a pushes a block weighing 5.0 n against a vertical wall (fig. 6-26). the coefficient of static friction between the wall and the block is 0.60, and the coefficient of kinetic friction is 0.40. assume that the block is no

Answers

Answer 1

(a) The block does not move a bit.

(b) The force on the block from the wall is −(12N)i+(5.0N)j

How can we calculate the force?

(a)

To know that the block is going to move or not we are using the formula,

We compare f and μF₁

If

f<μF₁,

the block does not slide on the wall

but if

f>μF₁,

the block does slide.

We are given,

F= This is the applied force

F₁= This is the normal force of the wall on the block.

f=This is the force of friction.

mg= This is the force of gravity.

The horizontal component of Newton’s second law is,

F-F₁=0

So, F= F₁ = 12N

and

μ F₁ =(0.60)(12N)=7.2N.

The vertical component is,

f-mg=0

so, f=mg=5.0N.

From the above calculation we can get that,

f<μF₁,

So The block does not move a bit

(b)Since the block does not move,

f=5.0N.

F₁ = 12N

So, The force of the wall on the block is

 

F(wall) =−F₁ i + f j=−(12N)i+(5.0N)j

Therefore from the above calculation we can conclude that, The force on the block from the wall is −(12N)i+(5.0N)j

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Question:

A 12N horizontal force pushes a block weighing 5.0 N against a vertical wall (Fig.). The coefficient of static friction between the wall and the block is 0.60, and the coefficient of kinetic friction is 0.40. Assume that the block is not moving initially. (a) Will the block move? (b) In unit-vector notation, what is the force on the block from the wall?

A Pushes A Block Weighing 5.0 N Against A Vertical Wall (fig. 6-26). The Coefficient Of Static Friction

Related Questions

(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

Answers

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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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=

Answers

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 car starts from rest and accelerates at 4 m/s2 until it reaches 36 m/s. How far did it travel at this time?

Answers

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 = velocity

However, 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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An 8.5kg cat is running 1.8m/s. How much kinetic energy does it have?

Answers

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

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.

Answers

Answer:

he would tap on the "close tab "button and see old the apps he has used in that period

Explanation:

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.

Answers

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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3. The runner ran a distance 100m with a force of 45N. How much work
was done? (W=Fx d)

Answers

Answer:

Hope my answer is understandable to you.

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)

Answers

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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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.

Answers

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 time

A 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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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.

Answers

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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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 ________.

Answers

The answer is Diffraction

the force that gravitation exerts upon a body, equal to the mass of the body times the local acceleration of gravity

Answers

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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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.

Answers

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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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

Answers

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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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 ?.

Answers

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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A boat travels 12. 0 m while it reduces its velocity from 9. 5 m/s to 5. 5 m/s. What is the magnitude of the boat’s acceleration while it travels the 12. 0 m?.

Answers

A boat travels 12. 0 m while reduces its velocity from 9. 5 m/s to 5. 5 m/s, while it travels the 12. 0 m, the acceleration of the boat is -2.5 m/s²

What is acceleration?

The rate at which an object's velocity with respect to the time changes is referred to as acceleration. It is a vector quantity to accelerate (in that they have magnitude and direction). The direction of the net force acting on an object determines the direction of its acceleration. According to Newton's Second Law, the amount of an object's acceleration is the combined result of two causes:

The size of the net balance of all external forces acting on that object is directly proportional to the magnitude of this net resulting force; The magnitude of the mass of that object, depending on the materials out of which it is built, is inversely proportional to the magnitude of the mass.

The given parameters;

distance traveled by boat, d = 12 m

initial velocity of boat, u = 9.5 m/s

final velocity of boat, v = 5.5 m/s

The acceleration of boat is calculated as;

[tex]v^{2}=u^{2}+2as\\ a=\frac{v^{2}-u^{2} }{2s}\\ a=\frac{5.5^{2}-9.5^{2} }{2*12}[/tex]

a=-2.5m/[tex]s^{2}[/tex]

Thus, the deceleration of boat is 2.5 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?

Answers

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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If you double the wavelength of light, what happens to the energy of the photons?.

Answers

Answer:

the energy of photon will be half.

Explanation:

If you need a deeper explanation please let me know. Hope I helped!

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.

Answers

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.

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.

Answers

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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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

Answers

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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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?

Answers

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:

The force applied at the handle of the rigid lever causes the lever to rotate clockwise about the pin b through an angle of 2°. Determine the average normal strain in each wire. The wires are unstretched when the lever is in the horizontal position.

Answers

The average normal strain in wires A, C and D is found to be 0.035, 0.035 and 0.059 respectively when there is a change in the angle by 2° clockwise.

A physical measurement called strain illustrates how much an object's dimensions vary while it is under stress. The ratio between the object's changed length and its initial length is known as the linear strain.

All wires are stretched when the stiff lever rotates 2° in a clockwise direction around pin B.

Elongation would be R x angle in radian

Elongation in the wire A = 200 mm x 3.142 x 2/180 = 6.982 mm

Elongation in the wire C = 300 x 3.142 x 2/180 = 10.473 mm

Elongation in the wire D = 500 x 3.142 x 2/180 = 17.455 mm

Therefore,

Average normal strain in the wire A = 6.982/200 = 0.03491

Average normal strain in the wire C = 10.473/300 = 0.03491

Average normal strain in the wire D = 17.455/300 = 0.05818

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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?

Answers

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/s²

Substituting 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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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?

Answers

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 current

Substitute 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 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?

Answers

Considering the definition of velocity, the magnitude of the helicopter's displacement is 700 meters.

Definition of velocity

Velocity 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 case

In 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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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?

Answers

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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At one location on the Earth, the rms value of the magnetic field caused by solar radiation is 1.80 μT. From this value, calculate (b) the average energy density of the solar component of electromagnetic radiation at this location.

Answers

The average energy density of the solar component of electromagnetic radiation at this location is determined as 2.58 x 10⁻ J.

Average energy density

The average energy density of the solar component of electromagnetic radiation at this location is calculated as follows;

U(avg) = (Brms)²/μ₀

U(avg) = (1.8 x 10⁻⁶)² / (4π x 10⁻⁷)

U(avg) = 2.58 x 10⁻⁶ J

Thus, the average energy density of the solar component of electromagnetic radiation at this location is determined as 2.58 x 10⁻ J.

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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

Answers

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 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?

Answers

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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