a roller coaster needs to complete a vertical loop that has radius 10 m what must its minimum speed be at top of loop ?

The magnitude of the centripetal acceleration of the child is F = 160 N.

We can solve this problem using the concept of centripetal force. The centripetal force is the force that keeps an object moving in a circular path, and is given by:

[tex]F = mv^2/r[/tex]

where F is the centripetal force, m is the mass of the object, v is its velocity, and r is the radius of the circle.

In this problem, the 30-kg child is sitting 3 m from the center of the merry-go-round, which is moving with a speed of 4 m/s. We can calculate the centripetal force acting on the child as follows:

[tex]F = mv^2/r[/tex]

F = (30 kg)(4 m/s)^2/(3 m)

F = 160 N

Therefore, the centripetal force acting on the child is 160 N. This force is provided by the frictional force between the child and the merry-go-round, which allows the child to move in a circular path with the merry-go-round.

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The following question may be like this:

A child (30 kg) sits 4m from the center of a merry-go-round moving at an angular velocity of 2.3 rad/s. What is the magnitude of the centripetal acceleration of the child.

E_total(θ) = Σ (Eθ e^(j(kd(i-1)cos(θ) + βi)))
This expression represents the total radiated field of the array, considering the individual contributions from horizontally polarized dipole elements with the given electric field Eθ and taking into account their positions and phase shifts within the array.

To find the expression for the total radiated field of the array, we need to consider the individual contributions of each dipole element in the array and sum them up. Since the antenna elements are horizontally polarized dipoles, we can express the radiated electric field Eθ for a single dipole as:

Eθ = âθ jµ (kIol / 4πr) e^(-jkr) |cos θ|

Here, âθ represents the unit vector in the θ direction, j is the imaginary unit, µ is the permeability, k is the wave number, Iol is the current at the location of the dipole, r is the distance from the dipole, and θ is the angle between the observation point and the dipole axis.

Now, we need to consider an array of N dipoles, each with its own location and phase shift. For simplicity, let's assume that all dipoles have the same current amplitude I0 and are uniformly spaced with a distance d along the x-axis.

To find the total radiated field for the array, we need to sum the contributions of each dipole element:

E_total(θ) = Σ E_i(θ)

where E_i(θ) is the radiated field of the i-th dipole, and the summation goes from i=1 to N.

For each dipole in the array, we need to account for the phase shift due to its position along the x-axis and the additional phase shift βi introduced by the array feeding network:

E_i(θ) = Eθ e^(j(kd(i-1)cos(θ) + βi))

So, the total radiated field of the array is given by:

E_total(θ) = Σ (Eθ e^(j(kd(i-1)cos(θ) + βi)))

This expression represents the total radiated field of the array, considering the individual contributions from horizontally polarized dipole elements with the given electric field Eθ and taking into account their positions and phase shifts within the array.

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The photoelectric effect for a certain alloy has a threshold frequency of 6.90 x 10^14 hz. For light of this frequency The energy of one mole of photons is approximately 2.75 x 10^-13 kJ/mol.

To find the energy of one mole of photons, we can use the formula E = nhf, where E is the energy, n is the number of photons in a mole (Avogadro's number), h is Planck's constant, and f is the frequency.

the threshold frequency (f) = 6.90 x 10^14 Hz, Planck's constant (h) = 6.63 x 10^-34 Js, and Avogadro's number (n) = 6.022 x 10^23 mol^-1.
E = (6.022 x 10^23 mol^-1) x (6.63 x 10^-34 Js) x (6.90 x 10^14 Hz)
E = 2.754 x 10^-10 J/mol
Now, convert the energy from Joules to Kilojoules (kJ):
E = 2.754 x 10^-10 J/mol * (1 kJ / 1000 J)
E ≈ 2.75 x 10^-13 kJ/mol
So, the energy of one mole of photons for the given frequency is approximately 2.75 x 10^-13 kJ/mol.

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The relationship between the direction the stage/slide is moved and the direction of movement in the field of view is opposite to each other.

When the stage or slide is moved in one direction, the sample moves in the opposite direction within the field of view. This is due to the fact that light travels through a microscope lens and flips the image. As a result, the image seen in a microscope is inverted and reversed.The microscope's focus knobs and stage adjustments can be used to control the position of a specimen in the field of view. The stage is the platform on which the sample is placed, and the slide is the glass plate on which the sample is placed.When you move the slide, the direction of movement in the field of view is opposite to the direction in which the stage is moved. This is due to the inversion and reversal of the image caused by the microscope lens, which causes the image to appear to be moving in the opposite direction.

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Answer:

The characteristic of light behavior that best helps explain the photoelectric effect is that light carries particles called photons. When the photons of light strike the metal surface, they transfer their energy to the electrons in the metal, and if the energy of the photons is high enough, they can cause electrons to be emitted from the metal surface. This phenomenon is known as the photoelectric effect, and it was first explained by Albert Einstein in 1905.

When an ambulance with a siren emitting a whine at 1600 Hz overtakes and passes a cyclist pedaling a bike at 2.44m/s, the cyclist hears a frequency of 1590 Hz. the speed of The ambulance is 2.44625 m/s.

Since the cyclist is moving in the same direction as the ambulance, the relative speed between the two is the difference in their speeds.

Therefore, The relative speed between them is v = 1600 - 1590 = 10 Hz

For the observer, the ambulance appears to be moving away from him because the frequency heard by him is less than the actual frequency emitted by the ambulance.

 As per the Doppler effect, the following formula can be used to determine the relative velocity between the source and observer:

v = (f₂ - f₁) / f₁

where v is the relative velocity between the source and observer, f₁ is the frequency of the source, and f₂ is the frequency heard by the observer.

Substituting the given values in the above formula, we get:

v = (1590 - 1600) / 1600 = -0.00625

The relative velocity is negative because the ambulance is moving away from the cyclist.

As the cyclist is moving at 2.44 m/s, and the relative velocity between the two is -0.00625, the velocity of the ambulance can be determined as follows:

v = 2.44 - (-0.00625) = 2.44625 m/s

Therefore, the speed of the ambulance is 2.44625 m/s.

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Answer:

The name for this type of movie is "anthology film" or "portmanteau film."

The name for the type of movie where an object is passed from one person to another like The Red Violin or The Yellow Rolls Royce is called an "anthology film."

An anthology film is a type of film consisting of several short stories, often linked by a common theme or object. In this case, the object being passed from one person to another is the linking element that ties the stories together. Other examples of anthology films include Four Rooms, The Ballad of Buster Scruggs, and Pulp Fiction.

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The velocity of the elevator at the end of the fourth 5-second interval is 0 m/s.

We can use the following kinematic equation to relate the velocity of the elevator to the time elapsed: v = u + at

where v is the final velocity, u is the initial velocity (in this case, u = 0 m/s), a is the acceleration due to gravity (which is acting upward in this case), and t is the time elapsed.

From the graph, we can see that the scale reading (and hence the apparent weight of the student) is constant at 400 N during the first 20 seconds.

This means that the elevator is moving with a constant velocity during this time interval. Therefore, the velocity of the elevator at the end of the fourth 5-second interval (at 20 s) is the same as its initial velocity, which is 0 m/s.

Therefore, the velocity of the elevator at the end of the fourth 5-second interval is 0 m/s.

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The new angular momentum of the system, if each of the masses were instead a solid sphere 14.5 cm in diameter, is 0.008275 M kg · m² + 111 kg · m²/s. The mass M is unknown, so we cannot provide an exact value. However, we have shown the method to calculate the new angular momentum.

When answering questions on the Brainly platform, it is important to always be factually accurate, professional, and friendly. Additionally, one should be concise and not provide extraneous amounts of detail. Typos or irrelevant parts of the question should be ignored. When using specific terms, such as in the provided student question, one should incorporate those terms into the answer for clarity and accuracy.

The angular momentum of the system about the origin is given by:L = L1 + L2, whereL1 = I1ω1L2 = I2ω2I1 and I2 are moments of inertia and ω1 and ω2 are angular velocities.Let's assume that the rod is massless, and the masses m1 and m2 are concentrated at their ends, so we can write:I1 = m1r1², I2 = m2r2²where r1 = l/2 and r2 = l/2.I1 = (1/3)m1(l/2)² and I2 = (1/3)m2(l/2)²

The total moment of inertia of the system about the pivot point is:I = I1 + I2 = (1/3)(m1 + m2)(l/2)²The angular momentum of the system is:L = (1/3)(m1 + m2)(l/2)²(ω1 + ω2)When the speed of each particle is 6.40 m/s, we haveω1 = v1/r1 = 6.40/(l/2)ω2 = v2/r2 = 6.40/(l/2)So,L = (1/3)(m1 + m2)(l/2)²(2ω1) = (1/3)(m1 + m2)(l/2)²(2ω2)Therefore, L = (1/3)(m1 + m2)(l/2)²(2ω), whereω = ω1 = ω2 = 6.40/(l/2)The angular momentum of the system is L = (1/3)(m1 + m2)(l/2)²(2ω) = (1/3)(4.6 kg)((2.00 m)/2)²(2(6.40 m/s)) = 111 kg · m²/s.

If each of the masses were instead a solid sphere 14.5 cm in diameter, we can calculate the moment of inertia for each sphere. A solid sphere of uniform density has moment of inertia:I = (2/5)MR²where M is the mass of the sphere and R is the radius. Since the diameter is given as 14.5 cm, we have R = 7.25 cm = 0.0725 m. Thus:I = (2/5)M(0.0725 m)²The new moment of inertia for the system will be:I' = I + I + (1/3)(m1 + m2)(l/2)²where I is the moment of inertia of each sphere about its own center of mass.

So,I' = (2/5)M1(0.0725 m)² + (2/5)M2(0.0725 m)² + (1/3)(m1 + m2)(l/2)²We know that each sphere has a diameter of 14.5 cm, so its radius is 7.25 cm or 0.0725 m. Let the mass of each sphere be M. Therefore, I = (2/5)MR² = (2/5)M(0.0725 m)².Substituting the values,I' = 2(2/5)M(0.0725 m)² + (1/3)(4.6 kg)((2.00 m)/2)²= 0.008275 M kg · m² + 111 kg · m²/s

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Based on the information, we can infer that the correct answer is D. Frequency and wavelength are directly proportional, and pitch is the perception of frequency.

Sound waves are longitudinal waves that travel through a medium, such as air or water. The frequency of a sound wave refers to the number of cycles of compression and rarefaction that occur in one second, measured in Hertz (Hz). The wavelength of a sound wave refers to the distance between two consecutive points in the wave that are in phase, such as the distance between two consecutive compressions or rarefactions.

The pitch of a sound refers to how high or low it sounds to a listener. This perception of pitch is directly related to the frequency of the sound wave. A higher frequency sound wave produces a higher-pitched sound, while a lower frequency sound wave produces a lower-pitched sound.

Therefore, as the frequency of a sound wave increases, so does its pitch, while the wavelength decreases. Conversely, as the frequency decreases, the wavelength increases, and the pitch becomes lower.

In the case of the chirping bird, the students in the Physics classroom can observe that as the frequency of the bird's chirping increases, the pitch of the sound also increases, while the wavelength decreases. This relationship between frequency, wavelength, and pitch is an important concept in the study of sound waves and acoustics.

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a) Volume = 2.07074454 m^3. b) Heater needs to be on for approximately 45.7 minutes.

The issue gives us the underlying states of an unbending tank containing an immersed fluid fume blend of water at a strain of 100 kPa. The absolute mass of the blend is 5 kg, with just 75.6% of it being fluid. We are approached to decide the volume of the compartment and the time the electric opposition radiator should be turned on until all the water has disintegrated.

To address for the volume of the compartment, we first need to track down the particular volume of the underlying combination. Utilizing the given data that 75.6% of the complete mass is fluid, we can find the mass of the fluid and utilize the steam tables to decide the particular volumes of the immersed fluid and fume at 100 kPa. With this data, we can compute the absolute volume of the combination. The subsequent volume is around 2.07074454 m^3.

To make the opportunity expected for the radiator to disintegrate all the fluid, we can utilize the energy balance condition. We decide the energy expected to disintegrate all the fluid utilizing the particular enthalpy of the immersed fume at 100 kPa and the particular enthalpy of the soaked fluid at 100 kPa. We then, at that point, partition this energy by the force of the radiator, which is a consistent 3.4 kW, to get the time expected for the warmer to disintegrate all the fluid. The subsequent time is roughly 45.7 minutes.

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The total force on an object is calculated by multiplying its mass by its acceleration, and not the other way around

As a question answering bot on the Brainly platform, I will provide you with a brief guide to the best practices you should adopt when answering questions.

1. Always be factually accurate, professional, and friendly: Answering questions on Brainly requires you to maintain a professional tone and show friendliness to users. Your response should be free of errors, accurate, and backed by reliable sources.

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For example, if a question is about Newton's laws of motion, you should use terms such as acceleration, force, mass, motion, and others. Answer: The following statement about one of Newton's laws of motion is not correct:

the total force on an object is calculated by multiplying its mass times its acceleration. This statement is incorrect because the correct statement is that force is calculated by multiplying mass and acceleration.

Newton's second law of motion states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. .

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The internal resistance of the battery is 0.5 ohms.

The opposition to current flow inside a battery is known as its internal resistance or IR. Ionic resistance and electrical resistance are the two fundamental factors that affect a battery's internal resistance. One of the metrics used to determine a battery's capacity to transport electricity is internal resistance. The battery can handle a sizable quantity of current when the internal resistance value is low. A battery with high internal resistance, on the other hand, can only support a tiny quantity of current.

Given that,

Potential difference (V) = 11 volts

Electromotive force (E) = 12 volts

Current (I) = 2 amps

To find the internal resistance of the battery, we can use the formula:

V = E - Ir

Substituting these values, we obtain:

11 = 12 - 2r

r = 12 - 11 ÷ 2

r = 0.5 ohms.

Therefore, the internal resistance of the battery is 0.5 ohms.

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Answer:

The first step is to calculate the potential energy of the ball at the top of the first hill using the formula PE = mgh, where m is the mass of the ball, g is the acceleration due to gravity, and h is the height of the hill. PE = (8 kg) x (9.8 m/s^2) x (20 m) = 1568 J Next, we can use the law of conservation of energy, which states that the total energy of a closed system remains constant. This means that the potential energy at the top of the first hill must be equal to the kinetic energy at the bottom of the hill, since there is no external work done on the ball. So, using the formula KE = 1/2mv^2, where v is the velocity of the ball, we can solve for v: KE = 1

The Coefficient of Friction is 0.861

Let's begin by determining the initial kinetic energy of the Pellet:

K = (1/2)mv^2

K = (1/2)(0.0012 kg)(65 m/s)^2

K = 25.3875 J

Next, we need to determine the final kinetic energy of the pellet:

Kf = (1/2)mvf^2

Since the pellet is lodged in the cheese, it has no final velocity. Therefore, the final kinetic energy is 0.

Now, we can determine the work done by the frictional force:

Wfriction = K - Kf

Wfriction = 25.3875 J - 0

Wfriction = 25.3875 J

Since the cheese slides 25 cm, we know that the work done by the frictional force is equal to the force of friction multiplied by the distance the cheese slides:

Wfriction = Ff * d

25.3875 J = Ff * 0.25 m

Ff = 101.55 N

Finally, we can determine the coefficient of friction:

Ff = μ * N

101.55 N = μ * (0.120 kg * 9.81 m/s^2)

μ = 0.861

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The electric field between two parallel plates is directly proportional to the potential difference between them and inversely proportional to the distance between them. The correct answer is option: b.

We can use the formula E = V/d. In this scenario, the potential difference is 10 V and the electric field is 200 V/m. Solving for d, we get d = V/E = 10 V / 200 V/m = 0.05 m = 50 mm. Therefore, the distance between the plates is 50 mm, which corresponds to option (b). The other options can be eliminated because they either result in an electric field that is too high or too low for the given potential difference. Option b is correct.

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The maximum reading on the ammeter will be determined by the rate of change of the magnetic field through the coil, and the number of turns in the coil.

The maximum reading on an ammeter when a magnet is pulled away from a coil as quickly as possible depends on several factors. Firstly, it depends on the strength of the magnetic field of the magnet, the number of turns in the coil, and the rate of change of the magnetic field. A faster change in the magnetic field will induce a larger current in the coil and produce a higher reading on the ammeter.

Additionally, the resistance of the circuit and the sensitivity of the ammeter also play a role in determining the maximum reading. Therefore, the maximum reading on the ammeter will be higher if the magnetic field is stronger, the number of turns in the coil is larger, the rate of change of the magnetic field is faster, the resistance of the circuit is lower, and the sensitivity of the ammeter is higher.

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--The complete question is, On what factors does the maximum reading on the ammeter when the magnet is pulled away from the coil as quickly as possible?--

Answer:

We know that momentum (p) of an electron is given by:

p = mv

where m is the mass of the electron and v is its velocity.

The momentum of a photon is given by:

p = h/λ

where h is Planck's constant and λ is the wavelength of the photon.

Given that the momentum of the electron and photon are the same, we can set these two expressions equal to each other:

mv = h/λ

Solving for the velocity of the electron:

v = h/(mλ)

Now, the kinetic energy (K) of the electron can be calculated as:

K = 1/2 mv^2

Substituting the expression for v, we get:

K = h^2/(2mλ^2)

The energy (E) of the photon is given by:

E = hc/λ

where c is the speed of light.

Substituting the given wavelength, we get:

E = hc/66.8 nm

Using the values for Planck's constant (h) and the speed of light (c), we get:

E = (6.626 x 10^-34 J s)(3.00 x 10^8 m/s)/(66.8 x 10^-9 m)

E = 2.977 x 10^-18 J

Therefore, the energy of the photon is much greater than the kinetic energy of the electron.

The energy of a photon that has a wavelength of 66.8 nm is greater than that of an electron that has the same momentum.

Photons are electromagnetic waves, which means that they travel at the speed of light in a vacuum. The energy of a photon is given by the equation E = hc/λ, where E is the energy of the photon, h is Planck's constant, c is the speed of light, and λ is the wavelength of the photon.When an electron has the same momentum as a photon of wavelength 66.8 nm, its energy is given by the equation E = p^2/2m, where E is the energy of the electron, p is its momentum, and m is its mass. However, the energy of a photon with a wavelength of 66.8 nm is much greater than the energy of an electron with the same momentum.

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The volume of the helium in the balloon when the atmospheric pressure is 380 mmHg is 1520 mL.

To determine the volume of helium in the balloon, the combined gas law must be applied. The formula for the combined gas law is given by:

PV/T = constant

where P is pressure, V is volume, and T is temperature. Since the temperature and the amount of helium remains unchanged, the combined gas law can be written as P1V1 = P2V2 where P1 is the initial pressure, V1 is the initial volume, P2 is the final pressure, and V2 is the final volume.

Given that the initial pressure P1 = 760 mmHg and the final pressure P2 = 380 mmHg, the final volume V2 can be determined using:

P1V1 = P2V2

V2 = (P1V1)/P2

V2 = (760 mL)(760 mmHg)/(380 mmHg)

V2 = 1520 mL

Hence, the volume of the helium in the balloon when the atmospheric pressure is 380 mmHg is 1520 mL.

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The solenoid contains 75 turns to create a 0.295 t magnetic field at the center of the solenoid.

To find the number of turns in the solenoid, we can use the formula for the magnetic field inside a solenoid:

B = μ₀ * n * I

where B is the magnetic field strength (0.295 T), μ₀ is the permeability of free space (4π x 10⁻⁷ Tm/A), n is the number of turns per unit length (turns/m), and I is the current (7.45 A).

n = B / (μ₀ * I)
n = 0.295 T / (4π x 10⁻⁷ Tm/A * 7.45 A)
n ≈ 625.57 turns/m

Now, we need to find the total number of turns in the solenoid. Since the solenoid has a length of 12.0 cm, we need to convert that to meters:

Length = 12.0 cm * (1 m / 100 cm) = 0.12 m

Total turns = n * Length
Total turns = 625.57 turns/m * 0.12 m
Total turns ≈ 75.07

Since the number of turns must be a whole number, we can round this to the nearest whole number, which is 75 turns. So, the solenoid contains 75 turns.

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When the string breaks at point a, the ball will continue to move in a straight line tangent to the point on the circle where it broke free. The third curve most accurately represents the path the ball will take after the string breaks.

This means that the ball will continue moving in the direction it was moving at the moment the string broke. In the first curve, the ball appears to continue moving in a circle, which is not possible as it has lost its centripetal force.

The second curve shows the ball moving in a straight line in the direction of its velocity at point a, which is the correct direction. However, the curve appears to be too steep as the ball should continue moving in a straight line with constant velocity. The third curve shows the ball moving in a straight line with constant velocity, which is the correct behavior.

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When switch S1 is closed, the current in the circuit increases and flows through both the inductor and the resistor. The inductor opposes changes in current, so it initially behaves like a short circuit and the voltage across it is zero.

At this point,  voltage across  inductor starts to increase. When switch S2 is closed, current in the circuit starts to decrease. As a result, the voltage across the inductor will initially be greater than voltage across the resistor. The voltage across the inductor will gradually decrease as the magnetic field in the inductor collapses and  current approaches zero. Therefore, the voltage across  inductor will be larger than the voltage across the resistor at the moment switch S2 is closed.

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The light curve of a variable star, such as an RR Lyrae or Cepheid variable, contains information about the star's intrinsic brightness and its pulsation period.

A graph of a variable star's brightness over time is called a light curve. A variable star's brightness varies over time as a result of a variety of events, such as pulsations, eruptions, or eclipses. The intrinsic brightness of a variable star, such as an RR Lyrae or Cepheid variable, affects its pulsation period. By comparing the apparent brightness of a star to its intrinsic brightness, astronomers may use this connection, also known as the period-luminosity relationship, to calculate the star's distance from the Earth.

A variable star's light curve also provides details about the star's physical characteristics, including its mass, radius, and temperature. Astronomers can discover information about the star's structure and development by examining the light curve's shape and amplitude.

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When a rolling railroad car makes a perfectly elastic collision with railroad car B of the same mass, after the collision, car A is at rest. The speed of car B after the collision is equal to the initial speed of car A.

Before the collision, car A had a velocity of v, while car B had a velocity of zero because it was at rest. As a result of the collision, car A comes to a halt, while car B acquires the initial speed of car A.

Because the collision is elastic, the momentum and energy of the two cars are conserved.

A perfectly elastic collision is a collision in which both the momentum and kinetic energy of the system are conserved. This means that the total momentum and kinetic energy of the system before the collision is equal to the total momentum and kinetic energy of the system after the collision.

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There will be a maximum of 2n - 1 nodes in a binary tree with n levels. In the case of a binary tree with three levels, the maximum number of nodes is 2^3 - 1 = 7. This implies that the minimum number of nodes in a binary tree with 3 levels is seven (7).

The minimum number of nodes in a binary tree with 3 levels is seven (7).A binary tree is a tree data structure in which each node has no more than two children, which are referred to as the left and right children. The root node is at the top of the binary tree, and each node has a maximum of two child nodes.

The maximum number of nodes on each level is determined by the number of levels in a binary tree.In the first level of a binary tree, there is only one node: the root node. The root node has two children nodes in the second level, and each of those nodes has two children nodes in the third level.  

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The charge on the positive plate of each capacitor is q/2, and the potential difference across each capacitor is q/2×C1 and q/2×C2 respectively.

Assuming that the capacitors have capacitances C1 and C2, and the charge on the positive plate of each capacitor is q1 and q2 respectively. During the charging process, the battery supplies a potential difference v to the capacitors, which causes a charge q to flow through the circuit. According to the conservation of charge, the charge on the positive plate of each capacitor must be equal to q/2 (since the capacitors are in series, the charge on each capacitor is the same).

The potential difference across each capacitor can be calculated using the formula:

V = Q/C

where V is the potential difference, Q is the charge on the capacitor, and C is the capacitance.

For the first capacitor, we have:

V1 = q/2×C1

For the second capacitor, we have:

V2 = q/2×C2

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Explanation:

Potential energy = m * g * h    re-arrange to

PE/mg  = h     plug in the numbers

.06615 J / (9.81 m/s^2 * .0025 kg) = 2.7 m

Answer:

Radio waves are transmitted from a sender to a receiver.

However, these waves may be modulated.

There are two kinds of modulation:

     AM - amplitude of the electromagnetic waves is slowly changed

      FM - frequency of the electromagnetic waves is slowly modulated

A person's voice is used to modulate the waves as they are sent from the sender to the receiver.

The modulation is converted by the receiver from electromagnetic waves to audio waves.

These audio waves are used to produce an audio signal that can be interpreted by the person using the receiver.

(a) Kinetic Energy: 216 J, Potential Energy: 353.4 J. (b) Work Done: 2160 J.

(b) Total work done is equals to 2160J

(a) To find the kinetic energy (KE) and potential energy (PE) of a 12 kg cat running on a 3 m high wall with a speed of 6 m/s, we use the following formulas:

KE = 0.5 * mass * velocity²
KE = 0.5 * 12 kg * (6 m/s)²
KE = 216 J

PE = mass * gravity * height
PE = 12 kg * 9.81 m/s^²* 3 m
PE = 353.4 J

(b) To find the work done when the cat runs 10 m and then stops, we use the work-energy principle:

Work Done = Change in Kinetic Energy
Since the cat comes to a stop, the final KE is 0 J.

Work Done = Initial KE - Final KE
Work Done = 216 J - 0 J
Work Done = 2160 J

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Two objects have an electrically attractive force between them. The distance between them would have to be separated one hundred times to make the attractive force one hundred times weaker, which is ten times as much.

This attractive force is experienced by two charged particles that have opposite charges. On the other hand, two particles with the same charge experience a repulsive force. The electrical attractive force decreases as the distance between the two objects increases. This is known as Coulomb's law. By this law, the electrical force between two charged objects is directly proportional to the product of their charges and inversely proportional to the square of

the distance between them. According to the problem, the electrical attractive force between two objects is 100

times weaker when the objects are separated by a distance ten times greater than their original distance. Therefore, the objects would have to be separated to make the attractive force one hundred times weaker by a distance ten

times as much as their original distance.

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