Find the magnetic flux through a circular loop 4.6 cm in diameter oriented with the loop normal at 56 ∘ to a uniform 75 mt magnetic field.

Answers

Answer 1

The magnetic flux through the circular loop is 7.95 x 10⁻⁴ Wb.

To find the magnetic flux through a circular loop with a diameter of 4.6 cm, oriented at 56 degrees to a uniform 75 mT magnetic field, follow these steps:

1. Calculate the area (A) of the circular loop using the formula A = πr², where r is the radius (half the diameter): A = π(0.023 m)²≈ 1.66 x 10⁻³ m².

2. Convert the magnetic field (B) from mT to T: B = 75 mT × 10⁻³ = 0.075 T.

3. Calculate the angle (θ) in radians: θ = 56° × (π/180) ≈ 0.977 radians.

4. Use the magnetic flux (Φ) formula: Φ = B × A × cos(θ).

5. Calculate the magnetic flux: Φ = 0.075 T × 1.66 x 10⁻³ m² × cos(0.977) ≈ 7.95 x 10⁻⁴ Wb.

To know more about magnetic flux click on below link:

https://brainly.com/question/24214683#

#SPJ11

Related Questions

a force f is applied to a 2.0 kg, radio-controlled model car parallel to the x- axis as it moves along a straight track. the x-component of the force varies with the x-coordinate of thecar.
The work done by the force when the car moves from x=0.0m to x=7.0m is?
What is the speed of the car at x=4.0m?

Answers

To calculate the work done by the force when the car moves from x=0.0m to x=7.0m, we need to integrate the force over the distance traveled.W = ∫Fdx

Since the force varies with the x-coordinate of the car, we need to know the equation for the force as a function of x. Without that information, we can't calculate the work done.

To calculate the speed of the car at x=4.0m, we need to use the equations of motion. Assuming that the force is the only external force acting on the car, we can use:

F = ma

where F is the force, m is the mass of the car (2.0 kg), and a is the acceleration of the car.

Since the force varies with x, we need to know the equation for the force as a function of x. Without that information, we can't calculate the acceleration of the car, and therefore we can't calculate the speed at x=4.0m.

To know more about force:https://brainly.com/question/12785175

#SPJ11

A solid has a(n) ______ volume and maintains its _____ regardless of the container in which it is placed.

Answers

Answer:

it has a fixed volume and maintains it's shape

A capacitor has parallel plates of area 12 cm2 separated by 6.0mm . The space between the plates is filled with polystyrene (K=2.6, Em=2.0x107V/m).Find the permittivity of polystyrene. Express your answer using two significant figures

Answers

A capacitor has parallel plates of area 12 cm2 separated by 6.0mm. The space between the plates is filled with polystyrene the permittivity of polystyrene is 3.0x10^-11 F/m.

The permittivity of polystyrene can be found using the formula:

ε = (C/d) / ε0A

Where C is the capacitance of the capacitor, d is the distance between the plates, A is the area of the plates, and ε0 is the permittivity of free space.

First, we need to find the capacitance of the capacitor:

C = ε0KA/d

Substituting the given values:

C = (8.85x10^-12 F/m)(2.6)(0.0012 m^2) / 0.006 m

C = 3.06x10^-11 F

Now we can substitute this value along with the other given values into the formula for permittivity:

ε = (C/d) / ε0A

ε = (3.06x10^-11 F) / (0.006 m)(8.85x10^-12 F/m) / (0.00012 m^2)

ε = 2.96x10^-11 F/m

Rounding to two significant figures, the permittivity of polystyrene is 3.0x10^-11 F/m.

Learn more about the permittivity of polystyrene at brainly.com/question/30965100

#SPJ11

Which of the following is not a property of light?
a. light is a form of matter less dense than air
b. light travels in straight lines
c. light has different colors
d. light has different intensities, and cam be bright or dim

Answers

Answer: Light is not a form of matter, so a is not a property of light.

Explanation:

water flows in a 10-cm diameter pipe at a velocity of 0.75 m/s. the mass flow rate of water in the pipe is:

Answers

The mass flow rate of water in the pipe is approximately 0.58875 kg/s using the formula of mass flow rate.

To find the mass flow rate of water in the pipe, we'll use the formula:
Mass flow rate = Area of the pipe × Velocity × Density of water

Step 1: Calculate the area of the pipe.
[tex]Area = \pi * (Diameter / 2)^2[/tex]

Diameter = 10 cm = 0.1 m (convert cm to m by dividing by 100)

[tex]Area = \pi * (0.1 / 2)^2 = \pi × (0.005)^2 = 0.000785 m^2[/tex]

Step 2: Use the given velocity.
Velocity = 0.75 m/s

Step 3: Determine the density of water.
The density of water is approximately 1000 kg/m³.

Step 4: Calculate the mass flow rate.
Mass flow rate = Area × Velocity × Density
[tex]Mass flow rate = 0.000785 m^2 * 0.75 m/s * 1000 kg/m^3 = 0.58875 kg/s[/tex]

Learn more about mass flow rate here:

https://brainly.com/question/23159800

#SPJ11

the current is from left to right in the conductor showmn. the magnetic field is onto the page and point is at higher potential than point t. the charge carriers are
a. positive b. negative c. neutral d. absent e. moving near the speed of light

Answers

The charge carriers in the conductor are likely to be negative, and they are not absent, but their speed is not near the speed of light due to the effects of collisions in the conductor.

Based on the given information, we know that the conductor is experiencing a magnetic force due to the magnetic field pointing onto the page. Additionally, we know that the point labeled as "point" is at a higher potential than the point labeled as "t".

The direction of the current flowing from left to right in the conductor is indicative of the direction in which the charge carriers are moving. Given this information, we can determine that the charge carriers in the conductor must be negative because electrons are negatively charged and move opposite to the direction of conventional current flow.

Furthermore, the fact that the charge carriers are moving in a conductor does not necessarily imply that they are moving near the speed of light. The speed at which electrons move in a conductor is known as the drift velocity and is typically much slower than the speed of light due to collisions with other particles in the conductor.

For more such questions on Charge.

https://brainly.com/question/27986842#

#SPJ11

I need help with my physics homework
When a thin stick of mass M and length L is pivoted about one end, its moment of inertia is I=(1/3)ML^2. When the stick is pivoted about its midpoint, its moment of inertia is

A.) (1/12)ML^2
B.) (1/6)ML^2
C.) (1/3)ML^2
D.) (7/12)ML^2
E.) ML^2

Answers

The moment of inertia of the stick when it is pivoted about its midpoint is (1/6)ML². The answer choice is (B).

When the stick is pivoted about its midpoint, we can split it into two equal pieces of mass M/2 and length L/2, each with a moment of inertia of:

I₁ = (1/3)(M/2)(L/2)² = (1/12)ML²

The parallel axis theorem tells us that the moment of inertia of the whole stick about its midpoint is equal to the sum of the moments of inertia of the two pieces plus the moment of inertia of the stick as if it were a point mass at its center of mass:

I₂ = 2I₁ + (1/12)M(L/2)²

I₂ = (2/12)ML² + (1/48)ML²

I₂ = (1/6)ML²

Option B is correct.

To know more about inertia, here

brainly.com/question/3268780

#SPJ1

Name Period_Date Rotation: Worksheet 9 Angular Momentum The following masses are swung in horizontal circles at the end of a thin string at constant speed. a. A 2.0 kg mass moving at 2.0 on the end of a 2.0 m long thin string. b. A 3.0 kg mass moving at 1.om, on the end of a 2.0 m long thin string. c. A 1.0 kg mass moving at 3.0 on the end of a 2.0 m long thin string. d. A 2.0 kg mass moving at 1.0 on the end of a 4.0 m long thin string. e. A 2.0 kg mass moving at 2.0 on the end of a 4.0 m long thin string

Answers

The length of string is 16.0 kg·m²/s

What is Mass?

Mass is a fundamental property of matter that quantifies the amount of substance or material present in an object. It is a scalar quantity, meaning it only has magnitude and no direction. Mass is commonly measured in units such as kilograms (kg), grams (g), or other appropriate units depending on the context.

a. Mass: 2.0 kg

Velocity: 2.0 m/s

Length of string: 2.0 m

Angular momentum: 8.0 kg·m²/s

b. Mass: 3.0 kg

Velocity: 1.0 m/s

Length of string: 2.0 m

Angular momentum: 6.0 kg·m²/s

c. Mass: 1.0 kg

Velocity: 3.0 m/s

Length of string: 2.0 m

Angular momentum: 6.0 kg·m²/s

d. Mass: 2.0 kg

Velocity: 1.0 m/s

Length of string: 4.0 m

Angular momentum: 2.0 kg·m²/s

e. Mass: 2.0 kg

Velocity: 2.0 m/s

Length of string: 4.0 m

Angular momentum: 8.0 kg·m²/s

Learn more about Mass from the given link

https://brainly.com/question/86444

#SPJ1

When helium capture occurs with a carbon 12 nucleus, what results?
A) Nitrogen 14
B) Oxygen 16
C) Neon 20
D) Silicon 28
E) Nickel 56

Answers

When helium capture occurs with a carbon 12 nucleus, it results in Nitrogen 14.

Helium capture, also known as alpha capture, is a type of nuclear reaction in which a helium nucleus (consisting of two protons and two neutrons, denoted as an alpha particle) is captured by a target nucleus.

When a helium capture occurs with a carbon 12 nucleus (which has 6 protons and 6 neutrons), the resulting nucleus will have 8 protons and 8 neutrons. This results in the formation of a nitrogen 14 nucleus, which has 7 protons and 7 neutrons, denoted as 14N or Nitrogen-14.

Learn more about carbon 12 at

https://brainly.com/question/31324610

#SPJ11

the current in an electric hair dryer is 11aa. part a how much charge flows through the hair dryer in 4.0 minmin ?

Answers

To find the charge that flows through the electric hair dryer in 4.0 minutes, we need to use the formula:

charge = current x time

Substituting the given values, we get:

charge = 11 A x 4.0 min = 44 C

Therefore, the amount of charge that flows through the hair dryer in 4.0 minutes is 44 Coulombs.
Hi! To calculate the charge that flows through the electric hair dryer in 4.0 minutes, you can use the formula Q = I * t, where Q is the charge, I is the current, and t is the time.

Given that the current (I) in the hair dryer is 11 A, and the time (t) is 4.0 minutes (or 240 seconds, since 1 minute = 60 seconds), you can plug these values into the formula:

Q = 11 A * 240 s

Q = 2640 C

So, 2640 Coulombs of charge flow through the electric hair dryer in 4.0 minutes.

Learn more about electric hair dryer here;

https://brainly.com/question/29086609

#SPJ11

For ease of installation, a cabin that is used occasionally is supplied with baseboard electric heating. These are 30 amp circuits powered with 220 volts. To supply 70,000Btu/h (about 20kW)1. How many circuits are needed, and2. What is the resistance of each baseboard "strip" in a single circuit?

Answers

To supply 70,000 BTU/h (about 20 kW) of baseboard electric heating to the cabin, you would need 4 circuits, and the resistance of each baseboard strip in a single circuit would be approximately 7.3 ohms.

To determine how many circuits are needed and the resistance of each baseboard strip in a single circuit for a cabin with 70,000 BTU/h (about 20 kW) of baseboard electric heating, we'll need to follow these steps:

1. Convert the desired heating capacity to watts:
70,000 BTU/h * (1 kW / 3412.14 BTU/h) ≈ 20,500 W

2. Calculate the power per circuit:
Power per circuit = Voltage x Current = 220 V x 30 A = 6,600 W

3. Determine the number of circuits needed:
Number of circuits = Total Power / Power per circuit = 20,500 W / 6,600 W ≈ 3.1
Since you can't have a fraction of a circuit, you'll need 4 circuits to supply the required power.

4. Calculate the total resistance for each circuit:
Resistance (R) = Voltage² / Power = (220 V)² / 6,600 W ≈ 7.3 ohms.

Learn more about resistance:

https://brainly.com/question/17563681

#SPJ11

show that the transition matrix is regular and find its steady-state vector.

Answers

To show that a transition matrix is regular by raising the matrix to different powers until you find a power with all positive elements and its steady-state vector is equation πP = π while ensuring the elements of π sum to 1.

A transition matrix is regular if some power of the matrix has only positive elements, a steady-state vector is a probability vector that remains unchanged after being multiplied by the transition matrix. To demonstrate that the transition matrix is regular, raise the matrix to different powers until you find a power with all positive elements. If such a power exists, the matrix is considered regular.

Next, to find the steady-state vector, solve the following equation: πP = π, where π is the steady-state vector, and P is the transition matrix. Additionally, ensure the elements of π sum to 1, representing the total probability, you can solve this system of linear equations using methods like Gaussian elimination, matrix inversion, or iterative techniques. In summary, to show that a transition matrix is regular, find a power of the matrix with all positive elements, then, to find the steady-state vector, solve the equation πP = π while ensuring the elements of π sum to 1.

Learn more about transition matrix at:

https://brainly.com/question/28026040

#SPJ11

for a particular process at 300 k, δg δ g = -10.0 kj and δh δ h = -7.0 kj. if the process is carried out reversibly, the amount of useful work (in kj) that .

Answers

The amount of useful work that can be obtained for this particular process at 300 K is -3.0 kJ.

For a reversible process, the amount of useful work (in kJ) that can be obtained is given by the equation:

w = -δg = δh - Tδs

where δs is the change in entropy of the system.

Since the process is carried out reversibly, δs can be calculated using the equation:

δs = δqrev / T

where δqrev is the heat absorbed by the system during a reversible process.

Since δh = -7.0 kJ and δg = -10.0 kJ, we know that the process is exothermic (δh < 0) and spontaneous (δg < 0). Therefore, δqrev must be negative, indicating that heat is released from the system.

We can calculate δqrev using the equation:

δqrev = -Tδs = -T(δh / T) = -δh = 7.0 kJ

Substituting this value into the equation for work, we get:

w = -δg = δh - Tδs = -10.0 kJ - (-7.0 kJ) = -3.0 kJ

Therefore, the amount of useful work for this particular process at 300 K is -10.0 kJ.

Learn more about work here: brainly.com/question/31050706

#SPJ11

The question is often asked: Can an airfoil fly upside-down? To answer this, make the following calculation. Consider a positively cambered airfoil with a zero-lift angle of -2°. The lift slope is 0.1 per degree.a/ Calculate the lift coefficient at an angle of attack of 6º. b/ Now imagine the same airfoil turned upside-down, but at the same 6° angle of attack as part (a). Calculate its lift coefficient. c/ At what angle of attack must the upside-down airfoil be set to generate the same lift as that when it is right- side-up at a 6° angle of attack?

Answers

Yes, an airfoil can fly upside-down. To calculate the lift coefficient of a positively cambered airfoil with a zero-lift angle of -2° at an angle of attack of 6º, we use the lift slope of 0.1 per degree.

a/ The lift coefficient at 6º angle of attack would be 0.1 x (6-(-2)) = 0.8

b/ When the same airfoil is turned upside-down, the lift coefficient at the same 6° angle of attack would still be 0.8 because the lift coefficient only depends on the angle of attack and the shape of the airfoil, not its orientation.

c/ To generate the same lift as when the airfoil is right-side-up at a 6° angle of attack, the upside-down airfoil must be set to an angle of attack of -6º because the lift coefficient is proportional to the angle of attack.

Learn more about airfoil here:

https://brainly.com/question/30042281

#SPJ11

What is the output voltage of a 3.0000-V lithium cell in a digital wristwatch that draws 0.300 mA, if the cell’s internal resistance is 2.00 Ω ?

Answers

Output Voltage of the lithium cell = 2.9994 V

Output Voltage is the maximum voltage that a cell can offer after overcoming its own internal resistance that arises from the construction of the cell.

To find the output voltage of the lithium cell, you need to consider the voltage drop across the internal resistance due to the current draw. You can use Ohm's Law for this calculation: Voltage drop = Current × Resistance.

In this case, the current draw is 0.300 mA, and the internal resistance is 2.00 Ω. First, convert the current to amperes: 0.300 mA = 0.0003 A.

Now, calculate the voltage drop: Voltage drop = 0.0003 A × 2.00 Ω = 0.0006 V.

Finally, subtract the voltage drop from the initial cell voltage: Output voltage = 3.0000 V - 0.0006 V = 2.9994 V.

The output voltage of the lithium cell is approximately 2.9994 V.

To know more about voltage, visit https://brainly.com/question/2364325

#SPJ11

An automobile dealer calculates the proportion of new cars sold that have been returned a various numbers of times for the correction of defects during the warranty period. The results are shown in the following table. Number of returns 0 Proportions 0.28 0.36 0.23 0.09 0.04 (a) Graph the probability distribution function. (b) Calculate and graph the cumulative probability distribution. (b) Calculate and graph the cumulative probability distribution. Find the mean of the number of returns of an automobile for corrections for defects during the warranty period. (d) Find the variance of the number of returns of an automobile for correc- tions for defects during the warranty period.

Answers

(a) Bar graph with x-axis showing the number of returns and y-axis showing the proportion of new cars sold with that number of returns.

(b) Line graph with x-axis showing the number of returns and y-axis showing the cumulative proportion of new cars sold with up to that number of returns.

(d) Variance = 1.715 returns^2, calculated as [(0-0.95)^20.28]+[(1-0.95)^20.36]+[(2-0.95)^20.23]+[(3-0.95)^20.09]+[(4-0.95)^20.04].

In part (a), we represent the probability distribution function using a bar graph. The x-axis shows the number of returns, and the y-axis shows the proportion of new cars sold with that number of returns. In part (b), we plot the cumulative probability distribution using a line graph. The x-axis shows the number of returns, and the y-axis shows the cumulative proportion of new cars sold with up to that number of returns.

learn more about returns here:

https://brainly.com/question/29569139

#SPJ11

In a parallel circuit, the current through any resistor is directly proportional to the value of that resistor. True or False.

Answers

False. In a parallel circuit, the current through each resistor is not directly proportional to the value of that resistor. Instead, the current through each resistor is inversely proportional to the value of the resistor. This means that as the resistance of a resistor increases, the current through it decreases, and vice versa.

In a parallel circuit, the voltage across each resistor is the same, but the current flowing through each resistor can be different. This is because each resistor provides a different path for the flow of electricity. The total current flowing into the parallel circuit is divided among the different resistors according to their individual resistance values.

In summary, in a parallel circuit, the current through each resistor is inversely proportional to its value. This is because the total current flowing into the parallel circuit is divided among the different resistors according to their individual resistance values, and the voltage across each resistor is the same.

To know more about parallel circuit refer here:

https://brainly.com/question/11409042#

#SPJ11

A student wants to determine the angular speed w of a rotating object. The period T is 0.50 s +/- 5%. The angular speed ω is
ω = 2π/T
What is the percentage uncertainly of ω? A. 0.2%
B. 2.5% C. 5% D. 10%

Answers

The percentage uncertainty of the angular speed= 5%

To determine the percentage uncertainty of the angular speed ω, we can use the following formula:

Percentage Uncertainty of ω = (Percentage Uncertainty of T) * (Constant Value)

In this case, the percentage uncertainty of T is 5%, and the constant value is 2π (from the formula ω = 2π/T). Therefore:

Percentage Uncertainty of ω = (5%) * (2π)

However, since we're only interested in the percentage uncertainty, we don't need to multiply by the constant value (2π). So, the percentage uncertainty of ω is the same as the percentage uncertainty of T:

Percentage Uncertainty of ω = 5%

So, the correct answer is C i.e.5%

To know more about angular speed, visit https://brainly.com/question/30885221

#SPJ11

what wavelength bands were placed into which color guns

Answers

wavelength bands were placed into which color guns,

we need to understand that color guns are components of a cathode ray tube (CRT) display, commonly used in older televisions and monitors. CRT displays have three color guns: red, green, and blue (RGB). These color guns produce different wavelengths corresponding to their respective colors.

1. Red color gun: The red color gun corresponds to the wavelength band of approximately 620-750 nm.
2. Green color gun: The green color gun corresponds to the wavelength band of approximately 495-570 nm.
3. Blue color gun: The blue color gun corresponds to the wavelength band of approximately 450-495 nm.

By combining various intensities of these three primary colors, CRT displays can produce a wide range of colors on the screen.

Learn more about wavelength https://brainly.com/question/31503451

#SPJ11

What eclipse occurs when the Moon is in between the Sun and the Earth and the Moon partially or completely blocks out the Sun?

Answers

The eclipse that occurs when the Moon is in between the Sun and the Earth and partially or completely blocks out the Sun is known as a solar eclipse.

During a solar eclipse, the Moon casts a shadow on the Earth's surface, creating a path of totality where the Sun is completely blocked out, and a partial eclipse where only part of the Sun is covered. Solar eclipses occur only during a new moon when the Moon passes between the Sun and the Earth.

During a solar eclipse, the Moon's shadow falls on the Earth's surface, causing the Sun to appear as if it is being covered or "eclipsed" by the Moon. Depending on the alignment of the Sun, Moon, and Earth, a solar eclipse can be either partial or total.

Therefore, A total solar eclipse occurs when the Moon completely covers the Sun, and only the Sun's corona (outer atmosphere) is visible as a glowing ring around the Moon.

To know more about solar eclipse refer here :

https://brainly.com/question/1077760

#SPJ11

what is the sensitivity (in µa) of the galvanometer (that is, what current gives a full-scale deflection) inside a voltmeter that has a 1.00 mω resistance on its 30.5 v scale?

Answers

The sensitivity of the galvanometer inside the voltmeter is 30,500,000 µA.

Hi! To find the sensitivity (in µA) of the galvanometer inside a voltmeter with a 1.00 mΩ resistance on its 30.5 V scale, you can follow these steps:

1. First, note the full-scale voltage, V = 30.5 V, and the internal resistance of the voltmeter, R = 1.00 mΩ.
2. Use Ohm's law to calculate the current for full-scale deflection, I = V/R.
3. Convert the calculated current to microamperes (µA).

Now, let's calculate the sensitivity of the galvanometer:

1. V = 30.5 V, R = 1.00 mΩ = 0.001 Ω (since 1 mΩ = 0.001 Ω).
2. I = V/R = 30.5 V / 0.001 Ω = 30500 A.
3. Convert the current to µA: 1 A = 1,000,000 µA, so 30500 A = 30,500,000 µA.

So, the sensitivity of the galvanometer inside the voltmeter is 30,500,000 µA.

To know more about galvanometer refer here:

https://brainly.com/question/17247518

#SPJ11

A typical power for a laser used in physics labs is 0.75 mW. This laser would produce a beam that is about 1 mm in diameter I found the average intensity: to be 955 W/m2 I found the average energy density of this beam: 3.183*10^-6 J/m^3 I need help with this question. Lets say the laser beam is reflected completely off a mirror. What is the maximum force the beam can exert on the mirror? I did 955 x 2x (4pie x 10^-7)/(3*10^8) but says my answer is wrong, is this the right equation???

Answers

The maximum force of a typical power for a laser used in physics labs is 0.75 mW and would produce a beam that is about 1 mm in diameter can exert on the mirror is 5 x 10⁻⁹ N.

In physics, power is the amount of energy transferred or converted per unit time. In the International System of Units, the unit of power is the watt, equal to one joule per second. In older works, power is sometimes called activity. Power is a scalar quantity.

To find the maximum force the laser beam can exert on the mirror when it is reflected completely, you should use the following formula:

Force (F) = (2 × Power (P)) / Speed of light (c)

where Power (P) = 0.75 mW (convert to Watts: 0.75 x 10⁻³ W), and Speed of light (c) = 3 x 10⁸ m/s.

F = (2 × (0.75 x 10⁻³ W)) / (3 x 10⁸ m/s)

Thus, the maximum force of the beam can exert on the mirror is approximately 5 x 10⁻⁹ N.

Learn more about maximum force: https://brainly.com/question/14434333

#SPJ11

Johnny, of mass 65 kg, and Lucy, of mass 45 kg, are facing each other on roller blades. The coefficient of kinetic friction between the roller blades and concrete surface is 0.20. When Johnny pushes Lucy from rest he applies a force for 1.0 s. Lucy then slows down to a stop in another 8.0 s. Calculate:
a. The applied force exerted by Johnny on Lucy.
b. How long it takes Johnny to come to rest.

I tried calculated the force exerted but I would need acceleration which I don't have...any tips on how to solve this one??? help is appreciated!!

Answers

Answer:

John applied a force of approximately [tex]795\; {\rm N}[/tex] (on average, rounded) on Lucy.

John slows down to a stop after approximately another [tex]5.37\; {\rm s}[/tex].

(Assuming that [tex]g = 9.81\; {\rm N\cdot kg^{-1}}[/tex].)

Explanation:

Assuming that the surface is level. The normal force on Johnny will be equal to the weight of Johnny: [tex]N(\text{John}) = m(\text{John})\, g[/tex]. Similarly, the normal force on Lucy will be equal to weight [tex]N(\text{Lucy}) = m(\text{Lucy})\, g[/tex].

Multiply normal force by the coefficient of kinetic friction to find the friction on each person:

[tex]f(\text{John}) = \mu_{k}\, N(\text{John}) = \mu_{k}\, m(\text{John})\, g[/tex].

[tex]f(\text{Lucy}) = \mu_{k}\, N(\text{Lucy}) = \mu_{k}\, m(\text{Lucy})\, g[/tex].

Again, because the surface is level, the net force on each person after the first [tex]1.0\; {\rm s}[/tex] will be equal to the friction. Divide that the net force on each person by the mass of that person to find acceleration:
[tex]\displaystyle a(\text{John}) = \frac{\mu_{k}\, m(\text{John})\, g}{m(\text{John})} = \mu_{k}\, g[/tex].

[tex]\displaystyle a(\text{Lucy}) = \frac{\mu_{k}\, m(\text{Lucy})\, g}{m(\text{Lucy})} = \mu_{k}\, g[/tex].

(Note that the magnitude of acceleration is independent of mass and is the same for both John and Lucy.)

[tex]a = \mu_{k}\, g= (0.2)\, (9.81\; {\rm m\cdot s^{-2}}) = 1.962\; {\rm m\cdot s^{-2}}[/tex].

In other words, after the first [tex]1\; {\rm s}[/tex], both John and Lucy will slow down at a rate of [tex]1.962\; {\rm m\cdot s^{-2}}[/tex].

To find the speed of Lucy immediately after the first [tex]1.0\: {\rm s}[/tex], multiply this acceleration by the time [tex]t = 8.0\; {\rm s}[/tex] it took for Lucy to slow down to [tex]0\; {\rm m\cdot s^{-1}}[/tex]:

[tex]\begin{aligned}& (8.0\; {\rm s})\, (1.962\; {\rm m\cdot s^{-2}}) \\ =\; & (8.0)\, (1.962)\; {\rm m\cdot s^{-1}} \\ =\; & 15.696\; {\rm m\cdot s^{-1}}\end{aligned}[/tex].

Thus, in the first [tex]1.0\; {\rm s}[/tex], Lucy accelerated (from [tex]0\; {\rm m\cdot s^{-1}}[/tex]) to [tex]15.696\; {\rm m\cdot s^{-1}}[/tex].

The average acceleration of Lucy in the first [tex]1.0\; {\rm s}[/tex] would be [tex](15.696) / (1) = 15.696\; {\rm m\cdot s^{-2}}[/tex]. Multiply this average acceleration by the mass of Lucy to find the average net force on Lucy during that [tex]1.0\; {\rm s}[/tex]:

[tex]\begin{aligned}F_{\text{net}}(\text{Lucy}) &= m(\text{Lucy})\, a \\ &= (45)\, (15.696)\; {\rm N} \\ &= 706.320\; {\rm N}\end{aligned}[/tex].

This net force on Lucy during that [tex]1.0\; {\rm s}[/tex] is the combined result of both the push from Johnny and friction:

[tex]F_{\text{net}}(\text{Lucy}) = F(\text{push}) - f(\text{Lucy})[/tex].

Since [tex]f(\text{Lucy}) = \mu_{k}\, N(\text{Lucy}) = \mu_{k}\, m(\text{Lucy})\, g[/tex]:

[tex]\begin{aligned}F(\text{push}) &= F_{\text{net}}(\text{Lucy}) + f(\text{Lucy}) \\ &= F_{\text{net}}(\text{Lucy}) + \mu_{k}\, m(\text{Lucy})\, g \\ &= (706.320) \; {\rm N}+ (0.2)\, (45)\, (9.81)\; {\rm N} \\ &= 706.320\; {\rm N} + 88.290\; {\rm N} \\ &=794.610\; {\rm N}\end{aligned}[/tex].

In other words, Johnny would have applied a force of [tex]794.610\; {\rm N}[/tex] on Lucy.

By Newton's Laws of Motion, when Johnny exerts this force on Lucy in that [tex]1.0\; {\rm s}[/tex], Lucy would exert a reaction force on Johnny of the same magnitude: [tex]794.610\; {\rm N}[/tex].

Similar to Lucy, the net force on Johnny during that [tex]1.0\; {\rm s}[/tex] will be the combined effect of the push [tex]F(\text{push})[/tex] and friction [tex]f(\text{John}) = \mu_{k}\, m(\text{John})\, g[/tex]:

[tex]\begin{aligned}F_{\text{net}}(\text{John}) &= F(\text{push}) - f(\text{John}) \\ &= F(\text{push}) - \mu_{k}\, m(\text{John})\, g\\ &= 794.610\; {\rm N} - (0.2)\, (65)\, (9.81)\; {\rm N} \\ &= 667.080\; {\rm N}\end{aligned}[/tex].

Divide net force by mass to find acceleration:

[tex]\begin{aligned}\frac{667.080\; {\rm N}}{65\; {\rm kg}} \approx 10.2628\; {\rm m\cdot s^{-2}}\end{aligned}[/tex].

In other words, Johnny accelerated at a rate of approximately [tex]10.5406\; {\rm m\cdot s^{-2}}[/tex] during that [tex]1.0\; {\rm s}[/tex]. Assuming that Johnny was initially not moving, the velocity of Johnny right after that [tex]1.0\; {\rm s}\![/tex] would be:

[tex](0\; {\rm m\cdot s^{-1}}) + (10.2628\; {\rm m\cdot s^{-2}})\, (1.0\; {\rm s}) = 10.2628\; {\rm m\cdot s^{-1}}[/tex].

After the first [tex]1.0\; {\rm s}[/tex], the acceleration of both John and Lucy (as a result of friction) would both be equal to [tex]a = \mu_{k}\, g= (0.2)\, (9.81\; {\rm m\cdot s^{-2}}) = 1.962\; {\rm m\cdot s^{-2}}[/tex]. Divide initial velocity of Johnny by this acceleration to find the time it took for Johnny to slow down to a stop:

[tex]\displaystyle \frac{10.2628\; {\rm {m\cdot s^{-1}}}}{1.962\; {\rm m\cdot s^{-2}}} \approx 5.23\; {\rm s}[/tex].