic field = 0.150 - (- 0.1)
= 0.250 T
Area of coil = 500 m²
Induced emf = N[ change in flux]/time
flux = Area x magnetic field
Initial flux = 500 x 0.150 = 75 = 75 Tm²
Final flux = 500 x (-1.00) = 50 = - 50 Tm²
Change in flux = 75 + 50 = 125
Induced emf = 500(125) / 0.5
= 62500 / 0.5
= 125000 V
The average voltage is 125000 V
In contrast, a voltage that is too low can also be problematic since it prevents circuits from functioning and renders the devices that are constructed around them ineffective. To handle electronic devices properly and pinpoint the root causes of troubles when they arise, one must have a working knowledge of voltage and how to resolve related problems.
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assuming the lower arm has a mass of 2.8 kg and its cg is 12 cm from the elbow-joint pivot, how much force must the extensor muscle in the upper arm exert on the lower arm to hold a 7.5 kg shot put (fig. 12-7)?
The correct option is A, 1000N force must the extensor muscle in the upper arm exert on the lower arm to hold a 7.5 kg shot put.
Mm = mass of muscle
Me = mass of elbow
Mb = mass of ball
τ = Mad-> torque = mass * gravity * distance
-Mmad + Mead + M2ad = 0
Mm (9.80) (-.025m) + (2.8kg) (9.80) (.12m) + (7.5kg) (9.80) (.3m) = 0
Mm = 103.44kg
F = Ma = (103.44kg) (9.80)
= 1014N ~ 1000N
Force is a physical quantity that describes the interaction between objects or systems. It can be defined as the push or pull on an object resulting from the interaction between two or more bodies. The unit of force is the newton (N), and it is represented by the symbol F.
Force can change the motion of an object by accelerating,decelerating, or changing its direction. The magnitude and direction of a force are critical in determining how it will affect an object. There are several types of forces, including contact and non-contact forces. Contact forces involve direct physical contact between objects, while non-contact forces occur at a distance without physical contact.
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Complete Question: -
Assuming the lower arm has a mass of 2.8 kg and its CG is 12 cm from the elbow-joint pivot, how much force must the extensor muscle in the upper arm exert on the lower arm to hold a 7.5 kg shot put (Fig. 12-7)? ?????
A. 1000 N
B. 1500 N
C. 100 N
D. 500 N
E. 750N
