Kinetic energy is K = 1.82 × 10⁻³ eV.
⁵⁷Fe nucleus emits 14 keV photons at rest.
We have, Mc² = 8.6 × 10⁻⁹ J in the final state of the nucleus.
Let p(nucleus) be the moment of the nucleus and p(photon) be the momentum of the photon.
Then, by conservation of momentum since the total moment is zero.
p(nucleus) = p(photon) = E(γ) / c = 140 keV / c
The energy for the recoiling nucleus is given as:
E² = p²c² + (mc²)²
Now, Mc² = 8.60 × 10⁻⁹J =5.38 × 10¹⁰ eV = 5.38 × 10⁷ keV
Therefore,
(Mc² + K²) ² = (14 keV)² + (Mc²)²
(1 + K²/Mc²)² =(14/Mc²)² +1
The term (1 + K²/Mc²)² is less than 1 therefore, (14/Mc²)² + 1 is equal to 1 by clacualtor.
Now using binomial theorem,
(1 + K²/Mc²)² = √[1 + ((14/Mc²)²] = 1 + (1/2)(14/Mc²)²
K = 1.82 × 10⁻³ eV
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3. The runner ran a distance 100m with a force of 45N. How much work
was done? (W=Fx d)
Answer:
Hope my answer is understandable to you.
Four toy cars are moving at a constant speed until they experience an unbalanced force of 12 n each. Which toy car would have an acceleration of 3 m/s2 ?.
The car's acceleration would be for a mass of 4 kg is 3 m/s²
Given the information below:
12 Newtons of force.
Increasing speed Equals
By using Newton's Second Law of Motion, we can determine the mass of the car:
According to Newton's second law of motion, force is equal to the rate at which momentum changes. Force is defined as mass times acceleration for a constant mass.
force= mass* acceleration
This formula provides Newton's Second Law of Motion mathematically;
12= mass*3
mass=12/ 3
mass=4 kilogram
By changing the parameters in the formula, we obtain;
= 4 kilos of mass.
As a result, the vehicle with a mass of 4 kg would accelerate at 3 m/s².
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During a game of pool, a cue ball travels to the left with 70 N of force and collides with the four ball moving with a force of 50 N to the right. If you assign a
negative value to the force moving to the right, what is the net force of this system?
Answer:
net force= -50N +70N
=20N
Explanation:
The balls are moving in opposite directions as indicated and to the right is (-) while to left is (+). Therefore net force is equal to sum of the force
The cue ball travels to the left with a force of +70 N and collides with the four-ball moving towards the right with a force of -50 N.
What is Force?A push or a pull that alters or tends to alter an object's uniform motion or state of rest, as well as altering an object's direction or shape, is referred to as force. It either accelerates items or increases the pressure they are under. The interaction between two items is, to put it simply, a push or a pull on the object. It is the fundamental driver of motion starting from stillness.
Given information according to the question,
The cue ball travels to the left with a force of +70 N and,
The force by four balls moving to the right is -50 N.
Net force, N = 70 N - 50 N
N = 20 N towards the left direction.
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Charges of 3.00nC,-2.00 nC,-7.00 nC, and 1.00nC are contained inside a rectangular box with length 1.00m, width 2.00m, and height 2.50m. Outside the box are charges of 1.00nC and 4.00nC . What is the electric flux through the surface of the box? (a) 0(b) -5.64× 10² N . m²/C(c) -1.47 ×10³ N . m²/C(d) 1.47× 10³ N . m²/C(e) 5.64× 10² N . m²/C
The electric flux through the surface is 5.65×〖10〗^2 Nm^2/C ≈5.6×〖10〗^2 Nm^2/C
The electric flux through a surface describes the number of electric field lines that cross that surface. It is expressed as the surface integral of the electric field through that surface.
Gauss's law states that for a closed surface, the electric flux through that surface depends only on the total charge present inside that surface. Hence, for a closed surface, the electric flux can be computed without evaluating any integrals.
The charges are: q1=3.0nC, q2=−2.0nC, q3=−7.0nC, and q4=1.0nC
Gauss's Law provides that the net electric flux through a closed surface depends only on the net charge enclosed by the surface, by the equation:
ϕ=Qnet÷ϵ0
where,
Φ is the net electric flux through the closed surface.
Qnet is the net charge enclosed by the surface.
∈_0=8.85×〖10〗^(-12) C^2/Nm^2 is the permittivity of free space.
The net charge inside the box is:
Qnet = q1+q2+q3+q4
=3.0nC−2.0nC−7.0nC+1.0nC
= −5.0nC=−5.0×10−9C
The net electric flux through the box is:
Φ=Q_net/∈_0
Φ=(-5.0×〖10〗^(-9) C)/(8.85×〖10〗^(-12) C^2/Nm^2 )
Φ=5.65×〖10〗^2 Nm^2/C ≈5.6×〖10〗^2 Nm^2/C
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A nonconducting wall carries charge with a uniform density of 8.60μC/cm²(a) What is the electric field 7.00 cm in front of the wall if 7.00 cm is small compared with the dimensions of the wall? Explain.
The electric field at a distance of 7.00 cm is 8.60×10^−2C/m2
The charge per unit area of wall is
σ = (8.60×10^−6C/cm2)( 100cm /m)^2 = 8.60×10^−2C/m2
The electric field at a distance of 2.00 cm is then
E = σ /7∈0 = (8.60×10^−2C/m^2) / 7(8.85×10−12C2/N⋅m2)
= 1.38×10^9N/C away from the wall.
Electric field, an electric property associated with each point in space when the charge is present in any form. The magnitude and direction of the electric field are expressed by the value of E, called electric field strength or electric field intensity or simply the electric field.
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an astronomical unit is the average disce of earth from the sun approximately 1//5 *10^^8 the pseed of light is 3*10^88 express the speed of light in terms of astronomical units per min
Speed of light in terms of astronomical unit is 0.12AU/min.
What is an astronomical unit?The astronomical unit (symbol: au, or AU) is a measurement of length that is approximately 150 million kilometers (93 million miles) or 8.3 light minutes long, representing the distance between the Earth and the Sun. As Earth orbits the Sun, its actual distance from the Sun changes by roughly 3%, going from its greatest value (aphelion) to its smallest value (perihelion), and back again, once a year. Originally intended to represent the average of Earth's aphelion and perihelion, the astronomical unit has been precisely defined as 149597870700 m since 2012. The astronomical unit is mostly used to calculate distances within or around other stars and other solar systems. It is also a crucial element in the definition of the parsec, another astronomical measure of length.
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In a certain series R L C circuit, Irms=9.00A, ΔVrms=180V, and the current leads the voltage by 37.0⁰. (a) What is the total resistance of the circuit?
The total resistance of the RLC series circuit is determined as 20 ohms.
Total resistance of the circuit
The total resistance of the RLC series circuit is calculated as follows;
R = Vrms / Irms
where;
Vrms is the root mean square voltageIrms is the root mean square currentSubstitute the given parameters and solve for the total resistance
R = (180) / (9)
R = 20 ohms
Thus, the total resistance of the RLC series circuit is determined as 20 ohms.
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A man on a scooter travels directly west for 50 meters, it took the man 45 seconds to reach his destination. What was his velocity?
Answer:
1.2 m/s
Explanation:
You must divide the distance by time in order to find velocity! 50/45. He was going 1.2 m/s!
Answer: 34
Explanation:
Liam notices that his phone battery is depleting faster than he remembers it should. He suspects that running certain apps on his phone is using up his phone battery. He thinks it might be app 1, app 2, or app 3.
Find the independent, dependent, and controlled variables. What is your hypothesis.
Answer:
he would tap on the "close tab "button and see old the apps he has used in that period
Explanation:
When a wave encounters an obstacle or a slit that is comparable in size to its wavelength, it bends around it. This characteristic is called ________.
(ii) What happens to the field if instead the length of the solenoid is doubled, with the number of turns remaining the same? Choose from the same possibilities as in particular
Part A: Since the magnetic field is proportional to the number of turns per length (n), it follows that the magnetic field within the solenoid stays constant when both the number of turns and the length are doubled.
Answer C for portion B) is accurate; there are still the same number of turns per length.
What is the function of a solenoid?A solenoid, to put it simply, transforms electrical energy into mechanical work. Many turns of tightly wound copper wire make up the coil. A powerful magnetic field or flux is produced when an electrical current passes through this wire.
Many turns of tightly wound copper wire make up the coil. A powerful magnetic field or flux is produced when an electrical current passes through this wire.
The housing, which is often composed of iron or steel, encloses the coil and concentrates the magnetic field it produces.
By concentrating the magnetic field, which generates the necessary mechanical force, the plunger is drawn to the stop.
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A box is at rest on an inclined surface. Which diagram correctly illustrates all forces, including any component forces? Assume the x-axis is parallel to the surface.
A box is at rest on an inclined surface. The last diagram correctly illustrates all forces, including any component force, therefore the correct option is D.
Describe friction?When two physical objects' surfaces come into contact, a force called friction acts to hinder or resist the relative motion of the items. Any two surfaces of things cannot simply slide over or across one another due to the friction force. It depends on the amount of force used on the object.
Additionally, there should be no net vertical forces acting on the inclined block. Fv=0
Therefore, the appropriate diagram is D.
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A box is at rest on an inclined surface. Which diagram correctly illustrates all forces, including any component forces?
Assume the x-axis is parallel to the surface.
Review. (c) Assume the dipole is a compass needle-a light bar magnet-with a magnetic moment of magnitude μ . It has moment of inertia I about its center, where it is mounted on a frictionless, vertical axle, and it is placed in a horizontal magnetic field of magnitude B. Determine its frequency of oscillation.
The frequency of oscillation is [tex]\frac{1}{2\pi } \sqrt{\frac{\mu B}{I} }[/tex].
What is a magnetic moment?The magnetic moment is the magnetism of a magnet or other item that creates a magnetic field, as well as its orientation and strength. Electromagnets, permanent magnets, elementary particles like electrons, different compounds, and a variety of celestial objects are examples of things that have magnetic moments (such as many planets, some moons, stars, etc). The phrase "magnetic moment" typically refers to a system's magnetic dipole moment, which can be represented by an analogous magnetic dipole, which has a magnetic north and south pole that are barely separated from one another. For sufficiently small magnets or at sufficiently wide distances, the magnetic dipole component is adequate. For extended objects, additional terms may be required in addition to the dipole moment, such as the magnetic quadrupole moment.
[tex]T = \frac{ Id^{2}\theta }{dt^{2} }[/tex]
[tex]-\mu B\theta=\frac{ Id^{2}\theta }{dt^{2} }[/tex]
[tex]\frac{d^{2}\theta }{dt^{2} } = -(\frac{\mu BI}{\theta} )[/tex]
By Comparing the above equation with the SHM equation
[tex]\frac{d^2 \theta} {dt^{2} } = -\omega^{2} \theta[/tex]
[tex]\omega^{2} =\frac{ \mu B}{I}[/tex]
Frequency = [tex]\frac{\mu}{2\pi }[/tex]
=[tex]\frac{\sqrt{\frac{\mu B}{I} } }{2\pi}[/tex]
=[tex]\frac{1}{2\pi } \sqrt{\frac{\mu B}{I} }[/tex]
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A guitar's steel string vibrates (see Fig. 31.5). The component of magnetic field perpendicular to the area of a pickup coil nearby is given byB=50.0+3.20 sin 1046 πtwhere B is in milliteslas and t is in seconds. The circular pickup coil has 30 turns and radius 2.70mm. Find the emf induced in the coil as a function of time.
The emf induced in the coil as a function of time is 2.2 mV.
emf induced in the coil
The emf induced in the coil is calculated as follows;
emf = NAdB/dt
where;
N is number of turnA is the area of the coildB/dt is the change in magnetic field with timeA is area of the coil, A = πr² = π(2.7 x 10⁻³)² = 2.29 x 10⁻⁵ m².
dB/dt = 3.2cos(1046π) = 3.2
emf = (30 x 2.29 x 10⁻⁵ x 3.2) = 2.2 x 10⁻³ V
emf = 2.2 mV
Thus, the emf induced in the coil as a function of time is 2.2 mV.
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A 55.0-kg woman cheats on her diet and eats a 540 Calorie ( 540 kcal ) jelly doughnut for breakfast. (c) If the human body is only 25.0% efficient in converting chemical potential energy to mechanical energy, how many steps must the woman climb to work off her breakfast?
The woman needs to climb a step of 1.05 m to work off her breakfast.
What is potential energy?
The potential energy of an object is the energy that is stored in the object due to its position above the ground level.
The potential energy of the woman can be used to determine the number of steps she needs to climb.
potential energy + heat energy = chemical energy
1 kcal = 4184 J
0.540 kcal = ?
= 2259.36 J
P.E = mgh
55 x 9.8 x h = 0.25(2259.36)
h = 1.05 m
Thus, the woman needs to climb a step of 1.05 m to work off her breakfast.
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When thermal energy is removed from particles, what action occurs?
A The particles' energy is destroyed.
B The particles' temperature increases.
C The particles move more quickly.
D The particles' kinetic energy decreases.
When thermal energy is removed from particles, then the particles' kinetic energy decreases (Option D).
What is particles' kinetic energy?The expression particles' kinetic energy makes reference to the amount of motion energy (i.e. energy in movement) that contain the particles of an object, which depends on the temperature of the material.
In conclusion, when thermal energy is removed from particles, then the particles' kinetic energy decreases (Option D).
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A car starts from rest and accelerates at 4 m/s2 until it reaches 36 m/s. How far did it travel at this time?
The distance of a car that accelerates at 4 m/s² until it reaches 36 m/s is 162m.
How to calculate distance?The distance moved by a body can be calculated using the following formula:
S = ut + ½at²
Where;
S = distancet = time a = accelerationu = velocityHowever, the time taken must be calculated first as follows:
t = 36m/s ÷ 4m/s²
t = 9s
S = 0 × t + ½ × 4 × 9²
S = 0 + ½ × 81 × 2
S = 162m
Therefore, the distance of a car that accelerates at 4 m/s² until it reaches 36 m/s is 162m.
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a helicopter flies with an average velocity of 70.0\, \dfrac{\text{m}}{\text{s}}70.0 s m 70, point, 0, start fraction, start text, m, end text, divided by, start text, s, end text, end fraction for 10.0\, \text{seconds}10.0seconds10, point, 0, start text, s, e, c, o, n, d, s, end text. what is the magnitude of the helicopter’s displacement?
Considering the definition of velocity, the magnitude of the helicopter's displacement is 700 meters.
Definition of velocityVelocity is a physical magnitude that relates the displacement of an object, the time it takes to make this change in position and direction.
In other words, the velocity can be defined as the amount of space traveled per unit of time with which a body moves, considering the direction.
The velocity can be calculated using the expression:
velocity= displacement÷ time
This caseIn this case, you know:
Velocity = 70 m/sTime = 10 seconds.Replacing in the definition of velocity:
70 m/s= displacement÷ 10 s
Solving:
70 m/s× 10 s= displacement
700 m= displacement
Finally, the magnitude of the helicopter's displacement is 700 meters.
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when discussing a particular body, the action forces are defined as those forces that directly affect the acceleration of that body. with this in mind, classify the forces acting on each object according to whether they are action forces or reaction forces. to simplify matters, ignore the friction acting on the front tires of the car. be sure to answer both parts of the question.
The force acting on a car will be an action type of force.
What is Newton's second law?The effects of net force and mass on a material's acceleration are described by Newton's second law. Newton's second law is given as,
F = ma
Where m is the mass, a is the acceleration, and F is the force acting on a body.
The forces that actually affect a body's acceleration are referred to as the active forces when a specific body is under discussion. Ignore the resistance the car's front tires experience to make things easier.
A force of the action kind will be exerted on an automobile.
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the force that gravitation exerts upon a body, equal to the mass of the body times the local acceleration of gravity
The force that gravitation exerts upon a body, equal to the mass of the body times the local acceleration of gravity is known as weight.
Weight is the force of gravity acting on a body.
The formula is :
W =mg
Here,
W is the weight or force acting on the body. m is the mass of the body, and g is the gravitational acceleration.
Since weight is also a force, so its SI unit is also newton. The value of weight varies from place to place depending on the gravity. Its value can also be equal to zero.
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Four toy cars are moving at a constant speed until they experience an unbalanced force of 12 n each. Which toy car would have an acceleration of 3 m/s^2?.
The car that would have the acceleration of 3m/s^2 would be of mass 4 kg.
How Newton's law of motion applied to determine the mass of the car that would have an acceleration of 3m/s^2?For determining the mass of the car that would have 3m/s^2 acceleration, we will calculate net force .The net force acting on a given asset along with the total acceleration against the mass of the asset.The F = F1+ F2+F3.......Fn, here the body or the considered asset is not at rest .If the question would ask to consider a rest object then the net force would be , F= Fa + Fg, Fa is the force applied over the considered object in the question, Fg is the force due to gravity.To know more about Force and acceleration visit:
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An 8.5kg cat is running 1.8m/s. How much kinetic energy does it have?
Answer:
Im not sure if this is correct but it might be 15.3
Explanation:
8.5kg multiplied by 1.8 m/s is 15.3
Answer:
KE = 13.77 J
Explanation:
KE=1/2 mv^2
an object is dropped from a bridge and allowed to freefall to the ground. the height of the object over time can be modeled using h(t)
Dropped from a bridge and allowed to fall freely to the ground is an object. Modeling the object's height over time using h(t) = 144 - 16t2 is possible
What do you mean by Freefall?An item that is falling only due to gravity is said to be in free fall. This means that any moving object that is simply being affected by gravity is said to be "in a condition of free fall." An item of this kind will accelerate downhill at a rate of 9.8 m/s/s. If an item is just moving in one direction—downward or upward toward its peak—and is only affected by gravity, then its acceleration value is 9.8 m/s/s.
The initial velocity of an object being dropped from a height is zero meters per second (m/s) as opposed to being hurled.
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The most soaring vocal melody is in Johann Sebastian Bach's Mass in B Minor. In one section, the basses, tenors, altos, and sopranos carry the melody from a low D to a highA. In concert pitch, these notes are now assigned frequencies of 146.8Hz and 880.0 Hz . Find the wavelengths of(a) the initial note
The wavelength of initial node is 2.34m.
What is wavelength?The wavelength, which in physics refers to the length over which a periodic wave repeats, is its spatial period. It is the distance between two successive corresponding wave points of the same phase, such as two neighboring crests, troughs, or zero crossings, and it is a feature of both traveling waves and standing waves, as well as other spatial wave patterns. The spatial frequency is defined as the wavelength's inverse. Greek letter lambda, which means "wavelength," is frequently used to denote it. Sometimes, modulated waves, their sinusoidal envelopes, or waves created by the interference of several sinusoids are all referred to by the term wavelength.
Wave lengthλ=[tex]\frac{v}{f} = \frac{343 m/g}{146.6/g} =2.34m[/tex].
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A tennis ball with a speed of 17.9 m/s is
moving perpendicular to a wall. After striking
the wall, the ball rebounds in the opposite
direction with a speed of 16.0026 m/s.
If the ball is in contact with the wall for
0.0084 s, what is the average acceleration of
the ball while it is in contact with the wall?
Take "toward the wall" to be the positive
direction.
Answer in units of m/s².
The acceleration of the ball while it is in contact with the wall is 4036.023 m/s²
ball strikes the wall at a speed of 17.9m/sec
after striking its goes in opposite direction with a speed of 16.0026m/sec
We have given that speed towards the wall is positive
So, u = 17.9m/sec
v = -16.0026m/sec
t = 0.0084 sec
We know that acceleration is given by
a = v-u/t
where
v = final speed
u = initial speed
t = time taken
a = v-u/t
a = 17.9 - (-16.0026) / 0.0084
a = 33.9026 / 0.0084
a = 4036.023 m/s²
So the acceleration of the ball while it is in contact with the wall is 4036.023 m/s²
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If a cannonball were launched horizontally (launch angle of 0) with a speed of 35m/s from a height of 15m, how long would the cannonball remain in the air?
Since the cannonball was launched horizontally (launch angle of 0) with a speed of 35m/s from a height of 15m, the time the cannonball remains in the air is for 1.75 s
What is a projectile?A projectile is an object that moves through air in a parabolic path
How long would the cannonball remain in the air?Since the cannonball is a projectile and was launched horizontally (launch angle of 0) with a speed of 35m/s from a height of 15m, using the equation of motion y' - y = ut - 1/2gt² we find the time it takes the cannonball to reach the ground. or remain in the air
Since y' - y = ut - 1/2gt² where
y' = ground level = 0 my = height cannonball is launched from = 15 m, u = initial vertical speed of cannonball = 0 m/s (since it is launched horizontally), t = time cannonball is in the air, g = acceleration due to gravity = 9.8 m/s²Substituting the values of the variables into the equation and solving for t, we have
y' - y = ut - 1/2gt²
0 m - 15 m = 0 m/s × t - 1/2 (9.8 m/s²)t²
- 15 m = 0 m/s - (4.9 m/s²)t²
- 15 m = - (4.9 m/s²)t²
t² = -15 m/- (4.9 m/s²)
t² = 3.061 s²
t = √3.061 s²
t = 1.75 s
So, the time the cannonball remains in the air is for 1.75 s
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a water holding tank measures 115 m long, 45 m wide, and 9 m deep. traces of mercury have been found in the tank, with a concentration of 65 mg/l. what is the total mass of mercury in the tank? answer in units of kg
The tank that has a volume of 46575 m³ with a concentration of 65 mg/l has a total mass of mercury of: 3027.375 kg
To solve this problem the formulas and the procedures that we have to use are:
c= m(solute)/v(solution)v = long * wide * deepWhere
c = concentration of solutionm = mass of solutev = volume of solutionInformation about the problem:
long = 115 mwide = 45 mdeep = 9 m c= 65 mg/lv(solution)=?m(mercury)=?Using the volume formula we get:
v= long * wide * deep
v(solution) = 115 m * 45 m * 9 m
v(solution) = 46575 m³
By converting the volume units from m³ to liters we have:
v(solution) = 46575 m³ * 1000 l/1m³
v(solution) = 43.575*10^6 l
Applying the concentration formula and clearing the mass we get:
c= m(solute)/v(solution)
m(solute) = c * v(solution)
m(mercury) = 65 mg (mercury)/l (solution) * 43.575*10^6 l (solution)
m(mercury) = 3.027375*10^9 mg
By converting the mass units from (mg) to (kg) we have:
m(mercury) = 3.027375*10^9 mg * 1 kg/ 1 * 10^6 mg
m(mercury) = 3027.375 kg
What is a solution?In chemistry a solution is known as a homogeneous mixture of two or more components called:
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Explain in terms of energy the process
which takes place as a solid at its melting
point changes into a liquid at the same
temperature.
Explanation:
Endothermic reaction as heat from the environment is absorbed.
the transformation from solid to liquid is due to the latent heat of fusion/ enthalpy of fusion.
the heat energy absorbed from the environment is used to break the bonds of the solid structure therein converting it to a liquid. this is the reason why the temperature of the substance is constant at the state changes.
Sally has a car that accelerates at 5 m/s. If the car has a mass of 1000 kg, how much force does t
car produce?
F=
m=
a=
Answer:
5000N
Explanation:
Force is given by the formula F = ma where m is the mass and a the acceleration
Plugging in given values of m and a gives us
F = 1000 kg x 5 m/s² = 5000 Newtons or simply 5000N
A person wears a hearing aid that uniformly increases the sound level of all audible frequencies of sound by 30.0 dB . The hearing aid picks up sound having a frequency of 250Hz at an intensity of 3.0 × 10¹¹W/m² . What is the intensity delivered to the eardrum?
The intensity delivered to the eardrum is [tex]3.0 \times {10^{ - 8}}\,W/{m^2}$[/tex].
What is intensity?
The area is measured on a plane perpendicular to the direction of the energy's transmission, and the power transferred per unit area is known in physics as the intensity or flux of radiant radiation. The SI system's fundamental units are watts per square meter. The average power transmission across the course of a wave, such as sound waves or electromagnetic waves like light or radio waves, is referred to as the "intensity" of the wave. The term "intensity" can be used to characterize a wide range of energy exchange scenarios. For example, one may calculate the amount of kinetic energy that each drop of water from a sprinkler is carrying. It is possible to determine intensity using the energy density.
Calculations:
[tex]${\beta _1} = 10{\log _{10}}\left( {\dfrac{{{I_1}}}{{{I_0}}}} \right)$ and ${\beta _2} = 10{\log _{10}}\left( {\dfrac{{{I_2}}}{{{I_0}}}} \right)$$ = {\beta _2} - {\beta _1} = 10{\log _{10}}\left( {\dfrac{{{I_2}}}{{{I_0}}}} \right) - 10{\log _{10}}\left( {\dfrac{{{I_1}}}{{{I_0}}}} \right)$[/tex][tex]$ \ {\beta _2} - {\beta _1} = 10{\log _{10}}\left( {\dfrac{{{I_2}}}{{{I_0}}} \times \dfrac{{{I_0}}}{{{I_1}}}} \right)$ [Using $\log a - \log b = \log \left( {\dfrac{a}{b}} \right)$][/tex]
[tex]$ \arrow = {\beta _2} - {\beta _1} = 10{\log _{10}}\left( {\dfrac{{{I_2}}}{{{I_1}}}} \right)$\[ \arrow = \dfrac{{{\beta _2} - {\beta _1}}}{{10}} = {\log _{10}}\left( {\dfrac{{{I_2}}}{{{I_1}}}} \right)\][/tex]
[tex]\[ \arrow ={10^{\dfrac{{{\beta _2} - {\beta _1}}}{{10}}}} = \dfrac{{{I_2}}}{{{I_1}}}\]\[ \arrow ={I_2} = {I_1}{10^{\dfrac{{{\beta _2} - {\beta _1}}}{{10}}}}\]Thus, we have ${I_2} = 3.0 \times {10^{ - 11}}\,W/{m^2} \times {10^{\dfrac{{30.0}}{{10}}}}$$ \arrow= {I_2} = 3.0 \times {10^{ - 11}} \times {10^3}\,W/{m^2}$$ \arrow ={I_2} = 3.0 \times {10^{ - 8}}\,W/{m^2}$[/tex]
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