You lower a 2.8 kg solid gold statue into a container of water and measure the volume of displaced water. What volume will verify that it is pure gold if the density of gold is 19.3 g/cm3

Answer:

The time required to send the data from Earth to Moon will be 1.28s while for a two way communication, to send it back to the earth, it will take double time i.e. RTT = 2.56s

Explanation:

Distance between Earth and Moon = 385,000 km = 3.85 x 10⁸m

Speed of data travel = speed of light ≈ 3 x 10⁸m/s

As, v=d/t

t=d/v

[tex]t=\frac{3.85*10^{8} }{3*10^{8}}[/tex]

t=1.28s

RTT = Double of single way time taken = 2x1.28

RTT=2.56s

Answer: The boiling point of  solution is [tex]112.16^0C[/tex]

Explanation:

Elevation in boiling point:

[tex]T_b-T^o_b=i\times k_b\times \frac{w_2\times 1000}{M_2\times w_1}[/tex]

where,

[tex]T_b[/tex] = boiling point of solution = ?

[tex]T^o_b[/tex] = boiling point of toluene = [tex]110.63^oC[/tex]

[tex]k_b[/tex] = boiling point constant of toluene =[tex]3.40^oC/m[/tex]

m = molality

i = Van't Hoff factor = 1 (for non-electrolyte)

[tex]w_2[/tex] = mass of solute [tex](I_2)[/tex] = 7.94 g

[tex]w_1[/tex] = mass of solvent (toluene) = 69.2 g

[tex]M_2[/tex] = molar mass of solute [tex](I_2)[/tex]= 254g/mol

Now put all the given values in the above formula, we get:

[tex](T_b-110.63)^oC=1\times (3.40^oC/m)\times \frac{(7.94g)\times 1000}{254\times (69.2g)}[/tex]

[tex]T_b=112.16^0C[/tex]

Therefore, the boiling point (in °C) of a solution is 112.16

Answer:

constant deceleration required is 9 m/s²

Explanation:

Data provided in the question:

Initial Speed of the driver = 41 mph = 60 ft/s

Stopping distance = 200 ft

Now,

Since the car stops after 200 ft therefore final speed, u = 0 ft/s

from the Newton's equation of motion

we have  

v² - u² = 2as

where,  

v is the final speed  

u is the initial speed  

a is the acceleration

s is the distance

thus,

0² - 60² = 2a(200)

or

-3600 = 400a

or

a = - 9 m/s²

here, negative sign means deceleration

Hence,

The constant deceleration required is 9 m/s²

Answer:

work done on compressing spring will be 135 j

Explanation:

We have given spring constant [tex]K=3kN/cm=3\times \frac{1000N}{10^{-2}m}=3\times 10^5N/m[/tex] ( As 1 kN = 1000N and 1 m = 100 cm )

Spring is compressed by 3 cm

As 1 m = 100 cm

So [tex]3cm=3\times 10^{-2}m[/tex]

Work done on compressing spring is given by [tex]W=\frac{1}{2}kx^2[/tex]

So [tex]W=\frac{1}{2}\times 3\times 10^{5}\times (3\times 10^{-2})^2=13.5\times 10=135J[/tex]

So work done on compressing spring will be 135 j

The work a spring can produce after being compressed from its unloaded length can be calculated using the formula for potential energy stored in a spring. In this case, given the spring constant of 4 kN/cm and a compression of 3 cm, the spring can produce 18 kJ of work.

The work done by a spring, in this case, can be calculated using the formula for the potential energy stored in a compressed or stretched spring, which is given by PE = 1/2 * k * x². Here, k is the spring constant and x is the displacement or compression of the spring from its original length.

Given that the spring constant k = 4 kN/cm = 4000 N/cm and displacement x = 3 cm, we can substitute these values into the formula: PE = 0.5 * 4000 * (3)² = 18,000 N.cm = 18 kJ. The spring can therefore produce 18 kJ of work when it has been compressed 3 cm from its unloaded length.

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Answer:

E

Explanation:

Using Coulomb's law equation

Force of the charge = k qQ /d²

and E = F/ q

substitute for F

E = ( K Qq/ d² ) / q

q cancel q

E = KQ / d²

so twice  the distance of the from the point charge will lead to the E ( electric field ) decrease by a 4 = E/4. E is inversely proportional to d²

Answer:

d. 0.5 m/s along -x direction

Explanation:

Wave: A wave is a disturbance, that travels through a medium and transfers energy from one point to another, without causing any permanent displacement of the medium itself.

The general equation of a traveling wave can be expressed as

y = Acos(2πft-2πx/λ).................................. Equation 1

Where A = amplitude of the wave, f = frequency of the wave, λ = wavelength of the wave, x = linear distance, t = time, π = pie.

From the question,

the equation of the moving wave is

y = 0.12cos(4x+2t) ................................... equation 2

Comparing equation 1 and 2

-2πx/λ = 4x

λ  = -2π/4

λ  = -2(3.14)/4

λ  = -1.57 m.

Also,

2πft = 2t

f = 2t/2πft

f = 1/π

f = 1/3.14

f = 0.3185 Hz.

Recall that

v = λf.......................... Equation 3

Substitute the value of f and λ  into equation 3

v = -1.57(0.3185)

v = - 0.5 m/s.

Note: v is negative because - x direction

Hence the right option is d. 0.5 m/s along -x direction

Answer:

A technique in MRA where signal intensity depends on the direction of flow and thus requires gradient application in all three planes for proper signal acquisition is: Phase-contrast (PC-MRA)

Phase-contrast magnetic resonance imaging MRA  is a technique used in moving blood flow, where its speed is encoded in the magnetic resonance signal's phase after the applying bipolar gradient along any axis and the measurement point.

Explanation:

In this technique the bipolar gradient is manipulated varying its magnetic fields to be preset to a maximum expected flow velocity and it´s applied along any axis or axes depending on the direction along which flow is to be measured to get a reversed image of the bipolar gradient and the difference of the two images is calculated. The unaffected phase accrued during the application of the gradient, is 0 for stationary spins.  Since phase-contrast can only acquire flow in one direction at a time, 3 separate image acquisitions in all three directions must be computed to give a complete quantitative measurements of blood flow.  

Although this technique is slow,its strength lays in the possibility of calculating spins moving with a constant velocity of the applied bipolar gradient.  The accrued phase is proportional to both and the 1st moment of the bipolar gradient, thus providing a means to estimate gamma is the Larmor frequency of the imaged spins on moving tissues such as blood, which acquire a different phase since it moves constantly through the gradient, thus also giving its speed of the flow.

Answer:

1/2

Explanation:

This will lead us to simultaneous equation since there are two person involved doing the same job each day.

For Ted;

Since Ted can wax 8 cars or wash 10 cars in a day. Mathematically, we have

8x + 10w = 1... (1)

Where x is for waxing cars, w is for washing cars

Similarly for Tom,

Tom can wax 3 cars or wash 5 cars in a day as well, this gives us;

3x + 5w = 1... (2)

Equating 1 and 2, we have;

8x + 10w = 1... (1)

3x + 5w = 1... (2)

Using elimination method, we will multiply eqn 1 by 3 and eqn 2 by 8 to have;

24x + 30w = 3

24x + 40w = 8

Subtracting eqn 4 from 5 we have;

30w - 40w = 3 - 8

-10w = -5

w = 5/10

w = 1/2

Therefore each man's opportunity cost of washing a car is 1/2

Answer:

Explanation:

Archimedes principle states that the upward buoyant foce exrted on a body is equal to th wight o the liquid displaced.

Now, the buoyant force on the boat is given by:

[tex](m+m_b)g=V\rho g[/tex]

[tex]V[/tex] is the volum [tex]\rho[/tex] is the density [tex]m_b[/tex] is the mass of the boat and [tex]m[/tex] is the mass added to the boat.

[tex](m+m_b)g=(Sd)\rho[/tex]

[tex]S[/tex] is the surface area and [tex]d[/tex] is the depth.

[tex]m=Sd\rho - m_b...(1)[/tex]

The equation for thebest fit linis,

[tex]d=(0.374m/kg)m+0.11m[/tex]

Re-arrangethis equati for [tex]m[/tex]

[tex]m=\frac{d}{(0.374m/kg)}-\frac{0.11m}{0.374m/kg}...(2)[/tex]

From equations(1) and (2),

[tex]Sd\rho=\frac{d}{0.374m/kg}[/tex]

the density is,

[tex]\rho=\frac{1}{S(0.0374m/kg)}=\frac{1}{(25cm^2)(\frac{1m^2}{10^4cm^2})(0.374m/kg)}=1.069\times 10^3 kg/m^3[/tex]

Therefore, the density of the liquid is

[tex]\rho=1.07\times 10^3 kg/m^3[/tex]

To determine the density of the liquid, one needs to get the slope of the graph from the data given. Using this slope in the formula ρ = k/g, where 'g' is the gravity, gives the density of the liquid.

Let's first understand this concept with the help of Archimedes' Principle, which states that, the upward buoyant force exerted on a body immersed in a fluid, whether fully or partially submerged, is equal to the weight of the fluid that the body displaces. To determine the density of the liquid, we need the slope of the line from the graph.

Let's assume that the slope of the line is 'k' (which you will obtain from your graph). The slope of the line of best fit in the graph of m versus d will be m/d = ρVg/(Ag), where 'm' is the mass added, 'd' is the depth, 'ρ' is the density of the fluid, 'V' is the volume of the fluid displaced, 'A' is the cross-sectional area of the boat, and 'g' is the acceleration due to gravity.

We can write Volume 'V' = Ad, so the equation simplifies to k = ρg and hence the density ρ = k/g, where 'k' is the obtained slope and 'g' (assuming you are on the earth) is 9.81 m/s². Therefore, once you obtain the value of 'k', you can easily calculate the density of the liquid.

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Answer: two consecutive crests.

Explanation: A wave length is the distance from crest to crest or from a trough to another. The crest represent the highest maximum point and the trough represent the lowest point on the wave.

All waves undergoes some properties such as refraction, distraction,reflection and interference.

Answer:

option (A)

Explanation:

Torque is defined as the

Torque = Force x distance x SinФ

Where, Ф is the angle between force vector and the displacement

In case I:

torque = F x r x Sin 90 = F x r

In case II:

Torque = F x r x Sin 60 = 0.866 F r

So, the torque is more in first case.

Thus, option (a) is correct.

Final answer:

The best inference is that Mr. F's body is raising blood pressure by increasing blood volume with all the fluid intake and increasing heart rate. Something may be wrong with his blood volume.

Explanation:

The best inference from the given scenario is option D: His body is raising blood pressure by both increasing blood volume with all this fluid intake and increasing heart rate. Something may be wrong with his blood volume.

When Mr. F takes in a lot of fluid but puts out very little, it suggests that his body is retaining fluid. The increased fluid intake is causing an increase in blood volume, which in turn raises blood pressure. The slight increase in heart rate is also a compensatory mechanism to maintain adequate blood flow.

A fluid twice as dense as mercury would rise to approximately half the height of mercury in a barometer under normal sea-level conditions. This is due to the relation between hydrostatic pressure, density, and height of the fluid column.

Under normal sea-level conditions, atmospheric pressure supports a column of mercury about 760 mm high. This occurs due to the hydrostatic pressure, which is essentially the pressure exerted by a fluid due to gravity. In the case of a liquid twice as dense as mercury, the height of the liquid column would be half that of mercury under the same conditions. This is because the hydrostatic pressure is directly proportional to the density and height of the fluid column, which implies that for a given pressure, if we increase the density, the height decreases correspondingly. So, a liquid twice as dense as mercury would rise to approximately 380 mm in the barometer.

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A) The change in internal chemical energy is [tex]1.15\cdot 10^7 J[/tex]

B) The time needed is 1 minute

Explanation:

First of all, we start by calculating the power output of you and the bike, given by:

[tex]P=Fv[/tex]

where

F = 80 N is the force that must be applied in order to overcome friction and travel at constant speed

v = 8.0 m/s is the velocity

Substituting,

[tex]P=(80)(8.0)=640 W[/tex]

The energy output is related to the power by the equation

[tex]P=\frac{E}{t}[/tex]

where:

P = 640 W is the power output

E is the energy output

[tex]t = 30 min \cdot 60 = 1800 s[/tex] is the time elapsed

Solving for E,

[tex]E=Pt=(640)(1800)=1.15\cdot 10^6 J[/tex]

Since the body is 10% efficient at converting chemical energy into mechanical work (which is the output energy), this means that the change in internal chemical energy is given by

[tex]\Delta E = \frac{E}{0.10}=\frac{1.15\cdot 10^6}{0.10}=1.15\cdot 10^7 J[/tex]

B)

From the previous part, we found that in a time of

t = 30 min

the amount of internal chemical energy converted is

[tex]E=1.15\cdot 10^7 J[/tex]

Here we want to find the time t' needed to convert an amount of chemical energy of

[tex]E'=3.8\cdot 10^5 J[/tex]

So we can setup the following proportion:

[tex]\frac{t}{E}=\frac{t'}{E'}[/tex]

And solving for t',

[tex]t'=\frac{E't}{E}=\frac{(3.8\cdot 10^5)(30)}{1.15\cdot 10^7}=1 min[/tex]

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The magnitude of the electric field at the location of the 2.40 μC charge is 1250 N/C.

The magnitude of the electric field at the location of the 2.40 μC charge can be calculated using the equation:

E = F / q

Where E is the electric field, F is the force, and q is the charge.

In this case, the force is given as 3.00 mN, which is equal to 0.003 N, and the charge is 2.40 μC, which is equal to 2.40 x 10^-6 C. Plugging these values into the equation, we get:

E = (0.003 N) / (2.40 x 10^-6 C) = 1250 N/C

Therefore, the magnitude of the electric field at the location of the charge is 1250 N/C.

Answer:

The net force acting on the otter along the incline is 13.96 N.

Explanation:

It is given that,

Mass of the otter, m = 2 kg

Distance covered by otter, d = 85 cm = 0.85 m

It takes 0.5 seconds.

We need to find the net force acts on the otter along the incline. If a is the acceleration of the otter. It can be calculated using second equation of motion as :

[tex]d=ut+\dfrac{1}{2}at^2[/tex]

Here, u = 0 (at rest)

[tex]d=\dfrac{1}{2}at^2[/tex]

[tex]a=\dfrac{2d}{t^2}[/tex]

[tex]a=\dfrac{2\times 0.85}{0.5^2}[/tex]

[tex]a=6.8\ m/s^2[/tex]

The net force acting on the otter along the incline is given by :

F = ma

[tex]F=2\ kg\times 6.8\ m/s^2[/tex]

F = 13.6 N

So, the net force acting on the otter along the incline is 13.96 N. Hence, this is the required solution.

Answer:

[tex]F=13.6\rm N[/tex] Force acts on the otter along the incline

Explanation:

Given information:

Incline length [tex]s=\rm 85cm=0.85m[/tex]

Time [tex]t=0.5\rm sec[/tex]

Mass of otter [tex]m=2\rm kg[/tex],

Initial velocity [tex]u=0[/tex] as otter is in rest

Muddy incline so we can assume surface as friction less

By use equation of motion,

[tex]s=ut+\frac{1}{2} a t^2[/tex]

[tex]s=ut+\frac{1}{2} a t^2=0\times t+\frac{1}{2}\times a\times t^2[/tex]

[tex]0.85=0+\frac{1}{2} a (0.5)^2\\\\a=\frac{2\times0.85}{0.5^2}=6.8\rm m/s^2[/tex]

The net force act on the otter is

[tex]F=ma[/tex]

[tex]F=2\rm kg\times6.8\rm m/s^2[/tex]

[tex]F=13.6\rm N[/tex]

Hence [tex]F=13.6\rm N[/tex] force acts on the otter along the incline

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Answer:

- the Big Bang=the universe begins to expand.

-elements such as carbon and oxygen first exist.

-nuclear fusion begins in the Sun.

-earliest life on Earth.

-dinosaurs go extinct.

-earliest humans.

Explanation:

There are several events in history that changed the universe and human life. The events led to the most famous scientific discovery, evolution, technological development among others. The universe and human life have drastically changed due to the occurrence of the events such as the Big Bang and the presence of elements.

Answer:

A. The big bang and the universe begins to expand.

B. elements such as oxygen and carbon first exist

C .nuclear fusion begins in the sun

D. Earliest life on earth

E. Dinosaurs go extinct.

F. Earliest humans

Explanation:

-The big bang suggests that our universe was born 13.7 billion years ago in a massive expansion that exploded the space like a gigantic balloon.

- carbon and oxygen were as a result of nuclear fusion that we call stars. They consume their hydrogen, helium and lithium to produce heavy element when they're with a bang to spread element of life around the universe.

-when the central temprature of the sun reached 10 million degrees, nuclear burning of hydrogen into helium commenced after series of protosuns collapsed indirectly raising the central temperature.

- The cretaceous paleogene(k- Pg) extinction event occurrence about 66 million years ago which was sudden mass extinction of ¾ of plant and animals on the planet.

- The earliest member of the genus Homo which evolved around 2.8 million years ago.

Answer: D) 35.7km × 1 mile/1.609 km

Explanation:

Given that;

We need to convert 35.7km to miles

And we know that 1.609km makes 1 mile = 1.609km/1mile

To convert it to mile we need to obtain the number of miles per kilometre

= 1/(1.609km/mile)

= 1mile/1.609km

Then we can now multiply the conversion rate by the number.

= 35.7km × 1mile/1.609km

= 22.19 miles

Note that the sign must cancel out to give miles.

Answer:

Third-degree price discrimination

Explanation:

Third degree price discrimination according to Investopedia.com occurs when companies price products and services differently based on the unique demographics of subsets of its consumer base, such as students, military personnel, or seniors.

The magnitude of the force is 990 N

Explanation:

The work done by a force on an object is given by:

[tex]W=Fd cos \theta[/tex]

where

F is the magnitude of the force

d is the displacement

[tex]\theta[/tex] is the angle between the direction of the force and of the displacement

In this problem, we have the following:

W = 3500 J (work done by Max)

d = 5 m (displacement)

[tex]\theta=45^{\circ}[/tex] (direction at which the force is applied)

Solving for F, we find the magnitude of the force:

[tex]F=\frac{W}{dcos \theta}=\frac{3500}{(5)(cos 45^{\circ})}=990 N[/tex]

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To find the force Max exerts while moving the Pacman arcade game, use the formula Work = Force x Distance x cos(θ). Solve for force, giving Force = Work / (Distance x cos(θ)). Substituting the given values into the formula will provide the answer.

The work done can be used in the equation that relates work, force, and displacement to identify the force exerted by Max. The relationship between these concepts is expressed as: Work = Force x Distance x cos(θ), where 'θ' is the angle at which the force is applied.

In this scenario, the work done (W) is 3,500 joules, the distance (d) is 5 meters, the angle (θ) is 45 degrees, and the force (F) is what we're trying to find.

Rearranging the formula to solve for Force, we get: Force = Work / (Distance x cos(θ)).

Substituting the given values and doing the math, Max's exerted force will be calculated. The cos(45) is approximately 0.7071, and substituting this in our formula might aid us in accurately finding the force exerted by Max while moving the Pacman arcade game.

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Answer: g = GM0/R0

Explanation:

Second law of Newton (gravitational law) postulates that

The gravitational force on a body on the earth is

i) directly proportional to the mass of earth M0

ii) directly proportional to the mass of the object m

iii) inversely proportional to the raduis R0 of earth.

The gravitational constant G is the proportional constant linking all of these parameters

F = GM0m/R0

But F = mg

Where F is the weight (i.e gravitational force on the object)

m is the mass of the object and

g is the acceleration due to gravity

Hence mg = GM0m/R0

m is cancelled as it exists on

both sides

GM0/R0 = g

Therefore

g = GM0/R0

Answer:

4.18 kg.

Explanation:

Work done: Work is said to be done when ever a force move a body through a given distance. The S.I unit of work done is Joules (J)

Mathematically, work done is expressed as

W' = F×d.................... Equation 1

Where W' = work done, F = force , d = distance.

making F the subject of the equation,

F = W'/d............................. Equation 2

Note: The force need to lift the small dog n a basket = combined weight of the dog ans the basket.

Therefore,

W = F

Where W = combined weight of the dog and the basket.

Also

W = Mg

M = W/g............................. Equation 3

Where M = combined mass of the dog and the basket, g = acceleration due to gravity.

Given: W' = 201 J, d = 4.90 m.

Substitute into equation 2

F = 201/4.9

F = 41.02 N.

Since F = W = 41.02 N and g = 9.81 m/s²

Substitute these values into equation 3

M = 41.02/9.81

M = 4.18 kg.

Thus the combined mass of the dog and the basket = 4.18 kg.

Answer:

3.33 m/s

Explanation:

given,

mass of bullet, m = 20 g = 0.02 Kg

speed of bullet, v = 250 m/s

mass of rifle, M = 1.5 kg

speed of recoil, u = ?

initial speed of the bullet and the rifle is zero.

using conservation of momentum

(M + m) V = m v +  M u

(M + m) x 0 = 0.02 x 250 +  1.5 x u

 1.5 u = -5

   u = -3.33 m/s

negative sign represent that the recoil velocity is opposite to bullet velocity.

Hence, the recoil velocity is equal to 3.33 m/s

Answer:

The steam engine of James watt is more efficient than Newcomen ans more suitable for the industrial revolution.

Explanation:

James Watt is more widely know for working steam engine because Watt has created better engine which is suitable for the industrial revolution. The steam engine of James watt is more efficient than Newcomen. Watt developed the condensing arrangement by using piston which lessen the initial pressure leading to effectively worked than Newcomen's

The steam engine made by James Watt has a separate condenser from the original design which increases the efficiency of the engine.

A machine that converts hot steam and heat energy into work is called the steam engine.

Thomas Newcomen invented the first useful steam engine in 1712. The Newcomen's engine was used to pump water out of mines.

James Watt came up with a revolution in the steam engine in 1765. He invented a steam engine with a separate condenser. A steam engine with a separate condenser results in improved efficiency and the size of the engine is reduced as compared to the previous design. The engine uses less coal.

Hence we can conclude that the steam engine invented by James Newcomen is more efficient as compared to the engine invented by Thomas Newcomen.

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To determine the effective spring constant of a molecule of DNA, we can use Hooke's Law and Coulomb's Law. The effective spring constant of the DNA molecule is approximately -1.967 x 10-4 N/m.

To determine the effective spring constant of a molecule of DNA, we can use Hooke's Law, which states that the force required to compress or extend a spring is directly proportional to the displacement of the spring from its equilibrium position. In this case, we are given that the DNA molecule compresses 1.01% when it becomes charged, so we can set up the equation:

F = -kx

Where F is the force, k is the spring constant, and x is the displacement. The negative sign indicates that the force and displacement are in opposite directions. We can rearrange this equation to solve for k:

k = -F/x

Since we are given the percentage compression, we can calculate the displacement as a fraction of the original length:

x = (1.01/100) * 2.33 µm = 0.023533 µm

Now, we need to calculate the force. Since the ends of the molecule become singly ionized, one end becomes negatively charged and the other end becomes positively charged. This creates an electric field between the ends, and the molecule experiences an electric force. The magnitude of this force can be calculated using Coulomb's Law:

F = (ke * q1 * q2) / r2

Where F is the force, ke is the electrostatic constant (9.0 x 109 N m2 / C2), q1 and q2 are the charges on the ends of the molecule, and r is the distance between the charges. Since the ends are singly ionized, we can assume equal and opposite charges:

F = (ke * q2) / r2

Now we can substitute the values into the equation:

F = (9.0 x 109 N m2 / C2) * (1.6 x 10-19 C)2 / (0.023533 x 10-6 m)2 = 4.6307 x 10-12 N

Finally, we can substitute the values for force and displacement into the equation for the spring constant:

k = - (4.6307 x 10-12 N) / (0.023533 x 10-6 m) = -1.967 x 10-4 N/m

Therefore, the effective spring constant of the DNA molecule is approximately -1.967 x 10-4 N/m.

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The effective spring constant of the DNA molecule is approximately [tex]\( 9.54 \times 10^{-6} \) N/m.[/tex]

To determine the effective spring constant [tex]\( k \)[/tex] of the DNA molecule, we can use Hooke's Law, which states that the force [tex]\( F \)[/tex] exerted by a spring is proportional to the displacement [tex]\( x \)[/tex] from its equilibrium position, i.e.,[tex]\( F = -kx \)[/tex].

[tex]\[ x = \frac{1.01}{100} \times L = \frac{1.01}{100} \times 2.33 \times 10^{-6} \text{ m} \] \[ x = 2.3533 \times 10^{-8} \text{ m} \][/tex]

Next, we need to calculate the force [tex]\( F \)[/tex] that causes this compression. Since the molecule is ionized, the force can be calculated using Coulomb's Law, which states that the force between two point charges is:

[tex]\[ F = \frac{k_e \cdot q_1 \cdot q_2}{r^2} \][/tex]

Using Hooke's Law, we can express the force  as:[tex]\( F \)[/tex]

[tex]\[ F = k \cdot x \][/tex]

We can now solve for [tex]\( k \)[/tex]:

[tex]\[ k = \frac{F}{x} \][/tex]

Therefore, we can write:

[tex]\[ k = \frac{F}{x} = \frac{k_e \cdot q^2}{x \cdot r^2} \][/tex]

Thus, we have:

[tex]\[ k = \frac{k_e \cdot q^2}{x \cdot L^2} \][/tex]

Since we do not have the values for [tex]\( q \)[/tex], we can assume that the force is such that it causes a 1.01% compression, and we can use the percentage compression to represent the force. This means we can write:

[tex]\[ k = \frac{1.01 \cdot L}{x \cdot L} \] \[ k = \frac{1.01}{x} \][/tex]

Now we can plug in the value for [tex]\( x \)[/tex]:

[tex]\[ k = \frac{1.01}{2.3533 \times 10^{-8} \text{ m}} \] \[ k \approx 9.54 \times 10^{-6} \text{ N/m} \][/tex]

Therefore, the effective spring constant of the DNA molecule is approximately [tex]\( 9.54 \times 10^{-6} \)[/tex] N/m.

Source region: A large area of the earth's surface, where large masses of air originate with uniform temperature and humidity conditions characteristic of the region

In meteorology, an air mass is an air volume determined by its temperature and the amount of water vapour. Air masses span several hundreds or thousands of miles, and conform to the surface properties below them. They are categorized by latitude and by their areas of continental or maritime origin.

Still, from surface effects the air masses themselves are mild. The areas of the globe from which air masses are called source regions. A source area must have certain temperature and humidity properties which can stay constant for a considerable length of time to influence the air masses above it.

Explanation:

Let east be positive x axis and north be positive y axis

Velocity of boat = 2.8 m/s in a direction 52° north of west.

Velocity, v = -2.8 cos 52 i + 2.8 sin 52 j = -1.72 i + 2.21 j m/s

Time taken = 35 min = 35 x 60 = 2100 s

Displacement = Velocity x Time

Displacement =  (-1.72 i + 2.21 j)  x 2100

Displacement =  -3612 i + 4633.50 j m

Displacement along west = 3612 m

Displacement along north = 4633.50 m

Final answer:

To find the westward and northward distances traveled by the sailboat, we decompose the boat's velocity into westward and northward components and then multiply each component by the travel time of 2100 seconds (35 minutes). Calculations involving trigonometry such as cosine for the westward component and sine for the northward component will yield the respective distances.

Explanation:

The question asks for the distance traveled westward and northward by a sailboat that runs before the wind with a constant speed of 2.8 m/s, heading 52° north of west. To solve this, we can decompose the sailboat's velocity into its westward and northward components using trigonometry. The total time traveled is 35 minutes, which is equivalent to 2100 seconds (35 min x 60 s/min).

Westward Component (a)

The westward component of the velocity can be found using the cosine function:

Vwest = V * cos(θ)

Where V is the speed of the boat, and θ is the angle north of west. Plugging in the given values:

Vwest = 2.8 m/s * cos(52°)

The distance traveled westward is the westward component of the velocity multiplied by the time:

Distancewest = Vwest * time

Northward Component (b)

Similarly, the northward component of the velocity is:

Vnorth = V * sin(θ)

The distance traveled northward is:

Distancenorth = Vnorth * time

By calculating these components, we can determine how far the sailboat has traveled in both the westward and northward directions.

The particle with both forces acting on it will move at constant velocity

Explanation:

We can solve this problem by applying Newton's second law of motion, which states that the net force acting on a body is equal to the product between its mass and its acceleration:

[tex]F=ma[/tex]

where

F is the net force

m is the mass

a is the acceleration

For the particle in this problem, initially it has a forward force of

[tex]F_1 = 10 N[/tex]

Later, it encounters a second additional force in the opposite direction, therefore

[tex]F_2 = -10 N[/tex]

This means that the net force on the particle now is

[tex]F=F_1+F_2 = +10 +(-10) = 0[/tex]

As a consequence, the acceleration of the particle is zero:

[tex]a=0[/tex]

And this means that the particle moves with constant velocity.

Learn more about Newton's second law:

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The particle will not accelerate due to the offsetting forces, it will maintain a constant velocity or remain at rest, pursuant to Newton's Third Law of motion.

In the realm of Physics, the scenario outlined is a classic representation of Newton's Third Law of motion, which states that 'every action has an equal and opposite reaction'. Here, a particle is initially accelerated by a 10-N force. Then, it encounters a second force of the same magnitude but in the opposite direction. Essentially, these two forces cancel each other out because they are equal in magnitude, but opposite in direction. Therefore, the particle with both forces acting on it will not accelerate and will maintain a constant velocity, assuming it had a nonzero velocity to begin with. If it was initially at rest, it will remain at rest.

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Explanation:

We have equation of motion s = ut + 0.5 at²

        Initial velocity, u = 208 m/s

        Acceleration, a = -9.81 m/s²  

        Time, t = 8.9 s      

     Substituting

                      s = ut + 0.5 at²

                      s = 208 x 8.9 + 0.5 x -9.81 x 8.9²

                      s = 1462.68 m

      Displacement after 8.9 seconds  is 1462.68 m

Answer:

B > C > A > D

Explanation:

As we see four pairs of bees; conducting spheres; it seems as below

A down 4

B up 8

C down 6

D down 3

so

B > C > A > D