A new planet is discovered orbiting a star with a mass of [tex]3.5\times 10^{31}[/tex] kg at a distance of [tex]1.2\times10^{11}[/tex] m. Assume that the orbit is circular. What is the orbital speed of the planet? What is the orbital period of the planet?

Answer:

Explanation:

To solve this problem, we can use the principle of conservation of energy, which states that the initial mechanical energy of the marble (kinetic energy) is equal to its final mechanical energy (potential energy plus kinetic energy), neglecting any losses due to friction:

Initial kinetic energy = Final potential energy + final kinetic energy

1/2 mv^2 = mgh + 1/2 mv_f^2

where m is the mass of the marble, v is its initial speed, h is the height the marble reaches before coming to a stop, and v_f is the final speed of the marble (which is zero in this case).

(a) To find the distance the marble travels up the plane before coming to a stop, we need to find the height h, which we can do by solving the above equation for h:

h = (1/2 v^2)/(g sinθ)

where g is the acceleration due to gravity (9.8 m/s^2) and θ is the angle of inclination of the plane (which is not given in the problem, so we'll assume it's 30 degrees).

Plugging in the given values, we get:

h = (1/2 × 7.0^2)/(9.8 × sin30) = 6.4 m

Therefore, the marble travels 6.4 meters up the plane before coming to a stop.

(b) To find the time it takes the marble to travel up the plane, we can use the kinematic equation:

v_f = v_i + at

where v_i is the initial velocity (7.0 m/s), v_f is the final velocity (zero), a is the acceleration of the marble, and t is the time it takes to travel up the plane.

The acceleration of the marble can be found using the component of gravity along the plane, which is given by:

a = g sinθ

Plugging in the values, we get:

0 = 7.0 + (9.8 sin30)t

Solving for t, we get:

t = (7.0/4.9) sec = 1.4 sec

Therefore, the marble takes 1.4 seconds to travel up the plane.

The final velocity of the object is 8.96 m/s. The result is obtained by using the formula for work which equal to change in kinetical energy.

The force acting on the object is doing work on the object, which is equal to the change in kinetic energy of the object. We can use the following formula to solve for the final velocity.

Change in Kinetic Energy = Work

½m (v₁ - v₀)² = W

We have

Find the final velocity! (v₁ = ?)

Using the equation above, we can solve for the final velocity.

½(0.42) (v₁ - 3.4)² = 6.5

(v₁ - 3.4)² = 30.95

v₁ - 3.4 = √30.95

v₁ = 5.56 + 3.4

v₁ = 8.96

Hence, the final velocity of the object is 8.96 m/s.

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The statement "the resistivity of a wire is zero when no current is passing through it" is false. The resistivity of a wire is determined by the material the wire is made from and does not change when current is passed through it.

The measure of the resistance of a material to the movement of electrical current is called resistivity. It is calculated by taking the resistance of the object's cross-sectional area and length. The resistance of an object is defined as the ratio of the voltage drop across the object's terminals to the current that passes through it.

The definition of resistivity also implies that it is a property that is constant at a given temperature, and it is a characteristic of the material that is independent of its shape or size. Resistance is a characteristic of an object that depends on its size, shape, and material. It is the inherent opposition of a material to the flow of an electric current through it.

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Answer:

0.835cm or 1.145cm

Explanation:

We know that in simple harmonic motion, the speed is at its maximum at the equilibrium point (midpoint) and zero at the amplitude. Therefore, we need to find the displacement from the midpoint where the speed is half of its maximum.

Let's start by finding the maximum velocity. We know that the velocity is given by:

v = Aωcos(ωt)

where A is the amplitude, ω is the angular frequency, and t is the time. At the equilibrium point, where the displacement is zero, the velocity is at its maximum. Therefore:

v_max = Aω

Next, we need to find the velocity when the speed is half of v_max. The speed is given by the absolute value of the velocity:

speed = |v| = Aω|cos(ωt)|

When the speed is half of v_max, we have:

Aω|cos(ωt)| = 0.5v_max

Substituting v_max = Aω, we get:

|cos(ωt)| = 0.5

Since the cosine function oscillates between -1 and 1, we have two possible solutions:

cos(ωt) = 0.5 or cos(ωt) = -0.5

Solving for ωt, we get:

ωt = arccos(0.5) = π/3 or ωt = 2π/3

or

ωt = -arccos(0.5) = -π/3 or ωt = -2π/3

We only need to consider the positive solutions, since displacement is always positive. Therefore:

ωt = π/3 or ωt = 2π/3

The displacement corresponding to these times can be found using the equation for displacement in simple harmonic motion:

x = Acos(ωt)

Substituting ωt = π/3, we get:

x = 1.67cos(π/3) = 0.835 cm

Substituting ωt = 2π/3, we get:

x = 1.67cos(2π/3) = 1.145 cm

Therefore, the particle's speed equals one half of its maximum speed at a positive displacement of either 0.835 cm or 1.145 cm from the midpoint of its motion.

The resistance of a resistor which produces heat energy at a rate of 166.0 W when a current 6.44 A is run through it is: 25.8 ohms

The resistance of a resistor which produces heat energy at a rate of 166.0 W when a current 6.44 A is run through it can be determined using Ohm's Law. According to Ohm's Law, resistance is equal to the voltage divided by the current.

Therefore, in this case, the resistance can be calculated by dividing the voltage of 166.0 W by the current of 6.44 A, which results in a resistance of 25.8 ohms.

This resistance is known as electrical resistance and is measured in ohms. When a current runs through a resistor, it produces heat energy. The amount of heat energy produced is directly proportional to the current and resistance.

Thus, a higher resistance will lead to more heat energy produced. In the example, a current of 6.44 A with a resistance of 25.8 ohms produces 166.0 W of heat energy.

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The major objective of a flyby spacecraft is to watch and record without getting snared by the planet's gravity, which is why flyby spacecraft should not be mistaken with orbiter spacecraft.

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The speed acquired by the body is 49m/s and 59m/s respectively.

The speed can be calculated using the formula:

v= u + gt,  where v= final speed, u= initial speed = 0 for a freely falling body, g= acceleration due to gravity, t= time.

The speed acquired by a freely falling object 5 seconds after being dropped from a rest position is 49 m/s. This is because an object dropped from rest will accelerate at a rate of 9.8 m/s², so after 5 seconds it will be moving at a speed of 5 * 9.8 = 49 m/s.

The speed 6 seconds after being dropped from a rest position is approximately 59 m/s. This is because an object dropped from rest will accelerate at a rate of 9.8 m/s², so after 6 seconds it will be moving at a speed of 6 * 9.8 = 58.8 m/s.

In summary, the speed of an object dropped from rest 5 seconds after being dropped is 49 m/s, and 6 seconds after it is approximately 59 m/s.

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On an asteroid that is twice as far as Earth is from the sun, the strength of sunlight would be c. a quarter as great as on Earth.

Sunlight or solar radiation is the main source of energy that drives climate and weather patterns on Earth. The amount of solar radiation reaching Earth varies depending on the distance of the Earth from the Sun.

An asteroid is a small rocky body orbiting the sun. It is too small to be called a planet, and is instead classified as a minor planet, which is a term used for any astronomical object that is neither a planet nor a comet. They are primarily composed of materials that formed the solar nebula, a disk-shaped cloud of gas and dust left over after the formation of the solar system.Therefore, the strength of sunlight on an asteroid that is twice as far as Earth is from the sun would be a quarter as great as on Earth.

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A diffraction grating has 2,210 lines per centimeter, the angle of the first-order maximum is for 500 nm wavelength green light is: 11.27 degrees

The first-order maximum for 500 nm wavelength green light will occur at an angle of approximately 10.4° when using a diffraction grating with 2,210 lines per centimeter. Diffraction occurs when waves, such as light waves, encounter an obstruction or apertures, and their wave-like behavior is revealed.

The angle of diffraction is related to the wavelength of light and the separation between the lines of the diffraction grating. The angle of the first-order maximum for 500nm wavelength green light at a diffraction grating with 2,210 lines per centimeter can be determined using the equation:

[tex]θ = sin-1(λ/d)[/tex]
where θ is the angle of the first-order maximum, λ is the wavelength of the light, and d is the spacing between the lines of the diffraction grating.

In this case, λ is 500nm and d is 2,210 lines per centimeter, so:
[tex]θ = sin-1(500/2210)[/tex]
Solving for θ yields an angle of 11.27 degrees.

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The method of trying different approaches to solve a problem until one works is called trial and error.

It involves experimenting with different methods or strategies until the correct solution is found. It is a common problem-solving method used in many fields, including physics, mathematics, engineering, and computer science. It can be a time-consuming process, but it can also be an effective way to arrive at a solution when other methods fail.

What is trial and error method?

The trial and error method is a problem-solving strategy that involves experimenting with different solutions or approaches until the correct one is found. This method is commonly used when the problem is complex or the solution is not obvious. The trial and error method involves trying different approaches, observing the results, and adjusting the approach until the desired outcome is achieved. It is often a time-consuming process but can be effective in finding solutions when other methods fail.

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The voltage waveform is more sinusoidal than the current waveform.

This is because the voltage source is assumed to be an ideal source, which means that the voltage is supplied without loss or fluctuation while the current waveform is distorted due to the loads present in the circuit. When a voltage waveform is applied to a circuit with inductance and capacitance, the resulting current waveform will be distorted and will not be sinusoidal. The current waveform is affected by the presence of capacitance and inductance in the circuit, which cause the current to lag behind the voltage. The current waveform becomes more distorted as the load resistance increases.

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When the whole mass accelerates together as a single entity, the acceleration of the system is 0.62 m/s²

To determine the acceleration of the system, the mass on one end of the rope must be subtracted from the mass on the other end of the rope.

The mass of each child is 30 kg. The number of children is 13.

Therefore, 30 x 13 = 390 kg is the total mass of the children.

The mass of each parent is 60 kg. There are five parents.

So the total mass of the parents is 5 x 60 = 300 kg.

Total mass is the sum of the masses of the parents and children, which is 300 + 390 = 690 kg.

The force applied by the children is 150 N/child, and there are 13 children

So the total force applied by the children is 150 x 13 = 1950 N.

The force applied by the parents is 475 N/adult, and there are five parents, so the total force applied by the parents is 475 x 5 = 2375 N.

The net force is the difference between the forces applied by the children and the forces applied by the parents, which is 425 N to the east (2375 N - 1950 N).

Use the formula F = ma, where F is force, m is mass, and a is acceleration, to determine the acceleration of the system. The formula should be rearranged to solve for acceleration. a = F/m

Substitute the values into the formula:

a = 425 N / 690 kg

acceleration:a = 0.62 m/s²

Therefore, the acceleration of the system is 0.62 m/s².

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The voltage is V = I × R = 5 ohms.

The voltage across a 5 ohm resistor when the switch has been in position a for a long time is determined by Ohm’s Law.

This law states that the voltage (V) across a resistor is equal to the current (I) through it multiplied by the resistance (R). Therefore, the voltage across the 5 ohm resistor is V = I × R = 5 ohms.

This voltage can also be found by considering the flow of electrons. In a circuit with a battery and a switch, electrons flow from the positive terminal of the battery to the negative terminal.

When the switch is in position a, the 5 ohm resistor is in the path of the electrons and acts as a barrier.

This resistance causes the electrons to slow down and the voltage across the resistor is determined by the amount of this resistance.

The voltage across the 5 ohm resistor when the switch has been in position a for a long time is determined by Ohm’s Law and the amount of resistance the resistor provides. The voltage is V = I × R = 5 ohms.

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Answer: There are actually multiple limitations.

Explanation:

Some limitations of this model could be:

The distances between the objects are not accurately represented.

The model does not show the orbits of the planets around the Sun.

The model does not show the relative distances between the planets.

Hope this helps, and have a great day!

The general process by which a large diffuse cloud of gas turns into a star and surrounding planets are known as: star formation.

The Star Formation process starts with a giant molecular cloud of gas and dust, where the gravitational forces act on the cloud and it collapses under its own gravity. This collapse results in a disc-like structure, which is also known as a protoplanetary disc, and has the potential to form planets.

The center of the disc gets hotter and denser, and eventually, nuclear fusion begins, resulting in the formation of a star. The protoplanetary disc contains a lot of dust and gas, and as the temperature increases, some of the minerals and elements present in the dust start to melt and then solidify, eventually forming small planetesimals, which aggregate to form the larger planets.

As the planets move around in the disc, they can migrate inward and outward, and some can collide and merge with others, thus forming even larger planets.

The remaining gas and dust in the disc are eventually swept up by the planets or blown away by the star's radiation, and the planets settle into stable orbits. This is the general process by which a large diffuse cloud of gas turns into a star and surrounding planets.

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Thermionic diodes are the most widely used diodes because of their small size and weight, this statement is: false.

While thermionic diodes are still used in some applications, they are not the most widely used diodes.Thermionic diodes work by using the emission of electrons from a heated cathode, which then travel across a vacuum to a cooler anode.

This is also called a vacuum diode. While this technology was the basis for early electronics, it has largely been replaced by semiconductor diodes, which are much smaller, more efficient, and easier to manufacture.

Semiconductor diodes, such as silicon or germanium diodes, are used in a wide variety of applications, including rectifiers, voltage regulators, and switching circuits. They are small and lightweight, making them ideal for use in electronic devices such as cell phones, computers, and other portable electronics.

Additionally, semiconductor diodes have a much longer lifespan than thermionic diodes, making them a more reliable choice. While thermionic diodes may still be used in some specialized applications, such as in high-power vacuum tubes or in some scientific instruments, they are no longer the most widely used diodes.

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Well, materials may feel colder than others because they could:

So those are why they may feel colder

But . . .

Some items could be hotter becuase:

Those are my reasons why they can either be colder or hotter

If the guy on the left starts to pull on the pole, they will meet in the middle since the pole is massless and the surface is frictionless.

If the two guys are holding onto a massless pole and standing on horizontal frictionless ice, then there is no net external force acting on the system, and the center of mass of the system will remain stationary. When the guy on the left starts to pull on the pole, he exerts a force on the pole to the left. According to Newton's third law, the pole exerts an equal and opposite force on the guy to the right, causing him to move to the right.

The position where they will meet depends on the magnitudes of the forces that the guy on the left exerts on the pole and the distance between the two guys. If we assume that the guys initially hold the pole at its center of mass, then we can use the principle of conservation of momentum to determine where they will meet.

Since the center of mass remains stationary, the initial momentum of the system is zero. After the guy on the left starts pulling, the system gains a net momentum to the left equal to the force that he exerts on the pole multiplied by the time that he pulls. In order to conserve momentum, the guy on the right must move an equal distance to the right.

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The maximum potential difference between the two parallel conducting plates separated by 0.61 cm of air is approximately 18,300 volts, assuming a uniform electric field between the plates.

The greatness of the most extreme likely distinction between two equal directing plates isolated by 0.61 cm of air relies upon the electric field strength between the plates and the distance between them. On the off chance that the plates are associated with a voltage source, the expected contrast between the plates will be equivalent to the voltage provided. Be that as it may, in the event that there is no voltage source and the plates are uncharged, the most extreme potential contrast still up in the air by the breakdown voltage of air, which is around 3 million volts for each meter.

Expecting a uniform electric field between the plates, we can compute the potential contrast utilizing the condition V = Ed, where V is the likely distinction, E is the electric field strength, and d is the distance between the plates.

Utilizing the breakdown voltage of air and the distance between the plates of 0.61 cm (0.0061 m), we can compute the greatest likely distinction as follows:

V = Ed = (3,000,000 V/m) * (0.0061 m) = 18,300 volts

Consequently, the greatest likely contrast between the two equal directing plates isolated by 0.61 cm of air is roughly 18,300 volts, expecting a uniform electric field between the plates.

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The wavelength of the colored light is 4.00 x [tex]10^{-7}[/tex] m, or 4.00 x [tex]10^{-4}[/tex] cm.

The wavelength of a certain colored light with a frequency of about 7.5 x [tex]10^{14}[/tex] Hz can be calculated using the following equation: wavelength (λ) = velocity of light (c) / frequency (f). The velocity of light is a constant, so it is equal to 3.00 x [tex]10^{8}[/tex] m/s.

Plugging the given frequency into the equation, we get: λ = 3.00 x [tex]10^{8}[/tex]  m/s / 7.5 x [tex]10^{14}[/tex] Hz
Solving for wavelength, we get:
λ = 4.00 x [tex]10^{-7}[/tex] m, or 4.00 x [tex]10^{-4}[/tex] cm
This means that the wavelength of the colored light is 4.00 x [tex]10^{-7}[/tex] m, or 4.00 x [tex]10^{-4}[/tex] cm.

To summarize, the frequency of the colored light is 7.5 x [tex]10^{14}[/tex] Hz, and the corresponding wavelength is 4.00 x [tex]10^{-7}[/tex] m, or 4.00 x [tex]10^{-4}[/tex] cm. This can be calculated by using the equation: wavelength (λ) = velocity of light (c) / frequency (f).

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To drain a 6.0-V battery that can store 500.0 J of energy, the charge that must flow between the battery's terminals is 8,333 Coulombs. This is because the energy stored in a battery is equal to the voltage multiplied by the charge. Therefore, 500.0 J = 6.0 V x Q, where Q is the charge.

Solving for Q, we find that the charge must be 8,333 Coulombs. The voltage of the battery will remain the same until it is completely drained. This is because the voltage of a battery is a measure of the electric potential difference between the two terminals, and this does not change until all the energy stored in the battery has been transferred out. So, to completely drain the battery, 8,333 Coulombs of charge must flow between the battery's terminals.

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When a block is tied to a post with a cable and rotating with a constant velocity, on a horizontal smooth surface, the direction of its acceleration is towards the center of rotation.

Acceleration is a vector quantity that represents a change in velocity in terms of magnitude and direction. When an object changes direction, it is accelerating, and its direction of acceleration is perpendicular to its direction of motion. When an object rotates with a constant velocity, its speed remains constant, but its direction changes continuously. As a result, it is continuously accelerating towards the center of rotation, as in the case of a block tied to a post with a cable rotating on a horizontal smooth surface.

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The torque applied to the wrench can be calculated using the formula:

torque = force x distance

where force is the perpendicular force applied, and distance is the distance from the axis of rotation at which the force is applied.

So, torque = 15 N x 0.5 m = 7.5 Nm

However, since the force moves a distance of 10 cm as it turns, the work done is:

work = force x distance moved = 15 N x 0.1 m = 1.5 J

This means that some of the energy applied by the force is lost to friction or other factors, and not all of it is converted into torque.

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The electrostatic engines obtaining the highest degree of conversion of electric power into thrust and having the longest operational lifetime are also called electrospray thrusters.

Electrospray thrusters are a type of ion thruster that uses electrostatic forces to generate thrust, making them highly efficient and fuel-saving propulsion systems.
Electrospray thrusters use an electrical charge to atomize a propellant and accelerate it in a way that produces thrust. The electrical charge is created by an electrical field that ionizes the propellant and accelerates it out of the engine, resulting in high specific impulse and a long operational lifetime. The propellant is typically a liquid such as xenon, krypton, or argon.

As the propellant is atomized and accelerated, the electrostatic force pushes the ions away from the engine, creating thrust. This type of thruster is typically used in low-power and medium-power applications, such as CubeSats, nanosatellites, and interplanetary missions.

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The star is moving away from the observer. An observer on the Earth measured the wavelength of a photon as 768 nm, while the photon's rest wavelength was 780 nm.

What is the Doppler effect?

According to the Doppler effect, if the wavelength of the wave is measured at different positions, it will shift. In this situation, the observer on the Earth is seeing a shift in the photon's wavelength due to the motion of the star.

To be more specific, when the star moves away from the observer, the observer observes an increase in the wavelength. Therefore, the star is moving away from the observer.

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When two marbles of different masses collide, their velocities will change depending on the masses and the collision force. In this case, the 27.8 g marble was traveling to the right at 21.0 cm/s and overtook the 13.9 g marble traveling in the same direction at 11.5 cm/s.

After the collision, the 13.9 g marble moved to the right at 23.9 cm/s. The velocity of the 27.8 g marble after the collision can be calculated by applying the conservation of momentum.

Momentum is the product of mass and velocity, and when two objects collide, the total momentum is conserved. This means that the sum of the momentum of the two marbles before the collision must be equal to the sum of the momentum after the collision.

Thus, the velocity of the 27.8 g marble after the collision can be calculated by subtracting the momentum of the 13.9 g marble after the collision from the momentum of the 27.8 g marble before the collision. The resulting velocity of the 27.8 g marble after the collision is 17.1 cm/s.

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The possible direction in which an electromagnetic wave is traveling if the electric field is oscillating along the z-axis and the magnetic field is oscillating along the x-axis is the y-axis.

An electromagnetic wave is composed of two mutually perpendicular fields that oscillate perpendicular to the direction of the wave's propagation. They are the electric field and the magnetic field. An electromagnetic wave is created when a charged particle is accelerated. These waves can travel through a vacuum or any medium, including air and water, at the speed of light.

In this scenario, the electric field of the wave oscillates along the z-axis, while the magnetic field oscillates along the x-axis. As a result, the wave's propagation direction must be perpendicular to both fields. As a result, the wave must be propagating along the y-axis.This is why it's critical to comprehend the interplay between electric and magnetic fields in the context of electromagnetic waves.

It's also critical to recognize that an electromagnetic wave's direction of propagation is always perpendicular to the oscillation directions of the two fields, which are mutually perpendicular to each other.

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The pressure of a fluid that comes out of a pipe that was closed on both ends, but then is opened up on one end is equal to the atmospheric pressure.

This is because when the pipe was closed, the pressure inside the pipe is equal to the atmospheric pressure outside the pipe. When one end is opened, the pressure inside the pipe is still equal to the atmospheric pressure outside the pipe, so the pressure of the fluid that comes out is equal to the atmospheric pressure.

When a pipe that has been closed on both ends is opened at one end, the pressure of the fluid that comes out of the pipe is given by Bernoulli's principle.

The principle of Bernoulli states that the sum of pressure and kinetic energy per unit volume of an incompressible fluid is constant at all points along a streamline. If the fluid flows through a narrow constriction, the fluid's velocity must increase to maintain the mass flow rate (conservation of mass).

Bernoulli's principle can be represented mathematically as:

P + 1/2ρv² + ρgh = constant

where P is pressure, ρ is density, v is velocity,g is the gravity constant, h is the height

Therefore, the pressure of a fluid that comes out of a pipe that is opened up on one end is equal to the atmospheric pressure.

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To move an electron from infinitely far away to the origin, the amount of work done in electron volts is -13.6 eV.

When an electron is at infinity from the origin, its potential energy is zero. At the origin, the potential energy of the electron is -13.6 eV. This means that if an electron is brought from infinity to the origin, the electron gains -13.6 eV of potential energy.

The amount of work done to move the electron can be calculated by using the formula: W = ΔPE where W is the work done, and ΔPE is the change in potential energy of the electron.

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Yes, you will accelerate when you throw a heavy rock forward while standing on a frictionless surface. You will accelerate in the opposite direction to the rock.

The laws of motion developed by Sir Isaac Newton illustrate that an object in motion stays in motion unless an external force acts on it. So, when you toss a heavy rock forward on a frictionless surface, the rock will continue moving in the forward direction until something stops it.

The force that pushes the rock forward is equivalent in magnitude to the force that pushes you backward. Thus, the rock's mass is higher than yours; it will travel further than you, and you will accelerate in the opposite direction to the rock.

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