While running, a person dissipates about 0.6 J of mechanical energy per step per kilogram of body mass. If a 60-kg person runs with a power of 70 Watts during a race, how fast is the person running

Answers

Answer 1

Complete question is: While running, a person dissipates about 0.60 J of mechanical energy per step per kilogram of body mass. If a 60-kg person develops a power of 70 W during a race, how fast is the person running? (Assume a running step is 1.5 m long).

Answer: The person running at a speed of 2.91 m/s.

Explanation:

Given: Mass of runner = 60 kg

Runner dissipates = 0.6 J/kg per step

Average power = 70 W

1 step = 1.50 m

Energy dissipated by the runner is as follows.

[tex]\Delta E_{step} = 0.60 \times 60\\= 36 J[/tex]

Formula used to calculate the value of one step 'S' is as follows.

[tex]\frac{S}{\Delta t} = \frac{P_{avg}}{\Delta E_{step}} = \frac{70}{36}\\= 1.94\\S = 1.94 \Delta t[/tex]

It is known that average velocity is equal to the total distance divided by time interval.

So, total distance for the given situation is as follows.

[tex]d = S \times 1.5[/tex]

Hence, speed of the person is calculated as follows.

[tex]v_{avg} = \frac{d}{\Delta t}\\= \frac{S \times 1.5}{\Delta t}\\= \frac{1.94 \Delta t \times 1.5}{\Delta t}\\= 2.91 m/s[/tex]

Thus, we can conclude that the person running at a speed of 2.91 m/s.


Related Questions

A solid sphere and a hollow sphere each of mass M and radius R are released at the same time from the top of an inclined plane. Which one of the following statements is necessarily true?
A.Both spheres will reach the bottom at the same time.
B. The hollow sphere will reach the bottom with the greater kinetic energy.
C.The solid sphere will reach the bottom first.
D. The hollow sphere will reach the bottom first.
E. The solid sphere will reach the bottom with the greater kinetic energy.

Answers

Answer:

C. The solid sphere will reach the bottom first.

E. The solid sphere will reach the bottom with the greater kinetic energy.

Explanation:

To answer this,the sphere that has the smaller mass moment of inertia will be the one that will have the largest acceleration down the plane. And we know that higher acceleration means higher speed.

Now, moment of inertia of both spheres are;

I_solid sphere = (2/5)mr² = 0.4mr²

I_hollow sphere = (2/3)mr² = 0.67 mr²

Now, it is clear that the solid sphere has the smaller mass moment of inertia. This means that the solid sphere will have more acceleration and as well higher speed and will thus reach the bottom first.

Also, the higher the speed, the higher the kinetic energy since K.E = ½mv².

Thus, options C & E are correct.

A 5.0 A electric current passes through an aluminum wire of 4.0~\times~10^{-6}~m^2 cross-sectional area. Aluminum has one free electron per atom. The density of aluminum is 2.7~grams/cm^3, and the aluminum molar mass is 27 g. What is the electron number density (the number of electrons per unit volume) in the wire

Answers

Answer: The electron number density (the number of electrons per unit volume) in the wire is [tex]6.0 \times 10^{28} m^{-3}[/tex].

Explanation:

Given: Current = 5.0 A

Area = [tex]4.0 \times 10^{-6} m^{2}[/tex]

Density = 2.7 [tex]g/cm^{3}[/tex], Molar mass = 27 g

The electron density is calculated as follows.

[tex]n = \frac{density}{mass per atom}\\= \frac{\rho}{\frac{M}{N_{A}}}\\[/tex]

where,

[tex]\rho[/tex] = density

M = molar mass

[tex]N_{A}[/tex] = Avogadro's number

Substitute the values into above formula as follows.

[tex]n = \frac{\rho \times N_{A}}{M}\\= \frac{2.7 g/cm^{3} \times 6.02 \times 10^{23}/mol}{27 g/mol}\\= \frac{16.254 \times 10^{23}}{27} cm^{3}\\= 0.602 \times 10^{23} \times \frac{10^{6} cm^{3}}{1 m^{3}}\\= 6.0 \times 10^{28} m^{-3}[/tex]

Thus, we can conclude that the electron number density (the number of electrons per unit volume) in the wire is [tex]6.0 \times 10^{28} m^{-3}[/tex].

WILL GIVE 50 POINTS TO CORRECT ANSWER‼️

A capacitor has 4.33 x 10-7 C of
charge on it when 3.45 V is applied.
How much energy is stored in the
capacitor?

Answers

Answer:

7.47×10¯⁷ J

Explanation:

From the question given above, the following data were obtained:

Charge (Q) = 4.33×10¯⁷ C

Potential difference (V) = 3.45 V

Energy (E) =?

The energy stored in a capacitor is given by the following equation:

E = ½QV

Where

E => is the energy.

Q => is the charge.

V => is the potential difference.

With the above formula, we can obtain the energy stored in the capacitor as follow:

Charge (Q) = 4.33×10¯⁷ C

Potential difference (V) = 3.45 V

Energy (E) =?

E = ½QV

E = ½ × 4.33×10¯⁷ × 3.45

E = 7.47×10¯⁷ J

Thud, the energy stored in the capacitor is 7.47×10¯⁷ J

Answer:

The answer would be 7.47x10^-7J

Explanation:

Put in 7.47 then -7

if a seismic wave has a period of 0.0202s, find the frequency of the wave.

Answers

Answer:

49.5 Hz.

Explanation:

From the question given above, the following data were obtained:

Period (T) = 0.0202 s

Frequency (f) =?

The frequency and period of a wave are related according to the following equation:

Frequency (f) = 1 / period (T)

f = 1/T

With the above formula, we can obtain the frequency of the wave as follow:

Period (T) = 0.0202 s

Frequency (f) =?

f = 1/T

f = 1/0.0202

f = 49.5 Hz

Therefore the frequency of the wave is 49.5 Hz.

What is the magnitude of the current in the R= 6 Ω resistor?

kirchhoff

Answers

Answer:

Here's an explanation but not the answer

Explanation:

When a resistor is traversed in the same direction as the current, the ... Traversing the internal resistance r1 from c to d gives −I2r1. ... I1 = I2 + I3 = (6−2I1) + (22.5− 3I1) = 28.5 − 5I1.

Appliances A, B, and C consume 250, 480 and 1450 watts of power, respectively. The system voltage is 120V, and the circuit breaker is rated at 15 amps. Which combinations of the three appliances can be on at the same time, and which combinations will trip the circuit breaker

Answers

Answer:

Appliance A and B can work together without tripping

Explanation:

We will calculate the amount of current consumed by each appliances.

Appliance A

P = VI

I = P/V  

I = 250/120 = 2.08 A

Appliance B

I = 480 /120 = 4 A

Appliance C

I = 1450/120

I = 12.08 A

Hence, appliance C will trip the circuit as it consumes a lot of electricity.

PLEASE HELP ME WITH THIS ONE QUESTION
What is the rest energy of a proton? (c = 2.9979 x 10^9 m/s, mp = 1.6726 x 10^-27)

Answers

Answer:

Energy =  1.5032*10^(-10) Joules

Explanation:

By Einstein's relativistic energy equation, we know that the energy of a given particle is given by:

Energy = rest energy + kinetic energy.

            = m*c^2  + (γ - 1)*mc^2

Where γ depends on the velocity of the particle.

But if the proton is at rest, then the kinetic energy is zero, and γ = 1

Then the energy is just given by:

Energy = m*c^2

Where we know that:

mass of a proton = 1.67*10^(-27) kg

speed of light = c = 2.9979*10^(8) m/s

Replacing these in the energy equation, we get:

Energy = ( 1.6726*10^(-27) kg)*( 2.9979*10^(8) m/s)^2

Energy = 1.5032*10^(-10) kg*m^2/s^2

Energy =  1.5032*10^(-10) J

It is 2058 and you are taking your grandchildren to Mars. At an elevation of 34.7 km above the surface of Mars, your spacecraft is dropping vertically at a speed of 293 m/s. The spacecraft is to make a soft landing -- that is, at the instant it reaches the surface of Mars, its velocity is zero. Assume the spacecraft undergoes constant acceleration from the elevation of 34.7 km until it reaches the surface of Mars. What is the magnitude of the acceleration

Answers

Answer: [tex]1.23\ m/s^2[/tex]

Explanation:

Given

At an elevation of [tex]y=34.7\ km[/tex], spacecraft is dropping vertically at a speed of [tex]u=293\ m/s[/tex]

Final velocity of the spacecraft is [tex]v=0[/tex]

using equation of motion i.e. [tex]v^2-u^2=2as[/tex]

Insert the values

[tex]\Rightarrow 0-(293)^2=2\times a\times (34.7\times 10^3)\\\\\Rightarrow a=-\dfrac{293^2}{2\times 34.7\times 10^3}\\\\\Rightarrow a=-1.23\ m/s^2[/tex]

Therefore, magnitude of acceleration is [tex]1.23\ m/s^2[/tex].

In the series circuit, if the potential difference across the battery is 20 V and the potential difference across R1 is 12 V, what is the potential difference across R2

Answers

Answer:

The correct answer is "8 V".

Explanation:

Given:

Potential difference across battery,

= 20 V

Potential difference across R1,

= 12 V

Now,

On applying the Kirchorff loop, we get

⇒ [tex]E-I_1R_1-I_2R_2=0[/tex]

⇒ [tex]E-V_1-V_2=0[/tex]

⇒ [tex]V_2=E-V_1[/tex]

On putting values, we get

⇒      [tex]=20-12[/tex]

⇒      [tex]= 8 \ V[/tex]  

The potential difference across the resistance R2 will be "8 Volts.

What is Kirchoff;s law?

According to the kirchoff's law in a loop of a circuit when there are number of the resistances so the sum of all the potential differences will be zero.

It is given that:

Potential difference across battery,= 20 V

Potential difference across R1,= 12 V

Now,

On applying the Kirchorff loop, we get

⇒ [tex]\rm E-I_1R_1-I_2R_2=0[/tex]

⇒ [tex]\rm E-V_1-V_2=0[/tex]

⇒ [tex]\rm V_2=E-V_1[/tex]

On putting values, we get

⇒ [tex]V_2=20-12=8\ volt[/tex]

Hence the potential difference across the resistance R2 will be "8 Volts.      

To know more about Kirchoff's law follow

https://brainly.com/question/86531

 

motto that will help in reaching a goal in life that related the projectile motion ​

Answers

Explanation:

hmm! very good questions I hope u understand

The area around a magnet containing all of magnetic Lines of force is called

Answers

Answer:

Magnetic Field

Explanation:

The area around a magnet containing all of magnetic Lines of force is called the magnetic field.

A car moves round a circular track of radius 0.3m of two revolution per/sec find its angular velocity.

Answers

Answer:

the angular velocity of the car is 12.568 rad/s.

Explanation:

Given;

radius of the circular track, r = 0.3 m

number of revolutions  per second made by the car, ω = 2 rev/s

The angular velocity of the car in radian per second is calculated as;

From the given data, we convert the angular velocity in revolution per second to radian per second.

[tex]\omega = 2 \ \frac{rev}{s} \times \frac{2\pi \ rad}{1 \ rev} = 4\pi \ rad/s = 12.568 \ rad/s[/tex]

Therefore, the angular velocity of the car is 12.568 rad/s.

A basketball player shoots toward a basket 4.9 m away and 3.0 m above the floor. If the ball is released 1.8 m above the floor at an angle of 60 o above the horizontal, what must the initial speed be if it were to go through the basket

Answers

Answer:

  v₀ = 6.64 m / s

Explanation:

This is a projectile throwing exercise

          x = v₀ₓ t

          y = y₀ + v_{oy} t - ½ g t²

In this case they indicate that y₀ = 1.8 m and the point of the basket is x=4.9m y = 3.0 m

         

the time to reach the basket is

        t = x / v₀ₓ

we substitute

        y- y₀ = [tex]\frac{ v_o \ x \ sin \theta }{ v_o \ cos \theta} - \frac{1}{2} g \ \frac{x^2 }{v_o^2 \ cos^2 \theta }[/tex]

        y - y₀ = x tan θ - [tex]\frac{ g \ x^2 }{ 2 \ cos^2 \theta } \ \frac{1}{v_o^2 }[/tex]

         

we substitute the values

        3 -1.8 = 3.0 tan 60 - [tex]\frac{ 9.8 \ 3^2 }{2 \ cos^2 60 } \ \frac{1}{v_o^2}[/tex]

        1.2 = 5.196 - 176.4 1 / v₀²

        176.4 1 / v₀² = 3.996

        v₀ = [tex]\sqrt{ \frac{ 176.4}{3.996} }[/tex]

        v₀ = 6.64 m / s

A 2800-lbm car climbs a 1160 ft. long uphill road which is inclined at 15o (to the horizontal) and covers the distance in 12 sec. Determine the power required if the car covers the distance (a) at constant velocity, (b) from an initial velocity, at the bottom of the hill, of 10 mph to a final velocity of 50 mph at the top of the hill and (c) from an initial velocity of 45 mph to a final velocity of 15 mph. Neglect the effects of friction and wind resistance.

Answers

Answer:

a) P = 70054.3 W,  b)  P = 18820 W,  c)   P = 14116.7 W

Explanation:

Power is defined as work per unit of time

         P = W / t = F x / t

         P = F v

a) in this case the velocity is constant, let's use the equilibrium relation to find the force.

Let's set a reference system with the x axis parallel to the plane

           

        F - Wₓ = 0

         F = Wₓ

with trigonometry let's decompose the weight

        sin θ = Wₓ / W

        Wₓ = W sin θ

         

          F = W sin 15

          F = 2800 sin 15

          F = 724.7 lb

we look for the speed, as it rises with constant speed we can use the relations of uniform motion

          v = x / t

          v = 1160/12

          v = 96.67 ft / s

we calculate the power

          P = 724.7 96.67

          P = 70054.3 W

b) In this case, the speed of the vehicle changes during the ascent, so we use the relationship between work and the change in kinetic energy

           W = ΔK

           W = ½ m v_f² - ½ m v₀²

   let's reduce to the SI system

           v₀ = 10 mph (5280 ft / 1 mile) (1h / 3600 s = 14.67 ft / s

           v_f = 50 mph (5280 ft / 1 mile) (1 h / 3600s) = 73.33 ft.s

           

 mass :         m = w / g

           W = ½ 2800/32 (73.33² - 14.67²)

           W = 225841 J

we calculate the average power

           P = W / t

           P = 225841/12

           P = 18820 W

c) we repeat the previous procedure

          v₀ = 45 mph = 66 ft / s

          v_f = 15 mph = 22 ft / s

          W = ½ 2800/32 (22² - 66²)

          W = -169400 J

         

          P = W / t

          P = 169400/12

          P = 14116.7 W

Two kg of water is contained in a piston-cylinder assembly, initially at 10 bar and 200°C. The water is slowly heated at constant pressure to a final state. If the heat transfer for the process is 1740 kJ, determine the temperature at the final state, in °C, and the work, in kJ. Kinetic and potential energy effects are negligible.

Answers

Answer:

Explanation:

Given that:

mass of water = 2kg

Pressure P₁ = 10 bar

temperature T₁ = 200⁰ C

Obtaining the following value from superheated tables at P₁ = 10 bar and T₁ = 200⁰ C

v₁ = 0.2060 m³/kg

h₁ = 2827.9 kJ/kg

The heat transfer Q₁₋₂ = 1740 kJ

Using the energy balance equation:

Q₁₋₂ = m(h₂ - h₁)

1740 = 2(h₂ - 2827.9)

1740 = 2h₂ - 5655.8

1740 + 5655.8 = 2h₂

7395.8 = 2h₂

h₂ = 7395.8/2

h₂ = 3697.9 kJ/kg

Since P₁ = P₂ = 10 bar

Using the superheated table at P₂ = 10 bar and h₂ = 3697.9 kJ/kg;

v₂ = 0.4011 m³/kg

The temperature at final state = 600 °C

The work done [tex]W_{1-2} = \int P dv[/tex]

[tex]W_{1-2} = P\times m (V_2-V_1)[/tex]

= (10×10² kPa)×2kg (0.4011 - 0.2060) m³/kg

= (10×10² kPa)×2kg × 0.1951 m³/kg

= 390.2 kJ

2. Why is it necessary for rotation to occur within a
generator?

Answers

Answer:

ON

Explanation:

Locate your computer's Power button.

Press and hold that button until your computer shuts down.

Wait until you hear the computer's fans shut off, and your screen goes completely black.

Wait a few seconds before pressing and holding the power button to initiate your computer's normal startup.

The movement of the liquid in a thermometer shows changes in temperature. An increase in temperature indicates the molecules in the liquid *

Answers

Answer:

The movement of the liquid in a thermometer shows changes in temperature. An increase in temperature indicates the molecules in the liquid *

Explanation:

difference between work done against gravity and friction​

Answers

Mark Brainliest please


Friction is a nonconservative force. Therefore work done against friction cannot be stored as potential energy and later converted back to kinetic the way work against gravity can.

Gravity always pulls objects such as a desk, book or person down. Thus, when you jump, gravity causes you to land on the ground. Friction, however, doesn't pull objects down. ... Instead friction occurs when something like a machine or individual pulls a sliding object in the opposite direction of another object.


Friction and gravity exist in every aspect of a person’s life. For example, almost every movement you make, such as walking and running, involves friction. When you throw a ball up, gravity causes the ball to fall down. A person sliding a book across a table creates friction. Nevertheless, differences between gravity and friction also exist. Force affects gravity and friction in different ways.

A point source of light illuminates an aperture 1.70 m away. A 11.0 cm -wide bright patch of light appears on a screen 0.800 m behind the aperture. Part A How wide is the aperture

Answers

Answer:

7.48 cm

Explanation:

The diagrammatic representation of information is shown in the image below:

From the image, Δ X₁X₂ and Δ Y₁Y₂ are equivalent triangles.

where;

X₁X₂ = width of the aperture

Using equivalent triangles, It implies that:

[tex]\implies \dfrac{X_1X_2}{Y_1Y_2} = \dfrac{1.70}{1.70+0.800} \\ \\ \implies X_1X_2=\dfrac{1.70}{1.70+0.800}\times 11.0[/tex]

[tex]X_1X_2= \dfrac{1.70}{2.50}\times 11.0 cm[/tex]

X₁X₂ = 7.48 cm

The work function of titanium metal is 6.93 x 10-19 J. Calculate the kinetic energy of the ejected electrons if light of frequency 2.50 X 1015 s-1 is used to irradiate the metal.

Answers

Answer:

g m t o k liye cbbhhhf to be be free and ear is not a short time to be a short of a week and I am a short kat key and ear to be free and ear is not a short time and ear buds and duster for a short of a week of the action is not by the action is not a short time to make sure to be free and duster and not by the way to

Explanation:

ahhhhhhh to be be free and ear is nothing to be be free and ear is not a short time to be be free and ear is not by the class is not a a short time to be be free and

A particle with charge 3.01 µC on the negative x axis and a second particle with charge 6.02 µC on the positive x axis are each a distance 0.0429 m from the origin. Where should a third particle with charge 9.03 µC be placed so that the magnitude of the electric field at the origin is zero?

Answers

Answer:

The third particle should be at 0.0743 m from the origin on the negative x-axis.

Explanation:

Let's assume that the third charge is on the negative x-axis. So we have:

[tex]E_{1}+E_{3}-E_{2}=0[/tex]

We know that the electric field is:

[tex]E=k\frac{q}{r^{2}}[/tex]

Where:

k is the Coulomb constant q is the charger is the distance from the charge to the point

So, we have:

[tex]k\frac{q_{1}}{r_{1}^{2}}+k\frac{q_{3}}{r_{3}^{2}}-k\frac{q_{2}}{r_{2}^{2}}=0[/tex]

Let's solve it for r(3).

[tex]\frac{3.01}{0.0429^{2}}+\frac{9.03}{r_{3}^{2}}-\frac{6.02}{0.0429^{2}}=0[/tex]

[tex]r_{3}=0.0743\: [/tex]  

Therefore, the third particle should be at 0.0743 m from the origin on the negative x-axis.

I hope it helps you!

 

A horizontal force of 40N is needed to pull a 60kg box across the horizontal floor at which coefficient of friction between floor and box? Determine it to three significant figures even through that's quite unrealistic. How much work is done in overcoming friction between the object and floor if the box slides 8m along horizontally on the floor?

Answers

Answer:

Coefficient of friction is [tex]0.068[/tex].

Work done is [tex]320~J[/tex].

Explanation:

Given:

Mass of the box ([tex]m[/tex]): [tex]60[/tex] kg

Force needed ([tex]F[/tex]): [tex]40[/tex] N

The formula to calculate the coefficient of friction between the floor and the box is given by

[tex]F=\mu mg...................(1)[/tex]

Here, [tex]\mu[/tex] is the coefficient of friction and [tex]g[/tex] is the acceleration due to gravity.

Substitute [tex]40[/tex] N for [tex]F[/tex], [tex]60[/tex] kg for [tex]m[/tex] and [tex]9.80[/tex] m/s² for [tex]g[/tex] into equation (1) and solve to calculate the value of the coefficient of friction.

[tex]40 N=\mu\times60 kg\times9.80 m/s^{2} \\~~~~~\mu=\frac{40 N}{60 kg\times9.80 m/s^{2}}\\~~~~~~~=0.068[/tex]

The formula to calculate the work done in overcoming the friction is given by

[tex]W=Fd..........................(2)[/tex]

Here, [tex]W[/tex] is the work done and [tex]d[/tex] is the distance travelled.

Substitute  [tex]40[/tex] N for [tex]F[/tex] and [tex]8 m[/tex] for [tex]d[/tex] into equation (2) to calculate the work done.

[tex]W=40~N\times8~m\\~~~~= 320~J[/tex]

A 4.38 kg sphere makes a perfectly inelastic collision with a second sphere that is initially at rest. The composite system moves with a speed equal to one third the original speed of the 4.38 kg sphere. What is the mass of the second sphere?

Answers

Answer: The mass of the second sphere is 8.76 kg

Explanation:

The equation for a perfectly inelastic collision follows:

[tex]m_1u_1+m_2u_2=(m_1+m_2)v[/tex]

where,

[tex]m_1\text{ and }u_1[/tex] are the mass and initial velocity of first sphere

[tex]m_2\text{ and }u_2[/tex] are the mass and initial velocity of second sphere

v = final velocity of the system

We are given:

[tex]m_1=4.38kg\\u_2=0m/s\\v=\frac{u_1}{3}[/tex]

Rearranging the above equation, we get:

[tex]m_1u_1-m_1v=m_2v\\\\m_2=m_1\frac{u_1-v}{v}\\\\m_2=m_1(\frac{u_1}{v}-1)[/tex]

Plugging values in the above equation, we get:

[tex]m_2=4.38(\frac{3u_1}{u_1}-1)\\\\m_2=(4.38\times 2)=8.76kg[/tex]

Hence, the mass of the second sphere is 8.76 kg

How much heat is absorbed by 60g of copper when it is heated from 20°C to 80°C

Answers

Answer:

I HOPE THIS IS CORRECT

Explanation:

It is heated from 20°C to 80°C. We need to find the heat absorbed. It can be given by the formula as follows : So, 1386 J of heat is absorbed.

State the relation between acceleration and momentum​

Answers

Answer:

Acceleration is the rate of change in velocity. Momentum is the mass times the velocity. So if you multiply the mass times the acceleration, you get the of change of momentum.

40ml of Liquid A are poured into a beaker, and 40.0ml of Liquid B are poured into an identical beaker. Stirrers in each beaker are connected to motors, and the forces FA and FB needed to stir each liquid at a constant rate are measured.

a. FA will be greater than F B
b. FA will be less than FB
c. FA will be equal to FB
d. It's impossible to predict whether FA or FB will be greater without more information.

Answers

Answer:

d

Explanation:

there is not enough information about the liquid to know the force required for each. ie. stirring a cup of water is different than stirring a cup of pudding.

In which direction of the wave motion do longitude waves transfer energy ?

Answers

Answer:

Hello There!!

Explanation:

The answer is O parallel.

hope this helps,have a great day!!

~Pinky~

Question 24 of 33 Which of the following is an example of uniform circular motion? A. A car speeding up as it goes around a curve O B. A car slowing down as it goes around a curve 2 C. A car maintaining constant speed as it goes around a curve D. A car traveling along a straight road​

Answers

Answer:

Uniform Circular Motion is the Movement or Rotation of an Object along a circular Path at constant speed.

OPTION C IS YOUR ANSWER!.

How does the thickness of a planets atmosphere affect a planets average temperature

Answers

Answer:

The atmosphere of planets will block or enable heat coming from the sun

Charge of uniform density (80 nC/m3) is distributed throughout a hollow cylindrical region formed by two coaxial cylindrical surfaces of radii 1.0 mm and 3.0 mm. Determine the magnitude of the electric field at a point which is 2.0 mm from the symmetry axis.

Answers

Answer: Magnitude of the electric field at a point which is 2.0 mm from the symmetry axis is 18.08 N/C.

Explanation:

Given: Density = 80 [tex]nC/m^{3}[/tex] (1 n = [tex]10^{-9}[/tex] m) = [tex]80 \times 10^{-9} C/m^{2}[/tex]

[tex]r_{1}[/tex] = 1.0 mm (1 mm = 0.001 m) = 0.001 m

[tex]r_{2}[/tex] = 3.0 mm = 0.003 m

r = 2.0 mm = 0.002 m (from the symmetry axis)

The charge per unit length of the cylinder is calculated as follows.

[tex]\lambda = \rho \pi (r^{2}_{2} - r^{2}_{1})[/tex]

Substitute the values into above formula as follows.

[tex]\lambda = \rho \pi (r^{2}_{2} - r^{2}_{1})\\= 80 \times 10^{-9} \times 3.14 \times [(0.003)^{2} - (0.001)^{2}]\\= 2.01 \times 10^{-12} C/m[/tex]

Therefore, electric field at r = 0.002 m from the symmetry axis is calculated as follows.

[tex]E = \frac{\lambda}{2 \pi r \epsilon_{o}}[/tex]

Substitute the values into above formula as follows.

[tex]E = \frac{\lambda}{2 \pi r \epsilon_{o}}\\= \frac{2.01 \times 10^{-12} C/m}{2 \times 3.14 \times 0.002 m \times 8.85 \times 10^{-12}}\\= 18.08 N/C[/tex]

Thus, we can conclude that magnitude of the electric field at a point which is 2.0 mm from the symmetry axis is 18.08 N/C.

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