The dielectric constant is 2.11
What does the term "capacitance" mean?Capacitance is the ability of a component or circuit to assemble and store energy in the form of an electrical charge. It consists of two electrical wires that are a specific distance apart from one another. The void between the conductors can be filled with vacuum or a dielectric, an insulating material. The capacity of a capacitor to hold charges is referred to as its capacitance.
Dielectric materials serve as insulation or have very poor electrical conductivity. Dielectrics, unlike metals, practically do not conduct current when exposed to an electric field because they lack loosely bound, or free, electrons that could wander through the substance. Instead, there is electrical polarisation.
The capacitance of the empty capacitor ,C1 = 12µF = 12*10^-6F
Battery voltage= 12 V
charge, Q2= 2.5 x 10-5 C
Initial charge ,Q1 = C1V1
= 12* 12*10^-6
= 224 *10^-6C
Qk = Q1 + Q2
Qk = (2.24 + 2.5)*10^-5 = 4.74*10^-5
Ck = KC1
Only the charges differ; the voltage (V) across both capacitors stays constant.
Qk/V = K Q1/V
K = Qk/Q1
K = 4.74 *10^-5/2.24*10^-5
K = 2.11
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calculate the power required of a 60- kg person climbs a tree 5 meters high in 10 seconds. Acceleration due to gravity is 10 m/s 2.
The Power is equal to 300 J/s or 300 Watts.
A force that causes a displacement is what the term "quantity work" refers to. The duration of this force's action to produce the displacement has nothing to do with work or power. Sometimes the task is completed quite fast, and other times it is completed fairly slowly. For instance, it takes an unusually long time for a rock climber to raise her body a few meters up the cliff's edge. A trail hiker, on the other hand, could quickly raise her body a few meters if she chooses the simpler route up the mountain. Even though they both perform the same amount of labor, the hiker completes it in a lot less time than the rock climber.
The formula for power is ( P = [tex]\frac{W}{t}[/tex] ) or ( P = [tex]\frac{m \times a \times d}{t}[/tex] )
m ( mass ) = 60 kg
a ( acceleration ) = 10 m/s²
d ( distance ) = 5 m
t ( time ) = 10 s
P ( Power ) = ?
P = [tex]\frac{m \times a \times d}{t}[/tex]
= [tex]\frac{60\times 10 \times 5}{10}[/tex]
= [tex]\frac{3000}{10}[/tex]
= 300 J/s
= 300 Watts
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A body of mass 50 kg explodes and splits into three pieces. The first piece has a mass of 10 kg and a velocity of [-3,2] m/s, the second piece has a mass of 18 kg and a velocity of [5, -4] m/s. What is the velocity of the third piece?
.
The velocity of the third piece 2/11. (13 j - 15i)
What is velocity?Velocity is the directional velocity of a moving object as an indicator of the rate of change of position observed from a particular frame of reference and measured by a particular time standard.Velocity is a vector representation of the displacement an object or particle experiences with respect to time. The standard unit for velocity magnitude (also called velocity) is meters per second (m/s). Alternatively, centimeters per second (cm/s) can be used to express velocity magnitude.Simply put, velocity is the speed at which something moves in a particular direction. For example, the speed of a car traveling north on a highway, or the speed of a rocket after launch.To learn more about velocity from the given link:
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as infants extract an increasing number of potential word forms from the speech stream they hear, they begin to associate these with concrete, perceptually available objects in their world. this is referred to as multiple choice question.
Infants extracting an increasing number of potential word forms from the speech stream they hear, begin to associate these with concrete, perceptually available objects is referred to as statistical learning.
Statistical learning refers to the process by which infants extract potential word forms from the speech stream they hear and begin to associate them with concrete, perceptually available objects. This process is thought to be a crucial component of language development, as it allows infants to begin to understand the structure and meaning of the language they are exposed to.
Through statistical learning, infants are able to identify patterns and regularities in the speech they hear, such as the relationship between a word and the object it refers to. This ability enables them to begin to build a vocabulary and develop an understanding of the grammar and syntax of their native language. Additionally, statistical learning may also play a role in the development of other cognitive abilities, such as memory and attention.
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Your question seems incomplete, but I suppose the question was:
"As infants extract an increasing number of potential word forms from the speech stream they hear, they begin to associate these with concrete, perceptually available objects in their world. this is referred to as"
(a) what is the velocity vpi of the plank relative to the surface of the ice? (use the following as necessary: vgp, mg, and mp. indicate the direction with the sign of your answer. let the positive direction be in the direction that the girl walks.)
The final velocity of plank with respect to the ice will be (-Mg×Vgp)/(Mg+Mp) and it will be in direction opposite to the girl.
Mass of the girl, = Mg
Mass of the plank, = Mp
Velocity of the girl with respect to plank, = Vgp
Velocity of the plank with respect to ice, = Vpi
Velocity of girl with respect to ice, = Vgi
Initially both girl and the plank were at rest with respect to ice, so initial momentum of both was zero. So final momentum of both with respect to ice will be zero.
Mg×Vgi + Mp×Vpi = 0
Mg×Vgi = -Mp×Vpi .....equation (1)
We know that velocity of girl with respect to the ice will be the sum of velocity of the girl with respect to the plank and the velocity of the plank with respect to the ice.
Vgi = Vpi + Vgp.... put this value in equation (1)
Mg×(Vpi + Vgp) = -Mp×Vpi
Mg×Vpi + Mg×Vgp) = -Mp×Vpi
Vpi(Mg + Mp) = -Mg×Vgp
Vpi = -Mg×Vgp/(Mg + Mp)
A negative sign indicates that the velocity of the plank will be in the opposite direction to the girl.
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--The give question is incomplete, the complete question is:
"A girl of mass Mg is standing on a plank of mass Mp. Both are originally at rest on a frozen lake that constitutes a frictionless, flat surface. The girl begins to walk along the plank at a constant velocity Vgp to the right relative to the plank. (The subscript gp denotes the girl relative to the plank.)
What is the velocity Vpi of the plank relative to the surface of the ice? (Use the following as necessary: Vgp, Mg, and Mp. Indicate the direction with the sign of your answer. Let the positive direction be in the direction that the girl walks.)"--
A researcher wants to see if alcohol consumption will enhance driving performance. One group of participants drinks no
alcohol during the study, one group drinks 3 shots of alcohol, and another group receives 6 shots of alcohol. Participants are
tested in a driving simulator after and get a score for accuracy. The amount of alcohol consumed is the
a. dependent variable
b. independent variable
c. correlated variable
d. control variable
The amount of alcohol consumed will be b. independent variable when participants are tested in a driving simulator after and get a score for accuracy.
What is an Independent variable?
An independent variable is a variable that is manipulated or changed by the researcher in an experiment in order to observe its effect on the dependent variable. In other words, it is a variable that the researcher has control over and changes to test its impact on the outcome.
In this case, the independent variable is the amount of alcohol consumed, as the researcher is manipulating this variable to see how it affects driving performance (the dependent variable).
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A helicopter flies horizontally at a contant speed. This makes a 42500 N lift force at 78.3 degrees, and air resistance pushes back against it. What is the mass of the helicopter?
In order to calculate the mass of the helicopter, we must first calculate the force of the air resistance.
What is the mass of the helicopter?The mass of the helicopter can be calculated using the formula:
mass = lift force / (acceleration due to gravity x sin(angle of lift force))
mass = 42500 N / (9.81 m/s2 x sin(78.3°))
mass = 4289 kg.
The force of the air resistance is equal to the magnitude of the lift force multiplied by the sine of the angle of the lift force, which in this case is 42500N x sin(78.3°) = 39,941N. Now, since the lift force and the air resistance are equal and opposite, we can use Newton's second law of motion, F=ma, to calculate the mass of the helicopter.Thus, the mass of the helicopter is equal to the force of the air resistance divided by the acceleration of the helicopter, which is zero since it is moving at a constant speed.Therefore, the mass of the helicopter is 39,941N/0m/s2 = 39,941kg.The mass of the helicopter can be calculated using the principles of Newton's Second Law of Motion. According to this law, the force acting on an object is equal to its mass times its acceleration. Therefore, the mass of the helicopter can be calculated using the equation:m = F / a
where F is the lift force and a is the acceleration due to gravity (9.81 m/s^2).
Plugging in the given values, the mass of the helicopter can be calculated as:
m = 42500 N / (9.81 m/s^2)
m = 4317.3 kg
This theory is known as Newton's Second Law of Motion, which states that the net force on an object is equal to its mass times its acceleration. This law can be used to calculate the mass of the helicopter when the lift force and acceleration due to gravity are known.To learn more about Newton's Second Law of Motion refer to:
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two objects with different masses collide with and stick to each other on a frictionless surface. compared to before the collision, the system of two objects after the collision has A. the same amount of total momentum and the same total kinetic energy.
B. the same amount of total momentum but less total kinetic energy.
C. less total momentum but the same amount of total kinetic energy.
D. less total momentum and less total kinetic energy.
E. Not enough information is given to decide.
After colliding, the two objects come to rest together, preserving momentum but not kinetic energy. Some motion energy is transformed to thermal energy, or heat.
What is collision?A collision occurs in physics when particles, groupings of particles, or solid entities move toward one other and get close enough to interact and exert mutual effect. When two bodies come into direct touch with each other, this is referred to as a collision. The two bodies exert pressures on each other in this situation in a brief period of time. As a result of the collision, the energy and momentum of the bodies involved change. However, there are three types of collisions: elastic, inelastic, and absolutely inelastic. To summarize, momentum is preserved in all three types of collisions. What happens to the kinetic energy is what characterizes the impacts.
Here,
The two objects collide and come to rest together, retaining velocity but not kinetic energy. Some motion energy is converted to thermal energy, often known as heat.
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common transparent tape becomes charged when pulled from a dispenser. if one piece is placed above another, the repulsive force can be great enough to support the top piece's weight. assuming equal point charges (only an approximation), calculate the magnitude of the charge if electrostatic force is great enough to support the weight of a 13.0 mg piece of tape held 1.30 cm above another. (the magnitude of this charge is consistent with what is typical of static electricity.)
If one piece is placed above another, the repulsive force can be great enough to support the top piece's weight.
calculate the magnitude of the charge if electrostatic force?
The magnitude of charges on the electron and proton are `1.6xx10^(-19)` C.M Mass of the electrons is `m_(e)=9.1xx10^(-31)` kg and mass of proton is `m_(p)=1.6xx10^(-27)` kg .n the equation Felect = k • Q1 • Q2 / d2 , the symbol Felect represents the electrostatic force of attraction or repulsion between objects 1 and 2.The force is perpendicular to both the velocity v of the charge q and the magnetic field B. 2. The magnitude of the force is F = qvB sinθ where θ is the angle < 180 degrees between the velocity and the magnetic field.This force emerges from the interaction between two charged objects (or point charges) and its magnitude is calculated by F=kQ1Q2r2 F = k Q 1 Q 2 r.
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according to a newspaper account, a paratrooper survived a training jump from 1156 ft when his parachute failed to open but provided some resistance by flapping in the wind. allegedly he hit the ground at 99.25 mi/h after falling for 10 seconds. to test the accuracy of this account, you should first find the drag coefficient , assuming a terminal velocity of 99.25 mi/h and also that the deceleration of the paratrooper due to air resistence is proportional to his velocity, with constant of proportionality . remember that the acceleration due to gravity near the earth's surface is 32 ft/sec
a. Find rho.
b. Next, find the distance fallen in 6 seconds..
An object can encounter some resistance when moving through the fluid medium of air.
The drag force is the oppositional force applied by the air to a moving object. The size of the cross section A of the front face of the item, the density of the air, and the square of the object's velocity v all contribute to the drag force.
With motion exclusively in the vertical direction and letting
downward be positive, we have that
dv/dt = g - pv, where g = 32 ft/[tex]s^{2}[/tex], and so
dv/dt + pv = g. The integrating factor is [tex]e^{(pt)}[/tex], so
d/dt([tex]e^{(pt)}[/tex] * v) = g×[tex]e^{(pt)}[/tex] ----->
[tex]e^{(pt)}[/tex] * v = (g/p)*[tex]e^{(pt)}[/tex] + C ----->
v(t) = (g/p) + C×[tex]e^{(pt)}[/tex]
Now v(0) = (g/p) + C = 0, and so C = -g/p, giving us
v(t) = (g/p)×(1 - [tex]e^{(pt)}[/tex]).
Now we are given that lim(t->infinity)(v(t)) = 99 mi/h = 145.2 ft/s,
so since [tex]e^{(pt)}[/tex]-> 0 as t -> infinity we have g/p = 145.2 ft/s ------>
p = 32 ft/s^2 / (145.2 ft/s) = 0.2204 s^-1 .
Next, since we have defined downward as positive, the expression
we have for v(t) will equal dy/dt where y(0) = 0 and y increases as
the paratrooper falls. So
dy/dt = v(t) = (g/p)×(1 - [tex]e^{(pt)}[/tex])), so
y(t) = (g/p)×(t + (1/p)×[tex]e^{(pt)}[/tex]) + K.
Now y(0) = (g/p)×(0 + (1/p)) + K = 0 ----->
K = -(g/p^2) = 32 / 0.2204^2 = -658.76 ft, so
y(t) = (145.2)×(t + (4.5372)×e^(-0.2204×t)) - 658.76.
Next, y(6) = (145.2)×(6 + (4.5372)×e^(-0.2204×6)) - 658.76 = 444.84 feet.
The computed drag coefficient is substantially higher than anticipated.
The free fall distance is the longest distance an individual can travel in a predetermined amount of time. However, the distance covered in the time frame indicated in the news report is significantly greater than the greatest distance that could be covered. Consequently, the news story is exaggerated.
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fill in the blank. since parallax is a difference in the apparent position of an object viewed along two different lines of sight, a very blank distance between viewpoints (called the baseline) is required to see a parallax shift in a distant object.target 1 of 2 if the baseline is too___compared to the object's distance, the difference in perspective will not be____
Since parallax is a difference inside this apparent position of an item when viewed along two separate lines of sight, a very wide gap between perspectives (referred to as the baseline) is necessary to detect a parallax shift in a far-off object.
What does parallax shift mean?An object's position changing due to your motion is known as parallax. For instance, if you gaze at a close object and tilt your head slightly to the side, the thing appears to be moving back and forth.
We employ parallax because?One of the most crucial techniques astronomers use to determine distance is parallax. It is incredibly precise but can only be used for close stars. By calculating how close an object is, the technique appears to move against the background of more distant objects.
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Which of the following agents or mechanisms are not testable, and therefore cannot provide a scientific explanation:
Earth's magnetic field
Global warming
Birth rates
*Spiritual beliefs
Genetic code
The agents or mechanisms which are not testable, and therefore cannot provide a scientific explanation are spiritual beliefs.
Spiritual beliefs pertain to an existentialist view of life, death, and the essence of existence and involve a connection to a higher power. These beliefs also include ceremonies and behaviours like meditative practices or prayer as well as interaction with other believers.
Global warming is the gradual heating of the Earth's surface that has been seen ever since pre-industrial era (between 1850 and 1900), and is attributed to human activity, particularly the combustion of fossil fuels, which raises the concentrations of heat-trapping greenhouse gases.
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explain how a paradox work∞
Answer:
A paradox is a statement, proposition, or situation that seems illogical, absurd or self-contradictory, but which, upon further scrutiny, may be logical or true — or at least contain an element of truth. Paradoxes often express ironies and incongruities and attempt to reconcile seemingly opposing ideas.
Explanation:
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when rotating the device 360 degrees, as long as the does not extend outside the base of stability, the apparatus should remain stable. group of answer choices aerial device gravity circle box stabilizer jackknifed trailer
When rotating the device 360 degrees, as long as the does not extend outside the base of stability, the apparatus should remain stable: gravity circle.
What is the Centre of GravityThe Centre of gravity is a theoretical point in the body where the body’s total weight is thought to be concentrated. It is important to know the centre of gravity because it predicts the behaviour of a moving body when acted on by gravity. It is also useful in designing static structures such as buildings and bridges.
In a uniform gravitational field, the centre of gravity is identical to the centre of mass. Yet, the two points do not always coincide. For the Moon, the centre of mass is very close to its geometric centre. However, its centre of gravity is slightly towards the Earth due to the stronger gravitational force on the Moon’s near side.
In a symmetrically shaped object formed of homogenous material, the centre of gravity may match the body’s geometric centre. However, an asymmetrical object composed of various materials with different masses is likely to have its centre of gravity located at some distance away from its geometric centre. In hollow bodies or irregularly shaped bodies, the centre of gravity lies at a point external to the physical material.
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An electron is moving to the right with an initial speed of vo = 3.5 x 10E7 m/s when it enters a
region of space that is L = 3.3 cm wide with a uniform electric field pointing down of magnitude
E = 8.2E4 N/C.
An electron is moving to the right with an initial speed of vo = 3.5 x 10E7 m/s when it enters a
region of space that is L = 3.3 cm wide with a uniform electric field pointing down of magnitude
E = 8.2E4 N/C. The electron will experience electric field
What informs the electron with electric field?The electron will experience a force due to the electric field, which is given by the equation F = qE, where q is the charge of the electron (a negative value) and E is the electric field.
The force will cause the electron to accelerate in the direction of the field, which is opposite to its initial direction of motion. The acceleration of the electron can be calculated using the equation a = F/m, where m is the mass of the electron.
The distance the electron will travel before it exits the region of space can be calculated using the equation x = v_0t + 0.5a*t^2, where v_0 is the initial velocity and t is the time it takes for the electron to travel through the region.
Therefore, the correct answer is as given above
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The complete question goes thus:
An electron is moving to the right with an initial speed of vo = 3.5 x 10E7 m/s when it enters a
region of space that is L = 3.3 cm wide with a uniform electric field pointing down of magnitude
E = 8.2E4 N/C. What will happen to the electron?
base your answer to the following question on the cross section below, which shows the type of seismic waves recorded at various locations after an earthquake has occurred. point a is a location on earth's surface and x is the epicenter of the earthquake. syvum
The P-waves are the primary waves that are the fastest and the first to arrive at the seismometer.
Seismic waves, which are vibrations caused by the movement of the Earth's crust, are recorded at various locations after an earthquake has occurred. The type of seismic waves recorded at a particular location depends on its distance from the epicenter (point X) of the earthquake.
There are two main types of seismic waves: body waves and surface waves. Body waves, such as P-waves and S-waves, travel through the Earth's interior and can be recorded at any location. Surface waves, such as Love waves and Rayleigh waves, travel along the Earth's surface and are typically recorded closer to the epicenter.
The P-waves are the primary waves that are the fastest and the first to arrive at the seismometer. The S-waves are the secondary waves that are slower and arrive later than P-waves.
In general, the closer a location is to the epicenter, the stronger and more frequent the seismic waves will be.
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A crane uses 19000 watts of power to lift a 6200 kg chunk of metal in a certain amount of time, how much
power will he use to do the same amount of work in three times the time?
er
Power (in watt) will he use to do the same amount of work in three times the time:
m=100 kgg=10 m/sh=10 m
W=mgh=100×10×10=10000 J
P= t/W
10000/20
=500 W
What is watt?Watt is a unit of power or radiant flux in the International System of Units, equivalent to 1 joule/second or 1 kg⋅m²⋅s⁻³. It is used to quantify the energy transfer rate. The watt (abbreviated W) is the standard International System of Units (SI) unit of power (energy per unit of time) equal to one joule per second. Watts are used to indicate the rate at which electrical energy is dissipated, or electromagnetic energy is radiated, absorbed, or dissipated.Watt is defined as 1 watt = 1 joule per second (1W = 1 J/s), meaning 1 kW = 1000 J/s. A watt is the amount of energy (in joules) that an electrical device (such as a light) consumes per second while in operation. So a 60W light bulb consumes 60 Joules of energy per second.To learn more about watt from the given link:
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A bar having a length of 5 in. and cross-sectional area of0.7 m' is subjected to an axial force of 8000N. If the bar stretches 0.002m., determine the modulus of elasticity of the material. The material has linear- elastic behavior.
Answer:
Explanation:
he modulus of elasticity (E) can be calculated using the formula:Stress = Force / AreaStrain = Change in length / Initial lengthModulus of Elasticity (E) = Stress / StrainWe have the Force = 8000 N, Area = 0.7 m^2, Change in length = 0.002 m and initial length = 5 in = 0.127 mStress = Force / Area = 8000 N / 0.7 m^2 = 11428.57 N/m^2Strain = Change in length / Initial length = 0.002 m / 0.127 m = 0.0157Modulus of elasticity (E) = Stress / Strain = 11428.57 N/m^2 / 0.0157 = 727,279.9 N/m^2So the modulus of elasticity for the material of the bar is 727,279.9 N/m^2This is the ratio of the applied stress to the corresponding strain within the elastic limit, which is a measure of a material's resistance to deformation.
5. A cue ball with mass m = 0.25 kg moves with a velocity v = 66 m/s. It strikes a stationary eight ball (mass = 0.25 kg) and
projects it into a comer pocket. At what speed does the eight ball leave the collision?
Answer:
66 m/s
Explanation:
Since momentum of the body is conserved
mv=mv
0.25 kg×66m/s=0.25 kg×v
v =0.25kg×66m/s
0.25 kg
v =66m/s
which statement shows that the newly diagnosed astham patient understands how to use a peak expiratory flow meter (pefm)? hesi
"I understand how to properly use the PEFM to measure my peak expiratory flow and will use it daily to track my lung function," the newly diagnosed asthmatic states in the statement.
Option B is correct.
What is a PEFM (peak expiratory flow meter)?A peak flow meter measures how quickly you can expel air from your lungs by blowing as forcefully and quickly as you can. This is what peak flow means.
This drop indicates the possibility of an asthma attack. You can figure out what "triggered" the drop in blood pressure by measuring your peak flow, which medications to add or take off, and when you might need emergency care.
A peak flow meter is simple to use. How to figure out your peak flow:
either sit down or stand tall. Regardless of your choice, ensure that you always follow this procedure.Make sure the red marker is at the base of the meter.Breathe deeply until your lungs are full to the brim.Place the mouthpiece in your mouth. Seal your lips tightly onto the peak flow meter mouthpiece.Expel all of the air with one blow as quickly and forcefully as possible.Make a note of the number by the red marker on the meter.Returning the red marker to the peak flow meter's bottom after performing these actions three timesThe reading that is the highest of these three is your daily peak flow.Question incomplete:which statement shows that the newly diagnosed asthma patient understands how to use a peak expiratory flow meter (pefm)?
A. Wear gloves during blood glucose monitoring and during any other procedure that involves potential exposure to blood or body fluids.
B. "I understand how to properly use the PEFM to measure my peak expiratory flow and will use it daily to track my lung function."
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A photon of wavelength 29 pm is scattered by a stationary electron. What is the maximum possible energy loss of the photon? (m el = 9.11 × 10-31 kg, h = 6.626 × 10-34 J · s, c = 3.00 × 108 m/s)
The maximum possible energy loss of the photon is 2.7 x 10-14 J, which is much less than the energy of the photon, 7.3 x 10-19 J.
To Calculate the energy of the photon.
E = hc/λ
E = (6.626 × 10-34 J · s)(3.00 × 108 m/s)/(29 x 10-12 m)
E = 7.3 x 10-19 J
To Calculate the maximum possible energy loss of the photon.
Max energy loss = 2m el (c2)
Max energy loss = 2(9.11 x 10-31 kg)((3.00 x 108 m/s)2)
Max energy loss = 2.7 x 10-14 J
Compare the energy of the photon and the maximum possible energy loss.
Hence, maximum possible energy loss of the photon is 2.7 x 10-14 J, which is much less than the energy of the photon, 7.3 x 10-19 J.
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the distance between two successive maxima of a certain transverse wave is 1.2m height crests or maxima pass a given point along the direction of travek every 12a calcultae the wave speed
The wave speed is 01 m/s, which can be calculated by using the formula:
wave speed distance between two successive maxima/time interval between two successive maxima
In this case, the distance between two successive maxima is given as 1.2m and the time
interval between two successive maxima is given as 12s.
So, the wave speed can be calculated as:
wave speed = 1.2m/12s = 0.1 m/s
It is worth mentioning that the wave speed is a scalar quantity, which means it has only magnitude and no direction. The given information is about the transverse wave which is a type of wave in which the oscillation is perpendicular to the direction of energy transfer
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Which subatomic particles contribute to the mass of an atom
Answer:
Only protons and neutrons contribute to the mass of an atom.
Explanation:
find an expression for the oscillation frequency of an elec tric dipole of dipole moment 17 and rotational inertia i for small amplitudes of oscillation about its equilibrium position in a uni form electric field of magnitude e.
The frequency would be 1/2pi [tex]\sqrt{\frac{pE}{I}}[/tex].
We know that,
Tau=-pEsinФ captures the sense
and the size of the effect.
This is the restoring torque to return the tilted dipoles to their aligned equilibrium position.
If the amplitude of movement is small,
we may replace sinθ with θ in radians.
Thus τ≈−pEθ.
Since this has a simple negative proportionality to the angle of rotation, the dipole oscillates in a simple harmonic motion,
like a torsion pendulum with a torsion constant
κ=pE. In this case, angular frequency ω is given by
ω² = [tex]\frac{k}{I}[/tex] = [tex]\frac{pE}{I}[/tex]
where I denotes thee rotational inertia of the particular dipole. The frequency of oscillation is
f= ω/ 2pi
= 1/2pi [tex]\sqrt{\frac{pE}{I}}[/tex]
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Why is B the correct answer? Thanks :)
The final speed is v and the change in the total kinetic energy is 6mv² (Option B)
How do I determine the final velocity?The final speed after the collision can be obtained as illustrated below:
Mass of 1st object (m₁) = 2mspeed of 1st object (u₁) = 3vMass of 2nd object (m₂) = 4mspeed of 2nd object (u₂) = 0Final speed (v₀) = ?Momentum before = momentum after
m₁u₁ + m₂u₂ = v₀(m₁ + m₂)
Divide both sides by (m₁ + m₂)
v₀ = [m₁u₁ + m₂u₂] / (m₁ + m₂)
v₀ = [(2m × 3v) + (4m × 0)] / (2m + 4m)
v₀ = [6mv + 0] / 6m
v₀ = 6mv / 6m
v₀ = v
Thus, the final speed is v
How do I determine the change in the kinetic energy?First, we shall determine the total initial kinetic energy. Details below:
Mass of 1st object (m₁) = 2mspeed of 1st object (u₁) = 3vMass of 2nd object (m₂) = 4mspeed of 2nd object (u₂) = 0Total Initial Kinetic energy (KE₁) =?KE₁ = ½m₁u₁² + ½m₂u₂²
KE₁ = [½ × 2m × (3v)²] + [½ × 2m × 0²]
KE₁ = [m × 9v²] + 0
KE₁ = 9mv²
Next, we shall determine the total final kinetic energy. Details below:
Total mass (m) = 2m + 4m = 6mFinal speed (v₀) = vTotal final Kinetic energy (KE₂) =?KE₂ = ½mv²
KE₂ = ½ × 6m × v²
KE₂ = 3mv²
Finally, we shall determine the change in the kinetic energy of the car can be obtained as follow:
Total Initial Kinetic energy (KE₁) = 9mv²
Total final Kinetic energy (KE₂) = 3mv²
Change in total kinetic energy (ΔKE) =?
ΔKE =KE₁ - KE₂
ΔKE = 9mv² - 3mv²
ΔKE = 6mv²
In conclusion,
Final speed = vChange in total kinetic energy = 6mv²Thus, the correct answer is Option B
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the apparatus above is used to study conservation of mechanical energy. a spring of force constant 40 n/m is held horizontal over a horizontal air track, with one end attached to the air track. a light string is attached to the other end of the spring and connects it to a glider of mass m . the glider is pulled to stretch the spring an amount x from equilibrium and then released. before reaching the photogate, the glider attains its maximum speed and the string becomes slack. the photogate measures the time t that it takes the small block on top of the glider to pass through. information about the distance x and the speed v of the glider as it passes through the photogate are given below.
The reason for the modest preference for 1/2 kx2 is that you only need to measure one variable—the displacement x—in order to identify the stored energy. Utilizing 1/2 F/x necessitates measuring both displacement and force, which is frequently difficult to do.
Do kinetic and potential energy in a spring have the same value?When a spring is stretched x distances from its equilibrium point and its mass is moving with velocity v, the spring's kinetic energy and elastic potential energy are equal, or 1/2mv2 = 1/2kx2.The restoring force indicated by Hooke's Law is propelled by spring potential energy, a store of energy. When calculating the spring potential energy, U=1/2kx2—the equation for the potential energy function—instead of Hooke's Law—is essentially utilized.The reason for the modest preference for 1/2 kx2 is that you only need to measure one variable—the displacement x—in order to identify the stored energy. Utilizing 1/2 F/x necessitates measuring both displacement and force, which is frequently difficult to do.To learn more about displacement refer to:
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A barrel rider is moving in a circle with a speed of 7.0 m/s. The acceleration of the rider is 7.2 m/s/s. The speed of the object is somehow increased to 14.0 m/s (i.e., doubled). The new acceleration would be _____ m/s/s. (Assume that the radius of the circle is not changed.)
The new acceleration of the barrel rider if the speed is doubled is 14.4m/s².
How to calculate acceleration?Acceleration in physics refers to the amount by which a speed or velocity increases i.e. the change of velocity with respect to time.
The acceleration of a moving body is directly proportional to the speed of that body i.e. an increase in speed equates to an increase in acceleration.
According to this question, a barrel rider is moving in a circle with a speed of 7.0 m/s. The acceleration of the rider is 7.2 m/s². However, the speed of the object is somehow increased to 14.0 m/s.
This suggests that the acceleration of the rider will also be doubled and hence, be 14.4m/s².
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The speed of light is about 300,000 km/sec. The average distance between the Earth and the Sun (1
AU) is about 150 million km. Approximately how long will it take light to travel to 1 AU?
It will take approximately 8.3 minutes for light to travel from the Earth to 1 AU
The speed of light is a constant value of about 300,000 km/sec. To find out how long it will take light to travel to 1 AU (which is about 150 million km), we can use the formula:
Time = distance/speed
So we can substitute the values into the formula:
time = 150 million km / 300,000 km/sec
By solving the equation we get:
time = 500 seconds or approximately 8.3 minutes
Therefore, it will take approximately 8.3 minutes for light to travel from the Earth to 1 AU, which is the average distance between the Earth and the Sun.
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A proton is fired horizontally into a 1.0×10^5 N/C vertical electric field. It rises 1.0 cm vertically after having traveled 7.0 cm horizontally. What was the proton's initial speed?
The initial horizontal speed of the proton is 0.16 m/s.
What is the time of motion of the proton?
The time of motion of the proton is calculated by applying the following kinematic equation.
t = √ ( 2gh )
where;
h is the height risen by the protong is the acceleration due to gravityt = √ ( 2 x 9.8 x 0.01 )
t = 0.44 second
The initial horizontal speed of the proton is calculated as;
d = Vₓt
Vₓ = d / t
Vₓ = ( 0.07 m ) / ( 0.44 s )
Vₓ = 0.16 m/s
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Suppose we imagine the Sun to be about the size of a grapefruit. Which of the following describes the size and distance of Earth on the same scale? Select the right answer A. Earth is the size of a marble about 25 miles away from the Sun. B. Earth is the size of a tip of a ballpoint pen about 15 meters away from the Sun.
C. Earth is the size of a tip of a ballpoint pen about 1 meter away from the Sun. D. Earth is the size of a golf ball about 15 meters away from the Sun. E. Earth is the size of a golf ball about 1 meter away from the Sun.
The correct option is B. Earth is the size of the tip of the ballpoint pen about 15 metres away from the Sun.
Radius of the sun = 7× 10⁸ m
Radius of the earth = 6.37 × 10⁶ m
Radius of the grape fruit = 7.6 × 10⁻² m
As the sun is said to be the size of the grapefruit, scale = (7.6 × 10⁻²)/(7× 10⁸) = 10⁻¹⁰
This means the scale is approximately, 1: 10⁻¹⁰
So, the size of the earth = 6.37× 10⁶ ×10⁻¹⁰ = 6.37×10⁻⁴ m (size of ballpoint)
As we know that the distance between the sun and the earth = 14.9 × 10¹⁰ m
So, in our scale, distance between the sun and the earth = 14.9× 10¹⁰× 10⁻¹⁰ = 14.9 m
which is approximately 15 meters.
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A 4-kg bowling ball rolls at a speed of 15 m/s on the ground. Circle one: KE / GPE / both
Answer:
KE
Explanation:
It has KE only because it is in motion, but 0 GPE because it is on the ground. For it to have any GPE it would have to be at some height above the ground.