Find the resultant of these two vectors 2.00 x 10^2 units due east and 4.00x10^2 units 30.0 north of west

Each capacitor in the series combination would have a charge of 2.5 μC. This is because, in a series combination of capacitors, the charge on each capacitor is the same.

In a series combination of capacitors, the same amount of charge is stored on each capacitor. This is because capacitors in a series combination have the same potential difference (voltage) across them. Therefore, the charge on each capacitor is directly proportional to the capacitance of that capacitor. In this case, since the total charge supplied by the battery is 5.0 μC and there are two identical capacitors in series, each capacitor would have a charge of 2.5 μC.

learn more about capacitors here:

https://brainly.com/question/17095663

#SPJ11

Density = m kg / 0.5921 m^3. This will give you the density of the compressed gas in kg/m^3. Just plug in the provided mass value for "m" to get your solution.

To calculate the density of the compressed gas, you will need to use the formula for density, which is:

Density = Mass / Volume

You are given the total mass of the compressed gas and the radius of the spherical container. First, we need to find the volume of the container using the formula for the volume of a sphere:

Volume = (4/3) × π × r^3

where r is the radius of the sphere. In this case, r = 0.521 m.

Calculate the volume of the spherical container
Volume = (4/3) × π × (0.521)^3
Volume ≈ 0.5921 m^3

Calculate the density of the compressed gas
Now that we have the volume, we can find the density using the given mass of the gas.

Density = Mass / Volume

Assuming you meant to provide a mass value, let's call it "m" kg for the compressed gas. Substitute the values into the formula:

Density = m kg / 0.5921 m^3

This will give you the density of the compressed gas in kg/m^3. Just plug in the provided mass value for "m" to get your solution.

To know more about Density visit:

https://brainly.com/question/29775886

#SPJ11

The puck's angular velocity on the shorter string would be 160 rpm.

The conservation of angular momentum states that the product of the moment of inertia and the angular velocity is conserved as long as there are no external torques acting on the system. Therefore, we can use the following equation to solve this problem:

I₁ × ω₁ = I₂ × ω₂

where I₁ and I₂ are the moments of inertia of the puck on the longer and shorter strings, respectively, and ω₁ and ω₂ are the corresponding angular velocities in radians per second.

To solve for the angular velocity on the shorter string in revolutions per minute, we need to convert the angular velocity from radians per second to revolutions per minute. Since there are 2π radians in one revolution and 60 seconds in one minute, we can use the following conversion factor:

1 radian per second = (1/2π) revolutions per minute

Now, let's find the moments of inertia of the puck on the longer and shorter strings. The moment of inertia of a point mass rotating about an axis perpendicular to its motion is given by:

I = mr²

where m is the mass of the puck and r is the distance from the axis of rotation to the mass. On the longer string, the distance from the axis of rotation to the center of mass of the puck is 50 cm, so the moment of inertia is:

I1 = m(0.5)² = 0.25m

On the shorter string, the distance from the axis of rotation to the center of mass of the puck is 25 cm, so the moment of inertia is:

I2 = m(0.25)² = 0.0625m

Now we can plug these values into the conservation of angular momentum equation:

I₁ × ω₁ = I₂ × ω₂

0.25m × (40 rpm) × (2π/60) = 0.0625m × ω₂ × (2π/60)

Simplifying and solving for ω₂ in rpm:

ω₂ = (0.25/0.0625) × 40 = 160 rpm

So the puck's angular velocity on the shorter string is 160 rpm.

To know more about angular

https://brainly.com/question/2207653

#SPJ4

The speed of a rollercoaster is the greatest at the bottom of a hill or drop. This is because potential energy is converted into kinetic energy as the rollercoaster descends.

The rollercoaster accumulates potential energy as it climbs up the hill, which is a form of stored energy due to its height above the ground. As the rollercoaster reaches the top of the hill, it has the maximum potential energy, and as it begins to descend, this energy is converted into kinetic energy, which is the energy of motion.

The rollercoaster gains more and more kinetic energy as it accelerates down the hill, and this kinetic energy is what gives it its high speed. The speed of the rollercoaster decreases as it ascends the next hill, as the kinetic energy is once again converted into potential energy. The rollercoaster's speed is also influenced by the forces of friction and air resistance, which can slow it down. However, at the bottom of a hill, the rollercoaster experiences minimal friction and air resistance, allowing it to reach its maximum speed.

To know more about rollercoaster click here:

https://brainly.com/question/28357233

#SPJ11

The correct answer is (D) the cross-sectional area. Inside an ideal solenoid, the magnetic field is generated by the current flowing through the wire windings.

What is Magnetic Field?

Magnetic field is a fundamental concept in physics that describes the region of space around a magnet or a moving electric charge where magnetic forces can be detected. It is a vector field that is characterized by both its strength and its direction.

The windings are wrapped closely together in a cylindrical shape, with each winding contributing to the overall magnetic field. Due to the close spacing of the windings, the magnetic field inside the solenoid is nearly uniform and parallel to the axis of the cylinder.

The strength of the magnetic field inside the solenoid is directly proportional to the current flowing through the windings and the number of windings per unit length. It is also affected by the magnetic properties of the core material, but an ideal solenoid assumes a perfect, infinitely long, and infinitely thin cylindrical shell with no magnetic materials, so the answer (B) is incorrect.

Learn more about Magnetic Field from the given link

https://brainly.com/question/14411049

#SPJ4

The image of an object placed a great distance away from and in front of a converging lens will be formed at the focal point of the lens.

When an object is placed at a great distance from a converging lens, the light rays coming from the object will be parallel to each other. As these parallel rays pass through the lens, they converge and meet at a point known as the focal point of the lens. This is the point where the image of the object is formed.

Therefore, if an object is placed a great distance away from and in front of a converging lens, its image will be formed at the focal point of the lens.

To know more about converging lens, visit;

https://brainly.com/question/15123066

#SPJ11

The slope of the solid-liquid phase boundary of water is approximately 22.4 bar/K by using the Clapeyron equation.

To use the Clapeyron equation to estimate the slope of the solid-liquid phase boundary of water, we need to find the difference in densities of ice and water, the enthalpy of fusion, and the temperature difference between the two phases.

Given

Enthalpy of fusion, ΔH = 6.008 kJ/mol

Density of ice, ρs = 0.91671 g/[tex]cm^{3}[/tex]

Density of water, ρl = 0.99984 g/[tex]cm^{3}[/tex]

Let's assume we are looking at the phase boundary at a temperature of T K. Then, the temperature difference between the two phases is ΔT = T - 273.15 K.

We can then calculate the slope of the solid-liquid phase boundary as follows

dP/dT = ΔH/ΔV * T / (P2 - P1)

Where ΔV = ρl - ρs is the difference in specific volume between the two phases.

We can rearrange the equation as

dP/dT = ΔH/ΔV * (P2 - P1) / T

We know that at the melting point, the pressure of ice and water is equal, so P1 = P2. Therefore, we can simplify the equation to

dP/dT = ΔH/ΔV * P / T

Where P is the common pressure of ice and water at the melting point.

Now we can plug in the values

ΔH = 6.008 kJ/mol = 6008 J/mol

ΔV = ρl - ρs = 0.99984 g/[tex]cm^{3}[/tex] - 0.91671 g/[tex]cm^{3}[/tex] = 0.08313 g/[tex]cm^{3}[/tex] = 8.313e-5 kg/[tex]m^{3}[/tex]

P = 1 atm = 1.01325 bar

T = 273.15 K

dP/dT = (6008 J/mol / 8.313e-5 kg/[tex]m^{3}[/tex]) * (1.01325 bar) / (273.15 K) = 22.4 bar/K

Therefore, the slope of the solid-liquid phase boundary of water is approximately 22.4 bar/K.

To know more about Clapeyron equation here

https://brainly.com/question/29652045

#SPJ4

According to the question The units of index of refraction are: E. None of these.

Refraction is the bending of light rays as they pass from one medium, such as air, to another medium, such as water. The angle of refraction is determined by the angle of incidence, and by the ratio of the refractive indices of the two media. Refraction occurs when the speed of light is changed upon entering a medium, such as when light passes from air into glass, or from water into air. Light is also affected by the presence of particles in the medium, such as air molecules. Refraction is responsible for many optical effects, including mirages, rainbows, and the appearance of objects being bent when half-submerged in water. Refraction is also an important component of the human eye, allowing it to focus light onto the retina.

To learn more about refraction

https://brainly.com/question/27932095

#SPJ4

The centripetal force acting on the Lincoln Continental will be four times greater than the centripetal force acting on the Yugo. This is because centripetal force is directly proportional to mass.

Mass is an intrinsic property of matter that measures its inertia, or resistance to acceleration. It is the fundamental measure of matter and is measured in kilogram (kg). It is commonly used to describe the amount of matter in a particular object or substance. Mass is distinct from weight, which is the measure of the force of gravity acting on an object. Mass remains constant regardless of gravity or location, while weight can vary depending on the location and strength of gravity. Mass is also different from density, which is the measure of the amount of matter in a given volume.

To learn more about mass

https://brainly.com/question/86444

#SPJ4

C) the wavelength of the light equals the separation of the slits.

Constructive interference of light from two slits will occur when the path difference between the light from the two slits is an integer multiple of the wavelength of the light.

Wavelength is a measure of the distance between repeating units of a wave, such as a sound wave or a light wave. Wavelengths are measured in the direction of the wave's travel and are usually expressed in units of meters (m).

Since the two slits are closely spaced together, the path difference between the light from the two slits is equal to the separation of the slits. Therefore, constructive interference of light from two slits will occur when the wavelength of the light is equal to the separation of the slits.

Therefore the correct answer is C.

To learn more about wavelength

https://brainly.com/question/29213586

#SPJ4

The units of a magnetic field are: B. C⋅s/m.  The strength and direction of a magnetic field are typically represented by vectors, and the unit of magnetic field is the tesla (T) in the International System of Units (SI).

What is Magnetic Field?

A magnetic field is a vector field that describes the magnetic influence on moving electric charges, such as electrons, protons, and other charged particles. The magnetic field is created by the motion of electric charges or by magnetic materials such as magnets. It is a fundamental concept in physics and plays a crucial role in many areas of science and technology.

This unit is also known as the tesla (T), which is the standard unit of measurement for magnetic fields. Other common units of magnetic field include gauss (G), which is equal to 10^−4 T, and the oersted (Oe), which is a non-SI unit commonly used in the field of magnetism.

Learn more about Magnetic Field from the given link

https://brainly.com/question/14411049

#SPJ4

According to the question, the critical angle for total internal reflection within the water is 48.9 degrees.

Reflection is a process of thinking deeply and critically about a particular topic or experience. It is a way to gain deeper understanding and create connections between the past and the present. Reflection is often used to help people make sense of their own experiences and to gain insight into the impact of their actions. Reflection can also be used as a way to make sense of the world around us, to gain insight into different perspectives, and to develop empathy for people from different backgrounds.

In this case, the incident medium is water and the refracting medium is glass. Therefore, we can solve for the angle of incidence (θi) using the following equation: sin θi = (1.50/1.33) × sin θr

where θr is the angle of refraction in the glass. Since θr is 90 degrees when total internal reflection occurs, the critical angle for total internal reflection in water is:

θi = sin-1((1.50/1.33) × sin 90) = 48.9 degrees

To learn more about reflection

https://brainly.com/question/29139385

#SPJ4

An ideal Carnot engine extracts 529 J of heat from a high-temperature reservoir during each cycle, and rejects of heat to a low-temperature reservoir during the same cycle. The efficiency of the engine is 0.57.

The efficiency of an ideal Carnot engine is given by:
efficiency = (T_high - T_low) / T_high
where T_high is the temperature of the high-temperature reservoir, and T_low is the temperature of the low-temperature reservoir. We are given that the engine extracts 529 J of heat from the high-temperature reservoir during each cycle, and rejects Q_low amount of heat to the low-temperature reservoir during the same cycle. Since the engine is ideal, all the heat extracted from the high-temperature reservoir is converted into work, and all the heat rejected to the low-temperature reservoir is taken from the engine. Therefore, the net work done by the engine during each cycle is:
W = Q_high - Q_low = 529 J - Q_low
The efficiency of the engine is given as ɛ = W / Q_high = (529 J - Q_low) / 529 J.
We can rearrange this equation to get:
Q_low = 529 J - ɛ * 529 J.
Substituting the given values, we get:
Q_low = 529 J - 0.62 * 529 J = 201 J.
Therefore, the efficiency of the engine is:
ɛ = (529 J - 201 J) / 529 J = 0.62.
So, the answer is A) 0.57.

To know more about heat, click here https://brainly.com/question/30603212

#SPJ11

The amplitude of the vibrations of a spring is 19cm

What is amplitude?

The largest displacement or distance made by a point on a wave or vibrating body relative to its equilibrium position is its amplitude. It is equivalent to the vibration path's half-length.

Distance between the wave's resting position and its highest displacement is known as amplitude. Frequency is the quantity of waves that pass by a particular place each second. Period: the amount of time needed for a wave cycle to finish.

Simple harmonic motion is a continuous back-and-forth movement through an equilibrium, or central, position such that the maximum displacement on one side of the position is equal to the maximum displacement on the other.

Amplitude will be displacement /2

i.e. 38/2 ⇒ 19cm

To learn more about amplitude use:

https://brainly.com/question/3613222

#SPJ4

There n is the number of moles, R is the ideal gas constant (8.314 J/molK) and V₁ and V₂ are the initial and final volumes of the gas, respectively.

Moles are small animal species belonging to the family Talpidae, which includes various types of mammals commonly referred to as "shrew-moles" or "mole-shrews". They are commonly found in temperate regions of Europe, Asia, and North America and have been known to inhabit a wide range of habitats, from woodlands to grasslands and even wetlands. Moles are small burrowing animals that have a cylindrical body, a pointed snout, and short legs. They have short, velvety fur that helps to camouflage them in the soil and are well adapted to living in underground tunnels. Moles have a strong sense of smell and use their long, sensitive snouts to search for food. They feed mainly on small invertebrates such as earthworms, insects, and larvae.

The change in entropy (ΔS) can be calculated using the equation:

ΔS = nRln(V₂/V₁)

In this case, n = 1.50 moles and V₁ = V₂/2.

Therefore, ΔS = (1.50 moles)(8.314 J/molK)ln(2) = 11.47 J/K

To learn more about moles

https://brainly.com/question/28180503

#SPJ4

When an object is placed farther from a convex mirror than the focal length, the image is virtual, upright, and diminished (smaller than the object).

A convex mirror is a type of mirror that curves outward, away from the center. It has a focal length that is always positive.

When an object is placed at a distance greater than the focal length, the light rays diverge and do not converge at a real point.

Instead, they appear to originate from a virtual point behind the mirror. In this case, the image formed is virtual, upright, and diminished.
For objects placed farther from a convex mirror than the focal length, the image created will be virtual, upright, and smaller than the object itself.

For more information on convex mirror kindly visit to

https://brainly.com/question/30258064

#SPJ11

The ratio of the voltage across capacitor C1 to the voltage across capacitor C2 is equal to the ratio of the capacitance of capacitor C1 to the capacitance of capacitor C2.

Voltage is an electrical potential difference between two points in a circuit. It is measured in volts, and is the amount of energy that is needed to move a single unit of charge from one point to another. Voltage is a measure of the energy per unit of charge, and is the electrical equivalent of pressure in a water system. Voltage is the cause of current, and is an important factor in the operation of electrical circuits.

The ratio of the voltage across capacitor C1 to the voltage across capacitor C2 can be determined using the following equation:

V1/V2 = C1/C2

Where V1 is the voltage across capacitor C1, V2 is the voltage across capacitor C2, C1 is the capacitance of capacitor C1, and C2 is the capacitance of capacitor C2.

Therefore, the ratio of the voltage across capacitor C1 to the voltage across capacitor C2 is equal to the ratio of the capacitance of capacitor C1 to the capacitance of capacitor C2.

To learn more about voltage

https://brainly.com/question/1176850

#SPJ4

Complete Question:

From her point of view, the induced current in the coil to her right is counterclockwise. This is because of the right-hand rule of electromagnetic induction.

The right-hand rule states that if the thumb of the right hand is pointed in the direction of the magnetic field, then the fingers will curl in the direction of the induced current.

This means that if the magnetic field is pointing to the right, then the induced current will be in the counterclockwise direction. This is because the force of the field is pushing the electrons in the coil to the left, which causes them to move in a counterclockwise direction around the coil.

Know more about right-hand rule here

https://brainly.com/question/9750730#

#SPJ11

The necessary series resistance is 108,000 Ω, which is option (D). The standard unit of resistance is the ohm (Ω).

What is Resistence?

Resistance is a measure of how much an object or material opposes the flow of electric current through it. It is the property of a material that determines the amount of current that will flow through it when a voltage is applied.

We can use the voltage divider formula to calculate the necessary resistance to extend the range of the voltmeter:

V_out = V_in * R2 / (R1 + R2)

Where V_out is the maximum voltage we want to measure (120 V), V_in is the maximum voltage that the voltmeter can measure without the added resistance (12 V), R1 is the internal resistance of the voltmeter (10,000 Ω), and R2 is the additional resistance we need to add.

R2 = (V_out * R1) / V_in - R1

R2 = (120 V * 10,000 Ω) / 12 V - 10,000 Ω

R2 = 108,000 Ω

Learn more about Resistence from the given link

https://brainly.com/question/17563681

#SPJ4

When a soprano and a bass start singing at the same time, from equally far away, you will hear the soprano first.

This is because higher frequency sound waves travel faster through air than lower frequency waves, which are produced by the bass. Sound waves travel through the air as vibrations that cause compressions and rarefactions in the air molecules. These vibrations create a wave that travels through the air and eventually reaches our ears. The speed at which sound travels through the air depends on the temperature and humidity of the air, but it is generally around 343 meters per second. However, the speed of sound is not the same for all frequencies. Higher frequency sound waves have a shorter wavelength, which means they require less time to complete one full cycle of compression and rarefaction. As a result, they travel faster through the air than lower frequency waves.In the case of a soprano and a bass singing from equally far away, the higher frequency sound waves produced by the soprano will reach your ears first because they travel faster through the air than the lower frequency waves produced by the bass.

Thus, the reason you will hear the soprano first is because higher frequency sound waves travel faster through air than lower frequency waves.

To know more about frequency waves, click here

https://brainly.com/question/14320803

#SPJ11

The bimetallic strip will bend towards the metal with the lower coefficient of linear thermal expansion (metal H), when uniformly heated. This is because as the temperature increases, both metals expand, but the one with the higher coefficient of expansion (metal G) will expand more and thus bend towards the metal with the lower coefficient of expansion (metal H). This phenomenon is used in various devices such as thermostats and thermal switches. It curves downward.

Linear thermal expansion is the tendency of a material to increase its length when its temperature increases. This is due to the fact that when a material is heated, its constituent atoms or molecules vibrate more vigorously, and this extra motion causes the material to expand. The degree of linear thermal expansion of a material is usually expressed in terms of its coefficient of linear expansion, which is the change in length per unit length per degree Celsius (or Kelvin).

To know more about linear thermal expansion please visit

https://brainly.com/question/31840116

#SPJ11

The efficiency of the heat engine is 57%, given by the ratio of the work output to the heat input.

The efficiency of a heat engine is given by the ratio of useful work output to the total heat energy input. In this case, the heat engine receives 7000 J of heat and loses 3000 J in each cycle. Therefore, the total heat energy input is 7000 J and the heat energy output is 3000 J. The useful work output is the difference between the heat energy input and the heat energy output, which is 4000 J (7000 J - 3000 J). Thus, the efficiency of the heat engine can be calculated as the ratio of useful work output to the total heat energy input, which is (4000 J / 7000 J) * 100% = 57%. Therefore, the correct answer is (A) 57%. This means that 57% of the heat energy input is converted into useful work output, while the remaining 43% is lost as waste heat.

To learn more about Efficiency, click here:
https://brainly.com/question/2676954

#SPJ11

) ΔT.

Both objects are given the same amount of heat, and Object 1 has three times the specific heat capacity and four times the mass of Object 2. Therefore, Object 1 will experience a smaller change in temperature compared to Object 2. However, the amount of heat given to both objects is the same, so the temperature change of Object 2 must be the same as Object 1. Hence, the answer is B) ΔT.

Learn more about temperature here:

https://brainly.com/question/11464844

#SPJ11

If an ideal gas molecule has a speed of 0.50 km/s at 20°C, 550 m/s is its speed at 80°C.

A molecule is a small particle composed of two or more atoms held together by chemical bonds. Molecules are the smallest unit of matter that can exist on its own and retain its chemical properties. They are composed of atoms of the same or different elements and can range in size from two atoms to millions of atoms. Molecules are important in the natural world and in human-made products. In the natural world, molecules are the building blocks of life and make up all living organisms. In human-made products, molecules are essential components in a variety of compounds and materials, such as plastics, drugs, and fuels.

The speed of an ideal gas molecule is proportional to the square root of the absolute temperature in Kelvin. Since the absolute temperature of 20°C is 293K and the absolute temperature of 80°C is 353K, the speed at 80°C would be √(353/293) x 0.50 km/s = 0.55 km/s (or 550 m/s).

To learn more about molecule

https://brainly.com/question/30337264

#SPJ4

In beta-minus decay, an electron is emitted and a proton is transformed into a neutron.

Beta-minus decay is a type of radioactive decay in which an atomic nucleus emits an electron and an antineutrino. This process occurs when there is an excess of neutrons in the nucleus, causing a neutron to transform into a proton, releasing an electron and an antineutrino in the process.

The emitted electron is referred to as a beta particle and has a negative charge. The proton that is transformed into a neutron during this process remains in the nucleus, causing a decrease in the atomic number by one. Beta-minus decay is an important process in nuclear physics and is used in a variety of applications, including radiometric dating and nuclear medicine.

To know more about the Beta-minus decay visit:

https://brainly.com/question/29073741

#SPJ11

Thermoses work by minimizing heat transfer. Heat transfer occurs in three ways: conduction, convection, and radiation. A thermos is designed to reduce all three types of heat transfer. The thermos is made up of two layers of glass with a vacuum in between, which helps to minimize heat transfer through conduction. The lid is also designed to reduce heat transfer through convection. It has a tight seal that prevents air from entering or leaving the thermos, which helps to minimize heat transfer through convection. Finally, the thermos is often coated with a reflective material that helps to reduce heat transfer through radiation. Overall, the combination of these factors makes a thermos a highly effective tool for keeping liquids hot or cold for extended periods.
Hi! Thermoses work because they minimize three main kinds of heat transfer: conduction, convection, and radiation. The design of a thermos includes a vacuum layer between the inner and outer walls, which prevents conduction and convection. The reflective coating on the inner wall reduces heat transfer through radiation. By minimizing these types of heat transfer, thermoses effectively keep hot liquids hot and cold liquids cold for an extended period.

To know more about Thermoses work visit:

brainly.com/question/19596740

#SPJ11

The value of k can be found by solving the equation above for k, and substituting the values of m, dx(0)/dt, and F_applied into the expression for the natural frequency to find the value of ω. So, displacement k = [tex](2mdx(0)/dt)/(x(0)^2) - (F_a*dt^2)/m^2[/tex]

The natural frequency of the structure, we need to solve the equation of motion for small oscillations about the equilibrium position. We can assume that the acceleration and displacement times are the same and use the small-angle approximation to simplify the calculations.

Motion for the structure is:

[tex]m*d^2x/dt^2 = k*x[/tex]

[tex]mw^2 = kA^2[/tex]

a = (F_applied)/m

dx/dt = a*dt

dx/dt = (F_applied)/m*dt

dt gives:

[tex]d(dx/dt)/dt = (F_a)/m\\d^2(dx/dt)/dt^2 = F_a/m^2[/tex]

[tex]d^2(dx/dt)/dt^2 = (F_a)/m^2*dt^2\\d^3(dx/dt)/dt^3 = (F_a*dt^2)/m^2[/tex]

k = [tex](2mdx(0)/dt)/(x(0)^2) - (F_a*dt^2)/m^2[/tex]

Therefore, the value of k can be found by solving the equation above for k, and substituting the values of m, dx(0)/dt, and F_applied into the expression for the natural frequency to find the value of ω.  

Learn more about displacement Visit: brainly.com/question/28370322

#SPJ4

Correct Question:

Assuming the acceleration and displacement times are the same, determine the natural frequency of the structure. discuss how you found the result.

If the distance between two charged point-like objects is increased by a factor of 4, the force between them will decrease by a factor of 16, or F/16.

When two charged point-like objects are separated by a distance R, the force between them is F. This relationship is described by Coulomb's law,

which states that the force between two charged particles is proportional to the product of their charges and inversely proportional to the square of the distance between them.

Therefore, if the distance between the particles is quadrupled, or increased by a factor of 4, the force between them will be reduced by a factor of 16, or F/16.

This is because the inverse square relationship means that the force decreases rapidly as the distance between the particles increases. This result can be derived mathematically by substituting 4R for R in Coulomb's law and simplifying the expression.

To learn more about : force

https://brainly.com/question/12970081

#SPJ11

Answer: Manipulated Variable

Explanation:

The thing that is changed on purpose is called the manipulated variable. Sometimes it is also called the independent variable, the scientist may change this to discover something new or change it for better results.

The work required to stretch the spring from 24 cm to 27 cm is approximately 4.50 J (joules). To calculate the work required, we can use Hooke's Law and the formula for work done on a spring:

Hooke's Law:

F = k × x,

where F is the force, k is the spring constant, and x is the displacement from the natural length.

First, we need to find the spring constant (k).

We are given that a 20-N force is required to stretch the spring to 30 cm (a 6 cm displacement).

20 N = k × 6 cm
k = 20 N / 6 cm ≈ 3.33 N/cm

Now, we can find the work (W) required to stretch the spring from 24 cm to 27 cm (a 3 cm displacement).

The formula for work done on a spring is:

W = (1/2) × k × (x₁² - x₂²),

where x₂ is the final displacement and x₁ is the initial displacement.

W = (1/2) × 3.33 N/cm × (3 cm² - 0 cm²)
W ≈ 4.50 J

To stretch the spring from 24 cm to 27 cm, approximately 4.50 J of work is required.

To know more about Hooke's Law, visit:

https://brainly.com/question/29126957

#SPJ11