A conductor of square with sides of length 2d, carries a current I uniformly distributed throughout its cross-sectional area.


The current in the conductor is directed out of the screen.


Ampère’s law is applied along the circle that touches the four sides of the conductor.


Select the expression that correctly represents the magnitude of the integral around the circle.


Group of answer choices


µ0(πd2I)


µ0(2πdI)


µ0(πI/4)


µ0(4I/π)

The time taken to reach zebra's top speedis 2.4 second by the cheetah.

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The harmonic mode of the pipe that resonates with a 1. 1 kHz source is second harmonic.

The length of the pipe is given as 30 cm = 30/100 m = 0.3 m

Speed of light is known to be 330 m/s

Frequency of the source is given as 1.1 kHz = 1100 Hz

We know the relation between frequency, harmonic mode and length as,

vn = n v / 2 l

where,

n is number of harmonic mode

v is speed of light

l is length

vn is frequency of nth harmonic in an open pipe

Putting in the values, by making n as subject we have,

n = vn × 2 l/v = 1100 × 2 × 0.3/330 = 2

Thus, the harmonic mode of the pipe is calculated to be 2nd harmonic mode.

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Answer:

It could either be b, or d, Your choice! (hint: I know the answer but pick one)

Answer:

Resistance to the flow of electricity in wires and resistance to the flow of water in pipes are similar in several ways:

Both are affected by the size of the conductor: In both cases, the resistance to flow is affected by the size of the conductor. A larger diameter wire or pipe will offer less resistance to the flow of electricity or water than a smaller diameter one.

Both are affected by the length of the conductor: The resistance to flow also increases with the length of the conductor. A longer wire or pipe will offer more resistance to the flow of electricity or water than a shorter one.

Both are affected by the material of the conductor: Different materials have different resistances to flow. In electrical wires, metals are commonly used as they have low resistance. In pipes, materials such as copper, plastic, or steel may be used depending on the specific application.

Both can be reduced by minimizing obstructions: Resistance to flow can be reduced in both cases by minimizing obstructions in the path of the flow. In pipes, for example, the use of smooth inner walls and proper pipe bends can help reduce resistance. In electrical wires, minimizing the number of connections and using high-quality connections can help reduce resistance.

Overall, resistance to flow is a fundamental concept that applies to the flow of electricity and water, and the factors affecting resistance are similar in both cases.

When a luminous object moves along the optical axis of a concave spherical mirror, if the object approaches the mirror and its focal point, the image of the object moves to infinity.

A concave mirror is a mirror with a reflecting surface that curves inward. A concave mirror, often known as a converging mirror, causes light to concentrate at a point known as the focal point when light rays hit it. The distance between the mirror's center and its focal point is known as the focal length. A concave mirror, for example, is used in searchlights to direct the beam of light, in telescopes to gather more light from faraway objects, and in headlights to concentrate the beam of light to illuminate the road ahead.

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The speed of the edge of a fidget spinner that has a diameter of 6.0 cm is 12.58 m/s.

To calculate the speed of the edge of the fidget spinner, we need to convert the rotational speed from revolutions per minute to radians per second, and then multiply by the radius of the spinner.

First, we convert 4000 rpm to radians per second:

4000 rpm = 4000 revolutions / 60 seconds = 66.67 revolutions per second

Each revolution is 2π radians, so:

66.67 revolutions per second = 66.67 * 2π radians per second = 419.47 radians per second

Now that we have the rotational speed in radians per second, we can calculate the speed of the edge of the fidget spinner:

speed = rotational speed x radius

The radius of the fidget spinner is half of its diameter, which is 6.0 cm / 2 = 3.0 cm = 0.03 m.

So, the speed of the edge of the fidget spinner is:

speed = 419.47 radians per second x 0.03 m = 12.58 m/s

Therefore, the speed of the edge of the fidget spinner is approximately 12.58 m/s.

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If the pressure in the pipe is 8940 n/m° and in the constricted section is 6705 n/m,  the rate at which oil is flowing through the pipe is 2.74 m^3/s.

The volume flow rate (Q) can be expressed as:

Q = Av

We can use the continuity equation to relate the velocities at the two different cross-sectional areas:

A1v1 = A2v2

Where:A1 and A2 are the cross-sectional areas at the two different points in the pipe

v1 and v2 are the fluid velocities at the two different points in the pipe

We can rearrange this equation to solve for v1 in terms of v2:

v1 = (A2/A1) * v2

Now we can use Bernoulli's equation to relate the pressure and velocity at the two different points in the pipe:

P1 + (1/2)ρv1^2 = P2 + (1/2)ρv2^2

We can rearrange this equation to solve for v2:

v2 = sqrt(2(P1 - P2) / ρ + v1^2)

Now we can plug in the given values to find v2:

v1 = ?

A1 = (π/4)(0.945 m)^2 = 0.664 m^2

A2 = (π/4)(0.567 m)^2 = 0.100 m^2

ρ = 821 kg/m^3

P1 = 8940 N/m^2

P2 = 6705 N/m^2

v2 = sqrt(2(8940 - 6705) / 821 + ((0.100/0.664) * v1)^2)

We can simplify this equation by assuming that the velocity at the wider section of the pipe (v1) is much smaller than the velocity at the constriction (v2), due to the principle of continuity. Therefore, we can neglect the second term in the equation, giving:

v2 = sqrt(2(8940 - 6705) / 821) = 11.98 m/s

Now we can use the continuity equation to find the volume flow rate:

Q = A1v1 = A2v2 = (π/4)(0.945 m)^2 * 11.98 m/s =2.74 m^3/s

Therefore, the rate at which oil is flowing through the pipe is 2.74 m^3/s.

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An operating lamp draws a current of 0. 50 ampere. the amount of charge passing through the lamp in 10 seconds is 5.00 Coulombs.

The amount of charge (Q) passing through a conductor is given by the product of current (I) and time (t):

Q = I * t

In this problem, we are given the following information:

The current passing through the lamp is I = 0.50 A

The time for which the current flows is t = 10 s

Using the above formula, we can calculate the amount of charge passing through the lamp as:

Q = I * t

Q = 0.50 A * 10 s

Q = 5.00 C

Thus, the amount of charge is 5.00 Coulombs.

The ampere, often shortened to amp, is the unit of electric current in the International System of Units.Ampere meter, commonly known as Ammeter is an electrical instrument used to measure electrical current in Amperes.

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Mike and Debra both have linear production possibilities frontiers (PPF), which show the maximum amount of two goods that can be produced given their resources and technology. However, their PPFs are different because they have different maximum production levels for trucks and computers.

Mike's PPF shows that he can produce a maximum of 10 million trucks or 10 million computers. This means that if he allocates all of his resources to producing trucks, he can produce 10 million of them, and if he allocates all of his resources to producing computers, he can produce 10 million of them. Debra's PPF, on the other hand, shows that she can produce a maximum of 9 million trucks or 3 million computers. This means that if she allocates all of her resources to producing trucks, she can produce 9 million of them, and if she allocates all of her resources to producing computers, she can produce 3 million of them.

Overall, Mike and Debra's PPFs show the trade-offs they face when deciding how to allocate their resources between producing trucks and computers. They must decide how much of each good to produce in order to maximize their production and meet their needs.

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The frequency you will hear when you are approaching a stationary source of sound at 20 m/s is 537 Hz.

What is the fundamental frequency of sound?

The fundamental frequency of sound is the lowest frequency produced by a vibrating object or sound source.

What is the speed of sound? The speed of sound is the distance covered by a sound wave per unit of time.

The given values are as follows:

frequency of sound = 500 Hz

speed of sound = 340 m/s

velocity of the observer = 20 m/s

Formula to find the frequency heard by the observer

The formula for finding the frequency of a sound wave observed by a moving observer is:

[tex]f\prime = \frac{f \times (v + v_o)}{(v - v_S)}[/tex]

Where, f' is the frequency observed

v is the speed of sound

f is the frequency of the sound source

[tex]v_S[/tex] is the velocity of the sound source

v₀ is the velocity of the observer

Substituting the given values into the above formula, f' = [tex]\frac{500 \times (340 + 20)}{(340 - 20)}

Hence, f' = 537 Hz

Therefore, when you are approaching the source of sound at 20 m/s, you will hear a frequency of 537 Hz.

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By using the formula:- [tex]mgh= \frac{1}{2} mv^{2} , v = \sqrt{2gh}[/tex], as the release height of the car increase the speed of the car increases.

As the release height of the car increases, the skid distance of the car increaseincrease due to increased velocity.

The directional speed of an object in motion, as measured by a specific unit of time and witnessed from a specific point of reference, is what is referred to as velocity.
Velocity can be defined as the rate at which something travels in a specific direction. Like the speed of a vehicle travelling north on a highway or the speed of a rocket after launch, for instance.
Less momentum with increased height. Less height, more speed. The rate at which it is exchanging height for velocity at any given moment in the fall is therefore equal to the velocity divided by the gravitational constant. As a result, at the top when its velocity is low, it loses only a tiny amount of height with each increase in velocity.
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complete question:-

When the spheres are separated by 0.5 m, the electric force between them is 1.44 x [tex]10^{20}[/tex] N.

To determine the electric force between two balloons, we can use Coulomb's law:

F = k * (q₁ * q₂) / r²

where F is the electric force, k is Coulomb's constant (9 × [tex]10^{9}[/tex] N·m²/C²), q1 and q2 are the charges on the balloons (2.0 x [tex]10^{7}[/tex] C), and r is the distance between the balloons (0.5 m).

Plugging in these values, we get:

F = 9 × [tex]10^{9}[/tex] * (2.0 x [tex]10^{7}[/tex])² / (0.5)²

F = 1.44 x [tex]10^{20}[/tex] N

Therefore, the electric force between the balloons is 1.44 x [tex]10^{20}[/tex] N when they are separated by a distance of 0.5 m.

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The power consumed by 18 watts.

What is power ?

Work is done at a certain rate according to power. P=Wt. The watt (W), which is equal to 1 joule per second (1J/s), is the SI unit of power. Power is the rate at which energy is used up since power is the transfer of energy. For instance, a 60-W light bulb uses about 60 J of energy every second.

What is current ?

A flow of electrical charge carriers, most frequently electrons or atoms lacking in electrons, is referred to as current. I in capital letters is a typical symbol for current. Ampere, which is denoted by the letter A, is the common unit.I, which is derived from the French term intensité du courant, is the commonly used symbol for current (current intensity).

Therefore,  power consumed by 18 watts.

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Contact metamorphism is least likely to occur in low-temperature areas with sedimentary rocks, such as the Earth's oceanic crust.

Contact metamorphism occurs due to heating, with or without burial, of rocks that lie close to a magma intrusion. It is characterized by low P/T gradients, as strong thermal gradients between an intruding magma and adjacent country rock are best established at shallow crustal level. It is a type of metamorphism where rock minerals and texture are changed, mainly by heat, due to contact with magma. Regional metamorphism is a type of metamorphism where rock minerals and texture are changed by heat and pressure over a wide area or region.

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When travelling at a speed of 28 m/s, the van experiences a total amount of friction force of 748 N.

Calculate the van's overall friction force (measured in N) at a speed of 28 m/s with an engine that produces 2.01 horsepower.

Engine power is calculated as

P = 2.01 hp, or 2.01 x 746, or 1502.46 W.

Van's top speed is 28 m/s.

The van's total work is equal to its change in kinetic energy, according to the work-energy theorem.

Hence, total work completed = Change in kinetic energy (K) -Change in kinetic energy (K)

= [tex](1/2) m (vf_2 - vi_2)[/tex] = [tex](1/2) m v^2[/tex]

where m is the van's mass

([tex]v_f[/tex]) = The van's final speed

([tex]v_i[/tex] )= The van's initial speed

As a result, the van is subject to a 748 N friction force (approx.). So, at a speed of 28 m/s, the van experiences a total friction force of 748 N.

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The work done by the capacitor is obtained as  1.36 * 10^-5 J

A capacitor is an electrical component that stores electrical energy in an electric field. It consists of two conductive plates separated by a non-conductive material, known as the dielectric.

When a voltage is applied across the plates, one plate becomes positively charged and the other becomes negatively charged, creating an electric field between them. The dielectric material prevents the charges from flowing between the plates and instead stores the energy in the form of an electric field.

Work done by the Capacitor = 1/2CV^2

= 0.5 * 2.72 * 10^-9 * (100)^2

= 1.36 * 10^-5 J

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Missing parts;

A 2. 72-nF parallel-plate capacitor is charged to an initial potential difference ΔVi = 100 V and is then isolated. The dielectric material between the plates is Pyrex glass, with a dielectric constant of 5. 6. What is the work done by the capacitor?

Answer:

The six steps of the scientific method include: 1) asking a question about something you observe, 2) doing background research to learn what is already known about the topic, 3) constructing a hypothesis, 4) experimenting to test the hypothesis, 5) analyzing the data from the experiment and drawing conclusions, and 6) communicating the results to others.

The metal cube will transfer some of its charge to the cylinder, causing both objects to have a net positive charge. This is because when two objects with opposite charges are brought into contact, they will exchange charges until they have the same magnitude and the same sign.

In this case, the cube with a greater charge will transfer charge until both objects have a positive charge.When an object has more electrons than protons is called a negative charge. A positive charge occurs when an atom has more protons than electrons. Electrons have a negative charge and protons have a positive charge. The unit of charge is the coulomb(C). Like charges repel each other.

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Question:

A metal cube with a negative charge -Q_1−Q 1 minus, Q, start subscript, 1, end subscript is brought into contact with a cylinder of a negative charge -Q_2−Q 2 minus, Q, start subscript, 2, end subscript, where

|Q_1| > |Q_2|Q1∣>∣Q 2∣vertical bar, Q, start subscript, 1, end subscript, vertical bar, is greater than, vertical bar, Q, start subscript, 2, end subscript, vertical bar.

The change in potential energy of the system during this time interval is -648 nJ.

The change in potential energy of a particle with charge q that moves from a point with potential V1 to a point with potential V2 is given by:

ΔPE = q x (V2 - V1)

where q is the charge of the particle, and

V2 and V1 are the potentials at the final and initial positions.

Therefore, the charge of the particle is 18 nC, and it moves from a point with potential V1 = 46 V to a point with potential V2 = 10 V.

Therefore, the change in potential energy is:

ΔPE = q x (V2 - V1) = 18 nC x (10 V - 46 V) = -648 nJ

The negative sign indicates that the potential energy of the particle has decreased, which means that the particle has lost potential energy as it moved from the point with higher potential to the point with lower potential.

Therefore, the change in potential energy of the system during this time interval is -648 nJ

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Answer:

On a wet marble floor, the friction is very less because marble floor has irregularities that get filled with water. We can walk only when there is more friction. Due to the less friction, we may slip. So, it is very difficult to walk on a wet marble floor.

Answer:

because marbles are always sliding and water makes them more slimy

The puck must rotate with a speed of 3.44 m/s to keep the hanging block at rest.

To keep the hanging block at rest, the tension in the string must be equal to the weight of the block. We can start by finding the tension in the string using the weight of the hanging block:

T = mg = (1.20 kg)(9.81 m/s^2) = 11.77 N

The tension in the string provides the centripetal force that keeps the puck moving in a circle. The centripetal force is given by:

F = ma = m(v^2/r)

where m is the mass of the puck, v is its speed, r is the radius of the circle, and a is the centripetal acceleration.

Solving for v, we get:

v = sqrt(ra) = sqrt(r(T/m)) = sqrt((0.40 m) × (11.77 N)/(0.20 kg)) = 3.44 m/s

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If the basketball has a radius of 12cm,the buoyant force on the basketball due to the water is 35.5 N.

When an object is submerged in a fluid, it experiences an upward force called the buoyant force. The magnitude of the buoyant force is equal to the weight of the fluid displaced by the object.

In this case, the basketball is submerged in water until half its volume is submerged. The volume of a sphere of radius r is given by:

V = (4/3) * pi * r^3

So, the volume of the basketball is:

V_basketball = (4/3) * pi * (0.12 m)^3 = 7.24 x 10^-3 m^3

Half of the volume of the basketball that is submerged is:

V_submerged = (1/2) * V_basketball = 3.62 x 10^-3 m^3

The weight of the water displaced by the basketball is equal to the weight of the volume of water that is submerged. The density of water is 1000 kg/m^3, so the mass of the displaced water is:

m_water = rho * V_submerged = 1000 kg/m^3 * 3.62 x 10^-3 m^3 = 3.62 kg

The buoyant force on the basketball due to the water is equal to the weight of the displaced water, which is:

F_buoyant = m_water * g

= 3.62 kg * 9.81 m/s^2

= 35.5 N

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The  centripetal force the passenger experience is 30167.52 N

The centripetal force experienced by the passenger can be calculated using the formula:

Fc = (m)(r)(ω^2)

where Fc is the centripetal force, m is the mass of the passenger, r is the radius of the loop, and ω is the angular speed of the roller coaster.

Given:

m = 80 kg

r = 12 m

ω = 3.14 rad/s

Substituting these values into the formula, we get:

Fc = (80 kg)(12 m)(3.14 rad/s)^2

Fc = 30167.52 N

Therefore, the passenger experiences a centripetal force of approximately 30167.52 N when the roller coaster reaches an angular speed of 3.14 rad/s.

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49.87 m.  is the horizontal displacement of the football when it lands back on the ground.

The horizontal displacement of the football can be determined using the formula

x = vxt,

where vx is the initial x-component of the velocity, and t is the time the football is in the air.

The initial x-component of the velocity (vx) can be calculated using the formula

vx = vcos(θ),

where v is the initial velocity, and θ is the angle of projection.

Therefore, vx = 28.65cos(37.18) = 25.36 m/s

The time the football is in the air (t) can be calculated using the formula t = 2vsin(θ)/g, where g is the acceleration due to gravity (9.81 m/s2).

Therefore, t = 2(28.65sin(37.18))/9.81 = 1.97 seconds

Finally, the horizontal displacement (x) can be calculated using the formula x = vxt.

Therefore, x = 25.36*1.97 = 49.87 m.

Therefore, the horizontal displacement of the football when it lands back on the ground is 49.87 m.

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Energy transfer is the movement of energy from one location to another. ... Energy transformation is when energy changes from one form to another – like in a hydroelectric dam that transforms the kinetic energy of water into electrical energy.

Energy transfer in physics refers to the movement of energy from one object or system to another. Energy can take various forms such as kinetic energy, potential energy, thermal energy, electromagnetic radiation, and chemical energy, among others. The transfer of energy can occur through different mechanisms such as work, heat, and radiation.

Work is the transfer of energy that occurs when a force acts on an object and causes it to move a certain distance. Heat transfer is the flow of energy from a hotter object to a cooler object, driven by a temperature difference between the two objects. Radiation is the transfer of energy in the form of electromagnetic waves or particles. Energy transfer is a fundamental concept in physics as it governs many natural phenomena such as heat flow, electrical power generation, and energy conversion in machines.

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The solution of expression $12.7\ge s-5.3$ is $s \leq 18$.

The expression $12.7\ge s-5.3$ is an inequality, which means that it expresses a range of values for the variable $s$. The symbol $\ge$ means "greater than or equal to," and in this context it indicates that $12.7$ is greater than or equal to $s-5.3$.

To solve for $s$, we can start by adding $5.3$ to both sides of the inequality:

\begin{align*}

12.7 &\ge s-5.3 \

12.7+5.3 &\ge s-5.3+5.3 \

18 &\ge s

\end{align*}

So the solution is $s \leq 18$. This means that any value of $s$ that is less than or equal to $18$ will satisfy the inequality. For example, $s=15$ would satisfy the inequality, because $12.7 \ge 15-5.3$. However, $s=20$ would not satisfy the inequality, because $12.7 \ngeq 20-5.3$.

What are the variables?

A variable is a symbol or letter that represents a value that can vary or change in a given context or problem. Variables are used to write mathematical expressions, equations, and functions.

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Complete question is: $12.7\ge s-5.3$ is $s \leq 18$.

The speed (in revolutions per minute) at which resonance vibrations will occur is 273.91 RPM.

The front-loading washing machine is mounted on a thick rubber pad that acts as a spring. When the rotor spins at radians per second, the rotor exerts a vertical force of newtons on the machine.

Resonance vibrations occur when the natural frequency of the machine matches the frequency of the external force applied to it. This can cause the machine to vibrate excessively and even damage it.

In this scenario, the natural frequency of the washing machine is related to its spring constant and the mass of the machine. Neglecting friction, resonance vibrations occur at RPMs.

Given,

The weight (with m/s) of the machine depresses the pad exactly 0.89 cm.

The rotor exerts a vertical force of N on the machine.

The natural frequency of a machine is given by:

f = 1/2π x √(k/m)

where f is the frequency of oscillation,

k is the spring constant of the spring,

m is the mass of the machine.

In this case, the weight of the machine depresses the spring by 0.89 cm.

So, the effective spring constant is given by,

k = F/x = (mg)/x

where F is the weight of the machine,

m is its mass,

g is the acceleration due to gravity,

and x is the amount by which the spring is compressed.

Substituting the given values,

k = (m x g) / x = (m x 9.8) / 0.0089 = 1101.12m N/m

Substituting the given values,

f = 1/2π x √(k/m) = 1/2π x √(1101.12m/m) = 4.9448 √m Hz

The frequency of oscillation is given in Hz.

To convert it to RPMs, we need to divide it by 60 (the number of seconds in a minute) and multiply it by 2π (the number of radians in a circle).

f = 4.9448 √m Hz = (4.9448 √m x 2π)/60 RPM

At resonance, the frequency of oscillation should match the frequency of the rotor.

So, the frequency of the rotor is given by,

f = ω/2π

where ω is the angular velocity of the rotor in radians per second.

Substituting the given values,

N = mg = F,

ω = N/(m x r) = 94.4912/r rads/s

where r is the radius of the rotor in meters.

Substituting these values in the equation for frequency,

f = ω/2π = (94.4912/r) / 2π = 15.0415 / r Hz

At resonance, the frequency of oscillation should match the frequency of the rotor.

Therefore,4.9448 √m = 15.0415 / r

Squaring both sides,19.4542 m = (15.0415/r)^2

Solving for r, r = 0.0275 m = 2.75 cm

Therefore, the radius of the rotor is 2.75 cm.

The speed (in revolutions per minute) at which resonance vibrations will occur is 273.91 RPM.

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The dewpoint when the air temperature is 28°C and the relative humidity is 47% is 15.9°C.

Temperature is a physical property of matter that quantitatively expresses hot and cold. It is measured with a thermometer, which may work through the bulk behavior of a thermometric material, detection of thermal radiation, or particle kinetic energy. Temperature is one of the principal parameters of thermodynamics. Temperature is also important in all fields of natural science, including physics, geology, chemistry, atmospheric sciences, medicine and biology.

The dewpoint is the temperature at which the air has reached its saturation point. At this point, water vapor will begin to condense into liquid droplets, forming dew.

To calculate the dewpoint when the air temperature is 28°C and the relative humidity is 47%, we use the formula:

Dewpoint (°C) = (Air Temperature (°C) * Relative Humidity) / 100 + (112 - Relative Humidity) / (x + 0.444)

Where x = (17.27 * Air Temperature (°C)) / ( Air Temperature (°C) + 237.3 ).

In this example, x = (17.27 * 28) / (28 + 237.3) = 0.39.

Plugging the values into the formula gives us:

Dewpoint (°C) = (28 * 47) / 100 + (112 - 47) / (0.39 + 0.444) = 15.9°C.

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Answer:

The F's accelerated

where m is the box's mass, an is its acceleration, and F net is the net force.

The net force in this situation is equal to the applied force less any potential frictional forces. The net force is just the force applied to the box, assuming the table is smooth and there is no friction:

F net = F

Thus, the equation can be rewritten as follows:

F = m * a

Inputting the values provided yields:

F = 6 kg times 0.18 m/s2 to get 1.08 N

As a result, 1.08 N of force F is needed to accelerate a 6 kilogramme box at a constant rate of 0.18 m/s2.