A mass weighing 4 pounds is attached to a spring whose constant is 2 lb/ft. The medium offers a damping force that numerically equal to the instantaneous velocity. The mass is initially released from a point 1 ft above the equilibrium position with a downward velocity of 14 feet/second. Determine the time at which the mass passes through the equilibrium position

Answer:

Option A

Explanation:

Ernest Rutherford concluded that the atom has a small, dense center which constitutes the mass of the whole atom. He called it a "Nucleus". He also said that most of the space in the atom is empty.

Answer:

because gravitational potential enegry is directly proportional to the height so more the height more the gravitational potential enegry. therefore gravitational potential enegry is greatest at high point than lower points.

Answer:

ΔU = 2.25 x 10⁸ J

t = 104.17 s

Explanation:

The change in internal energy of the engine can be given by the following formula:

ΔU = (Mass of Gasoline)(Energy Content of Gasoline)

ΔU = (1.5 x 10⁶ J/gallon)(15 gallon)

ΔU = 2.25 x 10⁸ J

Now, for the time of operation, we use the following formula of power.

P = W/t = ΔU/t

t = ΔU/P

where,

t = time of operation = ?

ΔU = Change in internal energy = 2.25 x 10⁸ J

P = Power of motor = 600 W

Therefore,

t = (2.25 x 10⁸ J)/(600 W)

t = (375000 s)(1 h/3600 s)

t = 104.17 s

Answer:

-   maximum displacement = 3.00nm

-   λ = 1.79m

-  f = 286.47 s^-1

Explanation:

You have the following equation for a sound wave:

[tex]s(x,t)=3.00nm\ cos(3.50m^{-1}x- 1,800s^{-1} t)[/tex]              (1)

The general form of the equation of a sound wave can be expressed as the following formula:

[tex]s(x,t)=Acos(kx-\omega t)[/tex]            (2)

A: amplitude of the wave = 3.00nm

k: wave number = 3.50m^-1

w: angular frequency = 1,800s^-1

- The maximum displacement of the wave is given by the amplitude of the wave, then you have:

maximum displacement = A = 3.00nm

- The wavelength is given by :

[tex]\lambda=\frac{2\pi}{k}=\frac{2\pi}{3.50m^{-1}}=1.79m[/tex]

The values for the wavelength is 1.79m

- The frequency is:

[tex]f=\frac{\omega}{2\pi}=\frac{1,800s^{-1}}{2\pi}=286.47s^{-1}[/tex]

The frequency is 286.47s-1

Answer:

1/4 of its original value

Explanation:

Newton's law of universal gravitation states that when two bodies of masses M₁ and M₂ interact, the force of attraction (F) between these bodies is directly proportional to the product of their masses and inversely proportional to the square of the distance (r) between these bodies. i.e

F ∝ [tex]\frac{M_1 M_2}{r^2}[/tex]       ------------(i)

From the equation above, it can be deduced that;

F ∝ [tex]\frac{1}{r^2}[/tex]

=> F = G [tex]\frac{1}{r^2}[/tex]       -----------(ii)

Where;

G = constant of proportionality called the gravitational constant

Equation (ii) can be re-written as

Fr² =  G

=> F₁r₁² = F₂r₂²              -----------(iii)

Where;

F₁ and r₁ are the initial values of the force and distance respectively

F₂ and r₂ are the final values of the force and distance respectively

From the question, if the distance doubles i.e;

r₂ = 2r₁,

Then the final value of the gravitational force F₂ is calculated as follows;

Substitute the value of r₂ = 2r₁ into equation (iii) as follows;

F₁r₁² = F₂(2r₁)²

F₁r₁² = 4F₂r₁²          [Divide through by r₁²]

F₁ = 4F₂                 [Make F₂ subject of the formula]

F₂ = F₁ / 4              [Re-write this]

F₂ = [tex]\frac{1}{4} F_1[/tex]

Therefore the gravitational force will be 1/4 of its original value when the distance between the bodies doubles.

Answer:

Q₂ = 5833.33 J

Explanation:

First we need to find the energy supplied to the heat engine. The formula for the efficiency of the heat engine is given as:

η = W/Q₁

where,

η = efficiency of engine = 30% = 0.3

W = Work done by engine = 2500 J

Q₁ = Heat supplied to the engine = ?

Therefore,

0.3 = 2500 J/Q₁

Q₁ = 2500 J/0.3

Q₁ = 8333.33 J

Now, we find the heat discharged to lower temperature reservoir by using the formula of work:

W = Q₁ - Q₂

Q₂ = Q₁ - W

where,

Q₂ = Heat discharged to the lower temperature reservoir = ?

Therefore,

Q₂ = 8333.33 J - 2500 J

Q₂ = 5833.33 J

Question:

A spaceship enters the solar system moving toward the Sun at a constant speed relative to the Sun. By its own clock, the time elapsed between the time it crosses the orbit of Jupiter and the time it crosses the orbit of Mars is 35.0 minutes

How fast is the spaceship traveling towards the Sun? The radius of the orbit of Jupiter is 43.2 light-minutes, and that of the orbit of Mars is 12.6 light-minutes.

Answer:

S = 5.508 × 10¹¹m

V = 2.62 × 10⁸ m/s

Explanation:

The radius of the orbit of Jupiter, Rj is 43.2 light-minutes

radius of the orbit of Mars, Rm is 12.6 light-minutes

Distance travelled S = (Rj - Rm)

= 43.2 - 12.6 = 30.6 light- minutes

= 30.6 × (3 ×10⁸m/s) × 60 s

= 5.508 × 10¹¹m

time = 35mins = (35 × 60 secs)

= 2100 secs

speed = distance/time

V = 5.508 × 10¹¹m / 2100 s

V = 2.62 × 10⁸ m/s

Answer:

[tex]v=21.36\,\,\frac{m}{s}\\[/tex]

[tex]m=1.2357\,\,kg[/tex]

Explanation:

Recall the formula for linear momentum (p):

[tex]p = m\,v[/tex]  which in our case equals 26.4 kg m/s

and notice that the kinetic energy can be written in terms of the linear momentum (p) as shown below:

[tex]K=\frac{1}{2} m\,v^2=\frac{1}{2} \frac{m^2\,v^2}{m} =\frac{1}{2}\frac{(m\,v)^2}{m} =\frac{p^2}{2\,m}[/tex]

Then, we can solve for the mass (m) given the information we have on the kinetic energy and momentum of the particle:

[tex]K=\frac{p^2}{2\,m}\\282=\frac{26.4^2}{2\,m}\\m=\frac{26.4^2}{2\,(282)}\,kg\\m=1.2357\,\,kg[/tex]

Now by knowing the particle's mass, we use the momentum formula to find its speed:

[tex]p=m\,v\\26.4=1.2357\,v\\v=\frac{26.4}{1.2357} \,\frac{m}{s} \\v=21.36\,\,\frac{m}{s}[/tex]

Answer:

The angular speed of the earth rotation is equal. Therefore

Our angular speed due to Earth’s rotation is same at every point on the earth irrespective of the elevation. So your angular speed due to earth’s rotation on the top floor of the building will be same as it is on the ground floor.

Explanation:

Answer:

The length = 27.52m

Explanation:

v=f x wavelength

Answer: The magnetic field points to the west.

Explanation:

If we take the plane as:

North = positive y-axis

East = positive x-axis.

We have that the electron is moving south, so the velocity of the electron can be written in vector form as:

V = (0, -v, 0)

Now, when the electron interacts with the magnetic field, the electron moves upwards.

We know that the interaction between an electron and a magnetic field is:

F = q*VxB

So we have that this force acts on the z-direction.

Now, to solve this we can use the righ hand rule.

First, we point wit our hand to the direction of the velocity (negative y-axis) now, we want that our thumb points up (the direction of the force) so the side where our palm faces is the direction of the field B.

But, remember that an electron has a negative charge, so the actual equation is:

F = -q*VxB

So the magnetic field actually points in the opposite direction of our palm, to the west.

Now, we can also solve it mathematically as:

F = (0, 0, f) = -q*(0, -v,0)x(a, b, c)

where B = (a, b, c) is the vector of the magnetic field.

     (0, 0, f) = -q*(-v*b -0, -0 + 0, 0 -(- a*v)) = -q*(-v*b, 0, a*v)

then we have that b must be equal to zero, and that:

f = -q*a*v

and f is positive, then we have:

a = -(f/q*v)

then the vector of the magnetic field is:

B = (-(f/q*v), 0, 0)

so it points in the negative x-axis, that is the West, as we found earlier.

Answer:

[tex]F(t)=m\,\,a(t)=6\,m\,t\,\hat i+14\,m\,\hat j+6\,m\,t\,\hat k\\F(t)=\,(6\,m\,t,14\,m,6\,m\,t)[/tex]

Explanation:

Recall that force is defined as mass times acceleration, and acceleration is the second derivative with respect to time of the position. Since the position comes in terms of time, and with separate functions for each component in the three dimensional space, we first calculate the velocity (with the first derivative, and then the acceleration as the second derivative:

[tex]r(t)=t^3\,\hat i+7\,t^2\,\hat j+t^3\,\hat k\\v(t)=3\,t^2\,\hat i+14\,t\,\hat j+3\,t^2\,\hat k\\a(t)=6\,t\,\hat i+14\,\hat j+6\,t\,\hat k[/tex]

Therefore, the force will be given by the product of this acceleration times the mass "m":

[tex]F(t)=m\,\,a(t)=6\,m\,t\,\hat i+14\,m\,\hat j+6\,m\,t\,\hat k[/tex]

Answer:

a) 2.933 m

b) 4.534 m

Explanation:

We're given the equation

v(t) = -0.4t² + 2t

If we're to find the distance, then we'd have to integrate the velocity, since integration of velocity gives distance, just as differentiation of distance gives velocity.

See attachment for the calculations

The conclusion of the attachment will be

7.467 - 2.933 and that is 4.534 m

Thus, The distance it travels in the second 2 sec is 4.534 m

Answer:

initial speed (u) = 0.8 m/s

acceleration (a) = 0.2 m/s/s

time (t) = 1.3 min    OR        1.3*60 seconds

            = 78 seconds  

we will use the second equation of motion to find the distance

distance (s) = ut + 1/2 a(t^2)

s = 0.8 * 78 + 1/2 * 0.2 * (6084)

s = 62.4 + 608.4

s = 670.8 m

Answer:

100 on average

Explanation:

The human body is a physical substance from where a human can breathe, drink, eat, walk, etc, and consists of various cells. A human being cannot live with their functions and when functions stop working that means a human being is dead.

Therefore, in the human body, there is also electricity that contains 100 watts on average.

So, According to the given situation, the correct answer is 100 on average.

Answer:

Explanation:

ω = angular velocity = 2π n = 2π x 72 / 60

= 7.536 rad /s

mass of head = 90 x .07 = 6.3 kg

moment of inertia of head = 2 /5 m R²

= .4 x 6.3 x .08²

= .016128 kg m²

moment of inertia of trunk + legs

= 1/2 m R²

= .5 x .8 x 90 x .12²

= .5184 kg m²

moment of inertia of arms

= 1/3 m L²

= 1 / 3 x .13 x 90 x .60²

= 1.404 kg m²

Total moment of inertia

I = 1.938 kg m²

kinetic energy = 1/ 2 I ω ²

where I is moment of inertia and ω is angular velocity

= .5 x 1.9338 x  7.536²

=55 J approx .

The definition of kinetic energy and moment of inertia allows finding the result for the kinetic energy of the dancer with arms extended is:

Given parameters

       *    Head 7%

       *    Arms 13%

       *   Trunk and legs 80%

To find.

The kinetic energy is the energy due to the movement, in this case the movement is rotational, therefore the expression is:

             KE = ½ I w²

The angular velocity is related to the frequency.

            w = 2π f

            w = 2π 1.2

            w = 7.540 s

The moment of inertia is a scalar, therefore it is a quantity that can be added, the total moment of inertia of the dancer is the sum of the moments of inertia of each part with respect to the axis of rotation of the person.

          [tex]I_{toal}= I_{head}+ I_{trunk}+I_{arms}[/tex]

The moments of inertia with respect to the centers of mass are tabulated.

Sphere        I = 2/5 mr²

Cylinder      I = ½ m r²

Rod             I = ⅓ m r²

The axis of rotation of the head and the trunk are in the axis of rotation of the person, therefore their moment of inertia is those corresponding to the center of mass.

At the end of the arms it is at a distance of D = [tex]\frac{r_2}{2}[/tex]  from the axis of rotation of the dancer, therefore to find the moment of inertia we must use the theorem of parallel axes, see attached.                  

              [tex]I_{arms} = I_{cm} + M D^2[/tex]

             [tex]I_{arms}[/tex]  = ⅓ m L² + m D²

            [tex]I_{arms} = m_{arms} ( \frac{L^2}{3} + D^2)[/tex]            

The masses of each part of the body are:

            [tex]m_{head}[/tex] = m 0.07

            [tex]m_{trunk}[/tex] = m 0.80  

            [tex]m_{arms}[/tex]  = m 0.13

Let's find the total  moment of inertia.  

            [tex]I_{total} = \frac{2}{5} \ 0.07m \ r_1^2 + 0.13m\ ( \frac{L^2}{3} + D^2) + \frac{1}{2} \ 0.80m \ r_2^2[/tex]  

            [tex]I_{total} = m ( 0.028 \ r_1^2 + 0.13 (\frac{L^2}{3} + D^2) + 0.40 \ r_2^2}[/tex]  

Let's calculate.  

           [tex]I_{total} = 90\ ( 0.028 \ 0.08^2 + 0.13\ ( \frac{0.6^2}{3} + 0.06^2) + 0.40 \ 0.12^2 )[/tex]

           [tex]I_{total}= 90 \ 0.0220 \\ \\I_{total} = 1.9806 \ Kg m^2[/tex]

we substitute in the kinetic energy

           KE = ½ 1.9806  7,540²

           KE = 56.3  J

In conclusion using the definition of kinetic energy and moment of inertia we can find the result for the kinetic energy of the dancer with the extended arms is:

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Answer:

k = 0.5 MN/m

Explanation:

Mass of the railcar, m = 5000 kg

Speed of the rail car, v = 1 m/s

The Kinetic energy(KE) of the railcar is given by the equation:

KE = 0.5 mv²

KE = 0.5 * 5000 * 1²

KE = 2500 J

The spring's compression, x = 0.1 m

The potential energy(PE) stored in the spring is given by the equation:

PE = 0.5kx²

PE = 0.5 * k * 0.1²

PE = 0.005k

According to the principle of energy conservation, Kinetic energy of the railcar equals the potential energy stored in the spring

KE = PE

2500 = 0.005k

k = 2500/0.005

k = 500000 N/m

k = 0.5 MN/m

Answer:

(a) max. height = 3.641 m

(b) flight time = 1.723 s

(c) horizontal range = 31.235 m

(d) impact velocity = 20 m/s

Above values have been given to third decimal.  Adjust significant figures to suit accuracy required.

Explanation:

This problem requires the use of kinematics equations

v1^2-v0^2=2aS .............(1)

v1.t + at^2/2 = S ............(2)

where

v0=initial velocity

v1=final velocity

a=acceleration

S=distance travelled

SI units and degrees will be used throughout

Let

theta = angle of elevation = 25 degrees above horizontal

v=initial velocity at 25 degrees elevation in m/s

a = g = -9.81 = acceleration due to gravity (downwards)

(a) Maximum height

Consider vertical direction,

v0 = v sin(theta) = 8.452 m/s

To find maximum height, we find the distance travelled when vertical velocity = 0, i.e. v1=0,

solve for S in equation (1)

v1^2 - v0^2 = 2aS

S = (v1^2-v0^2)/2g = (0-8.452^2)/(2*(-9.81)) = 3.641 m/s

(b) total flight time

We solve for the time t when the vertical height of the object is AGAIN = 0.

Using equation (2) for vertical direction,

v0*t + at^2/2 = S    substitute values

8.452*t + (-9.81)t^2 = 3.641

Solve for t in the above quadratic equation to get t=0, or t=1.723 s.

So time for the flight = 1.723 s

(c) Horiontal range

We know the horizontal velocity is constant (neglect air resistance) at

vh = v*cos(theta) = 25*cos(25) = 18.126 m/s

Time of flight = 1.723 s

Horizontal range = 18.126 m/s * 1.723 s = 31.235 m

(d) Magnitude of object on hitting ground, Vfinal

By symmetry of the trajectory, Vfinal = v = 20, or

Vfinal = sqrt(v0^2+vh^2) = sqrt(8.452^2+18.126^2) = 20 m/s

Answer:

a

  [tex]B = 0.0533 \ T[/tex]

b

  [tex]B = 0.04 \ T[/tex]

Explanation:

From the question we are told that

   The inner radius is [tex]r = 1.2 \ cm = 0.012 \ m[/tex]

   The  outer radius is  [tex]r_o = 2.4 \ cm = \frac{2.4}{100} = 0.024 \ m[/tex]

    The nu umber of turns is  [tex]N = 960[/tex]

    The current it is carrying is  [tex]I = 2. 5 A[/tex]

Generally the magnetic field is mathematically represented as

      [tex]B = \frac{\mu_o * N* I }{2 * \pi * r }[/tex]

Where  [tex]\mu_o[/tex] is the permeability of free space with a constant value    

            [tex]\mu = 4\pi * 10^{-7} N/A^2[/tex]

And the given distance where the magnetic field is felt is  r =  0.9 cm  =  0.009 m

Now  substituting values

     [tex]B = \frac{ 4\pi * 10^{-7} * 960* 2.5 }{2 * 3.142 * 0.009 }[/tex]

    [tex]B = 0.0533 \ T[/tex]

    Fro the second question the distance of the position considered from the center is  r =  1.2 cm  =  0.012 m

So the  magnetic field is  

        [tex]B = \frac{ 4\pi * 10^{-7} * 960* 2.5 }{2 * 3.142 * 0.012 }[/tex]

        [tex]B = 0.04 \ T[/tex]

The magnetic field at a distance of 0.9 cm from the center of the toroid is 0.053 T.

The magnetic field at a distance of 1.2 cm from the center of the toroid is 0.04 T.

The given parameters;

The magnetic field at a distance of 0.9 cm from the center of the toroid is calculated as follows;

[tex]B = \frac{\mu_o NI}{2\pi r} \\\\B = \frac{(4\pi \times 10^{-7})\times (960) \times (2.5)}{2\pi \times 0.009} \\\\B = 0.053 \ T[/tex]

The magnetic field at a distance of 1.2 cm from the center of the toroid is calculated as follows;

[tex]B = \frac{\mu_o NI}{2\pi r} \\\\B = \frac{(4\pi \times 10^{-7})\times (960) \times (2.5)}{2\pi \times 0.012} \\\\B = 0.04 \ T[/tex]

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Answer:

7.2 N

Explanation:

length of wire L  = 240 m

current I = 500 A

field strength B = 3 x 10^-5 T

magnetic force on a current carrying conductor F is given as

F = BILsin∅

The wires are perpendicular with field therefore sin∅ = sin 90° = 1

therefore,

F = BIL = 3 x 10^-5 X 500 X 240 = 3.6 N

If the wire exists between this two transmission lines, then total magnetic force on the wire = 2 x 3.6 = 7.2 N

Answer:

Explanation:

v= u + at

v is final velocity , u is initial velocity . a is acceleration and t is time

Initial velocity u = 0 . Putting the given values in the equation

v = 0 + g sin 18 x 3.5

= 10.6 m /s

For a skateboarder who starts from the rest, the speed when he reaches the bottom of the ramp will be 10.6 m/s.

The term "velocity" refers to a vector measurement of the rate and direction of motion. Velocity is the rate of movement in a single direction, to put it simply. Velocity can be used to determine how fast a rocket is heading into space and how fast a car is moving north on a congested motorway.

There are several types of velocity :

The pace at which a person's velocity changes is known as acceleration. This implies that an object is accelerating if its velocity is rising or falling. An object that is accelerating won't have a steady change in location every second like an item moving at a constant speed does.

According to the question, the given values are :

Time, t = 3.50 sec

Initial Velocity, u = 0 m/s

Use equation of motion :

v = u+at

v = 0+ g sin 18 × 3.5

v = 10.6 m/s.

So, the final velocity will be 10.6 m/s.

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#SPJ2

Explanation:

dark matter is a form of matter thought to account for approximately 85% of the matter in the universe and about a quarter of its total mass–energy density or about 2.241×10⁻²⁷ kg/m³. Its presence is implied in a variety of astrophysical observations, including gravitational effects that cannot be explained by accepted theories of gravity unless more matter is present than can be seen. For this reason, most experts think that dark matter is abundant in the universe and that it has had a strong influence on its structure and evolution. Dark matter is called dark because it does not appear to interact with the electromagnetic field, which means it doesn't absorb, reflect or emit electromagnetic radiation, and is therefore difficult to detect.

Answer:

Objects act differently in a gravity field than in an accelerating reference frame.

Explanation:

The main thrust of the theory general relativity as proposed by Albert Einstein boarders on space and time as the two fundamental aspects of spacetime. Spacetime is curved in the presence of gravity, matter, energy, and momentum. The theory of general relativity explains gravity based on the way space can 'curve', that is, it seeks to relate gravitational force to the changing geometry of space-time.

The Einstein general theory of relativity has replaced Newton's ideas proposed in earlier centuries as a means of predicting gravitational interactions. This concept is quite helpful but cannot be fitted into the context of quantum mechanics due to obvious incompatibilities.

Answer:

A - The orbital path of mercury around the sun has changed.

Explanation:

got right on edg.

Answer:

Pls see attached file

Explanation:

Answer:

The pressure produced on the air in the pump is 37.209 pounds per square inch.

Explanation:

By definition, the pressure is the force exerted on the piston divided by its area. Given that, force is distributed uniformly on the piston area, the formula to determine the pressure is:

[tex]p = \frac{F}{A}[/tex]

Where:

[tex]p[/tex] - Pressure, measured in pounds per square inch.

[tex]F[/tex] - Force exerted on the piston, measured in pounds.

[tex]A[/tex] - Piston area, measured in square inches.

If [tex]F = 16\,lb[/tex] and [tex]A = 0.43\,in^{2}[/tex], the pressure produced on the air in the pump is:

[tex]p = \frac{16\,lb}{0.43\,in^{2}}[/tex]

[tex]p = 37.209\,psi[/tex]

The pressure produced on the air in the pump is 37.209 pounds per square inch.

Answer:

B. A force that is equal in amount but oppositely directed to the force the lighter child is exerting.

Explanation:

If they are sitting at the same distance away from the pivot yet the seesaw is balanced, the only conclusion is the heavier child is exerting a lower force. This causes the pivot exertion and balances to be equal. The equilibrium of the pivot-seesaw is not affected by the weight because of force exertion.

Answer:

v = 31.84 cm/s or 0.318 m/s

the speed of the water leaving the end of the hose is 31.84 cm/s or 0.318 m/s

Explanation:

Given;

Diameter of hose d = 2.76 cm

Volume filled V = 20.0 L = 20,000 cm^3

Time t = 1.45 min = 105 seconds

The volumetric flow rate of water is;

F = V/t = 20,000cm^3 ÷ 105 seconds

F = 190.48 cm^3/s

The volumetric flow rate is equal the cross sectional area of pipe multiply by the speed of flow.

F = Av

v = F/A

Area A = πd^2/4

Speed v = F/(πd^2/4)

v = 4F/πd^2 ......1

Substituting the given values;

v = (4×190.48)/(π×2.76^2)

v = 31.83767439628 cm/s

v = 31.84 cm/s or 0.318 m/s

the speed of the water leaving the end of the hose is 31.84 cm/s or 0.318 m/s

Answer:

the energy of the photons is greater than the work function of the zinc oxide.

                     h f> = Ф

Explanation:

In this experiment on the photoelectric effect, it is explained by the Einstein relation that considers the light beam formed by discrete energy packages.

                    K_max = h f - Ф

in the exercise phase, they indicate that different wavelengths can inject electrons, so the energy of the photons is greater than the work function of the zinc oxide.

                     h f > = Ф

Answer:

1.2 s

Explanation:

Given:

v₀ = 8.0 m/s

v = -4.0 m/s

a = -10 m/s²

Find: t

v = at + v₀

(-4.0 m/s) = (-10 m/s²) t + (8.0 m/s)

t = 1.2 s

Answer:

V = 3.6 volts

Explanation:

From Ohm's Law, we know that:

V = IR

but,

R = ρL/A

Therefore,

V = IρL/A

where,

V = Potential Difference = ?

I = Current = 4 A

ρ = resistivity of copper = 1.68 x 10⁻⁸ Ω.m

L = Length = 70 m

A = Cross-sectional Area = πd²/4 = π(1.29 x 10⁻³ m)²/4     [16 gauge wire has a diameter of 1.29 mm]

A = 1.31 x 10⁻⁶ m²

V = (4 A)(1.68 x 10⁻⁸ Ω.m)(70 m)/(1.31 x 10⁻⁶ m²)

V = 3.6 volts

The potential difference across the given length of copper wire is obtained to be 3.6 V.

The resistance of the wire depends on the length, area of cross-section of the wire and resistivity of the material.

Given the length of the wire, [tex]L = 70\,m[/tex].

The diameter of a 16 gauge copper wire is given by, [tex]d = 1.29\times 10^{-3}\,m[/tex].

Therefore, the radius of the cross-section is;

[tex]r=\frac{d}{2} = \frac{1.29\times 10^{-3}\,m}{2} =6.45\times 10^{-4}\,m[/tex]

So, the resistance of the given length of wire can be written as,

[tex]R= \rho\, \frac{L}{A} =(1.68 \times 10^{-8} \, \Omega .m)\times \frac{70\,m}{\pi \times (6.45\times 10^{-4}m)^2} = 0.9\, \Omega[/tex]

According to Ohm's Law, we can write;

[tex]V=IR[/tex]

Substituting the known values, we get the voltage drop is;

[tex]V = 4A \times 0.9\Omega = 3.6\,V[/tex]

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