Nuclear decay occurs according to first-order kinetics. How long will it take for a sample of chromium-51 to decay from 35. 0 grams to 10. 0 grams? the half-life of chromium-51 is 28 days.

The speed of a wave with a frequency at 46 Hz as well as a wavelength = 1.7 meters is 78.2 m/sec.

The Greek letter λ is frequently used to represent wavelength. The name wavelength is also occasionally used to refer to modulated waves, their sinusoidal envelopes, or waves created by the interference of multiple sinusoids.

The distance between each trough or the difference between each wave's crest and the next one. One of "yardsticks" used to gauge radiation levels is this. The SI unit measuring wavelength is the metre, which is frequently abbreviated as m. The wavelength of an object is measured using its multiples and fractions.

Wavelength = 1.7 m

Frequency = 46 Hz

v denotes the wave's speed, w its wavelength, and f its frequency.

f = v/w,

= 46 =v/1.7

v = 78.2 m/sec

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A body is free falling from height h now at the middle that is at h/2 the body's K.E. = P.E

What is kinetic energy?

An object's kinetic energy is the energy it has as a result of motion. Applying force is necessary if we want to accelerate an object. We have to put in work to apply force. After the work is finished, the object will be moving at a new, constant speed because energy has been transferred to it.

There are only two cases in this phenomenon to occur:-

Case 1 - Something is tossed upward

When is the change in kinetic energy equal to the change in potential energy for an object thrown upward at some beginning velocity v0? The total amount of kinetic and potential energy is constant due to energy conservation. We want to know when the kinetic energy has decreased by half because we define our potential energy as zero at the launch point.

Case 2 - Simple harmonic oscillator

A restoring force proportionate to the displacement of the mass from equilibrium distinguishes a simple harmonic oscillator (such as a mass on a spring) from other oscillators:

F=− kx

This equation's solution yields the position as x=Acos(ωt+Ф), where A denotes the oscillation's amplitude, frequency, and phase. The frequency is expressed as Ф= [tex]\sqrt{k/m}[/tex]. The derivatives of the location can be used to calculate the oscillator's velocity and acceleration, which are both sinusoidal functions.

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Its top cruising speed is 90 miles per hour. (a) I discovered that the answer to the question, "What is the maximum distance the train can travel if it accelerates from rest till it reaches," was 22.665.

Given is the formula Acceleration=Deceleration=a

Maximum cruising speed: 1 mile = 5280 feet per hour (3600 s).

Time, t = 15 min = 1 min = 60 s

initial velocity, u=0

Replace the values

Distance=D

Distance total = s+d=2178+118800=120978 feet

Total distance = 22.665 miles, which is the furthest train can go.

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The current flowing through the resistors is 0.229 A

A resistor is an electrical component that controls or restricts how much electrical current can pass across a circuit in an electronic device.

A specified voltage can be supplied via resistors to an active device like a transistor.

An electrical component with two terminals that provides electrical resistance is called a resistor.

Resistors are frequently used in electronic circuits to reduce current flow, divide voltages, block transmission signals, and bias active elements.

Given; The value of the resistors are :

R1 = 41 ohm

R2 = 41 ohm

R3 = 71 ohm

R4 = 64 ohm

V = 24 V

At t = 0 sec when there is no flow of current through resistors R2 and R3

therefore the equivalent resistance is = R1 + R4

Thus V = I * R

24/ 41 + 64 = I

I = 0.229 A

thus the current flowing through the resistors is 0.229 A

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Similarity which leads about most of the object to let the bulb light is their conducting materials.

The behaviour (ie., brightness) of the bulb when objects made out of various materials are inserted into the circuit is as-

The bulb glows when connected to conducting object but it does not glow when some objects like eraser, wood, plastic etc. are used to complete the circuit as it is the non-conducting objects.

Paper is a non-conducting object.

Coins are normally made up of silver, gold and metal alloys and we know all metals conduct electricity.

Pencil lead is made up of graphite which is non-metal still it conducts electricity as graphite contains delocalised electron (free electrons). These electrons can move through the graphite, carrying charge from place to place and allowing graphite to conduct electricity.

Human fingers are conductors as whole body of a human is an excellent conductor of electricity. This reply on the fact that our fingers is 3 parts salty water - which means it's got lots of loose electric charges floating around in it.

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The work done on the ball during one period is 66.67 J.

What is acceleration?
The rate at which the speed and direction of a moving object change over time. A point or object moving straight ahead is accelerated when it accelerates or decelerates. Even though the speed is constant, motion on a circle accelerates because the direction is constantly shifting. Both effects contribute to a acceleration for all other motions. Acceleration is a vector quantity because it has both a greater acceleration. A vector quantity is also velocity. The velocity vector change over a time interval divided by time interval is the definition of acceleration.

The amount of work done on the ball during one period is equal to the force times the distance traveled, which is equal to the mass times the centripetal acceleration times the distance traveled. Thus, the work done on the ball during one period is equal to 4 kg x (5 m/s)2 / 1.5 m = 66.67 J.

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The internal energy of a system is 1542.52 J.

What is internal energy?

The internal energy of a thermodynamic system is the total energy contained within it. It is the energy necessary to create or prepare the system in its given internal state and includes the contributions of potential energy and internal kinetic energy.

First we convert calories into joules, 530 calories =530 calories × 4.184                                                                        = 2217.52 J

Formula, ΔE = q + w

Here, the system releases heat, so q is negative

Therefore, ΔE = -q + w

Now, put the values of q and w

ΔE = -675 + 2217.52 J

ΔE = 1542.52 J

Internal energy is the sum of ability power of the gadget and the machine's kinetic strength. The alternate in internal energy (ΔU) of a response is equal to the heat gained or lost (enthalpy trade) in a reaction whilst the reaction is administered at steady pressure. inside the study of thermodynamics, a usually perfect gasoline is taken into consideration as a running substance. The molecules of an ideal gasoline are mere mass points that exert no force on each other.

The SI derived unit used to degree strength or paintings. One joule is identical to the electricity used to accelerate a body with a mass of 1 kilogram using one newton of force over a distance of one meter. One joule is also equal to one watt-second.

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No alternative is appropriate once you start a ball moving in such a frictionless bowling alley; the force required to keep it rolling is.

The friction variance along the length of modern bowling alleys is modulated by an oil coating. The coefficient of friction is typically 0.04 in oiled regions and 0.2 in unoiled portions.

What does friction have to do with bowling?

A bowling ball goes more quickly the lower its coefficient of friction. The slower a ball moves down the path, the more friction it has. The form, weight, and surface texture of the ball are only a few of the variables that determine friction. When your ball makes contact with the lane, all of these elements affect friction.

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4P₀V₀ is the work done by the gas during process 1→2→6→5→1.

Therefore, the work performed by a gas expanding against an external pressure is negative, analogous to the work performed by a system on its surroundings. In contrast, when a gas is compressed externally, V₀ and the work is positive because the environment exerts force on the system.

The gas must release some energy into the environment when it expands in response to an external pressure. The overall energy of the gas is thus reduced as a result of the negative work. When a gas is compressed, energy is transferred to it, increasing its energy as a result of positive work.

Let's consider,

Work done = -W (As the energy is released)

External pressure = P₀

Volume of gas = V₀

So, the work done can be calculated as follows:

W = P x (dV)

-W = P₀ × V₀

Now according to the process given:

1→2→6→5→1

Energy flow increases up to 6 eventually decreases with loss of factor 4.

Hence, the energy of the system (work done) is:

-W = 4 × P₀ × V₀

-W = 4P₀V₀

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If the loops are moved closer to and farther from the magnets in exactly the same way then the emf generated around the wooden loop is equal to the emf generated around the wire loop.

Electromotive force (emf) can be described as the electric potential that is produced by either changing the magnetic field or is produced by an electrochemical cell.

The emf generated around the wooden loop is equal to the emf generated around the wire loop because Faraday's law is only concerned about how the flux is changing and is therefore independent of the material involved. The loop material is not involved in the magnetic flux expression, so an emf is generated anyhow as long as it experiences a change in magnetic flux since it moves near the end of the bar magnet, changing the magnetic flux through the loop.

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These speeds 4 s later is -20 m/s.

What is Acceleration due to Gravity?

The acceleration due to gravity would affect the radial component of an object at the surface of the earth. This would seem to us that the gravitational force acting on us on a vertical axis. This means that gravity would not affect any horizontal movement.

Determine the horizontal and vertical speeds, [tex]$v_x$[/tex] and [tex]$v_y$[/tex], of the baseball after t=4 seconds. We only recognize gravity as the force acting on the object, acting only on the vertical component. This means that the horizontal speed remains the same, such that

[tex]$$v_x=16 \mathrm{~m} / \mathrm{s}$$[/tex]

Now, we determine the vertical speed after the given time, t, by applying the kinematic equation,

[tex]$$v_y=v_{0 y}-g t$$[/tex]

where[tex]$g=9.81 \mathrm{~m} / \mathrm{s}^2$[/tex] is the acceleration due to gravity and t is the time. We proceed with the solution.

[tex]$$\begin{aligned}v_y & =v_{0 y}-g t \\& =18 \mathrm{~m} / \mathrm{s}-\left(9.81 \mathrm{~m} / \mathrm{s}^2\right)(4 \mathrm{~s}) \\& \approx-20 . \mathrm{m} / \mathrm{s}\end{aligned}$$[/tex]

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It will take 2.8 s  for the elevator to stop when it is moving with a speed of 2.5m/s

1)The cable will travel a linear distance equal to the distance covered by the elevator because it is constantly taut and neither slipping nor stretching.

2) Since the cylinder makes one full rotation, the cable's length is equal to the cylinder's circumference.

3) As a result, you must determine the cylinder's circumference, which is determined using the formula C = 2[tex]\pi[/tex] radius.

The radius is half the diameter: 1.2 m / 2 = 0.6 m

Hence, C = 2π × 0.6m = 3.8m

⇒ Distance run by the elevator = 3.8m

4) Now, assuming that the elevator decelerated uniformly from its starting speed of 2.7 m/s to a complete halt (Vf = 0), you use the related formulas:

i) [tex](V_{f})^{2}[/tex]= [tex](V_{o})^{2}[/tex] - 2ad ⇒ 2ad = [tex](V_{o})^{2}[/tex]- [tex](V_{f})^{2}[/tex] ⇒ a = [tex](V_{0})^{2}-(V_{f})^{2}[/tex]/ (2d)

a = [2.7 m/s]² / (2×3.8m) = 0.96 m/s²

ii) [tex]V_{f}[/tex] =  [tex]V_{0}[/tex]- at ⇒ t = [2.7 m/s] / (0.96 m/s²) = 2.8 s

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Prolog runtime will iteratively apply the rules to all the facts to find the matches and mismatches.

In physics, color is specifically associated with the particular range of wavelengths of electromagnetic radiation visible to the human eye. Such wavelengths of radiation make up a portion of the electromagnetic spectrum known as the visible spectrum. H. Light.

So colors have a physical basis. However, our perception of it is complicated by how the human visual system works. Some people have mutations that alter their ability to process incoming light and distort their perception of color.

Opticks is one of the great works of scientific history, documenting Newton's discoveries in his experiments with light passing through a prism. He identified the colors of his ROYGBIV (red, orange, yellow, green, blue, indigo, and violet) that make up the visible spectrum.

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it take for the radiation level of potassium-42 to drop to 1/16 of its original level is 48 hours.

Radiation can be divided into four main categories: alpha, beta, neutrons, and electromagnetic waves like gamma rays.The mass, intensity, and depth to which they pierce persons and things varies between them.

A beta particle is the first.Although they can exceed 50 mSv/yr, they normally fall between 1.5 and 3.5 millisievert per year.

The worst external risk is gamma radiation.Beta burns can occur when beta particles partially penetrate the skin.Alpha rays can't go through skin that is still intact.The cells in their route can be damaged by gamma and x-rays that travel through a person.

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So moving the slit towards the laser will increase the slit and screen distance and the screen and the fringe will be bigger. The other factors such as the angle of diffraction, and wavelength will remain unaltered in this case.

What is Diffraction?

In order to enter the region of the geometric shadow cast by the obstruction or aperture, waves must interact with one another or bend around its edges, which is referred to as diffraction. A secondary source of the wave that is propagating is in fact created by the diffracting item or aperture.

What is Fringe?

The band of alternating light and dark material called a fringe is produced via interference.

The formula is used to calculate the fringe width

β=λDd

Where β represents the bandwidth, λ represents the wavelength of the light, D represents the distance between the source and the screen, d represents the distance between the two slits

Hence, moving the slit towards the laser will increase the slit and screen distance and the screen and the fringe will be bigger. The other factors such as the angle of diffraction, and wavelength will remain unaltered in this case.

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The acceleration of the dragster is 33.1 m/s².

The final velocity of the dragster is 163.4 m/s.

The acceleration of the dragster is calculated by applying the following kinematic equation.

s = ut + ¹/₂at²

where;

s = 0 + ¹/₂at²

a = ( 2s ) / t²

a = (2 x 403.1) / (4.935²)

a = 33.1 ms/²

The final velocity of the dragster is calculated as follows;

v² = u² + 2as

v² = 0 + 2(33.1)(403.1)

v² = 26,685.22

v = √ (26,685.22)

v = 163.4 m/s

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Mass moment of inertia is a quantity that measures the degree of inertia of a body for rotational motion = ML²/9

A rigid body's moment of inertia, also referred to as its mass moment of inertia, angular mass, second moment of mass, or, more precisely, rotational inertia, is a property that establishes the torque required to achieve a desired angular acceleration about a rotational axis, much like mass establishes the force required to achieve a desired acceleration.

Depending on the axis selected and the distribution of the body's mass, a change in the body's rate of rotation will need a greater torque for bigger moments.

The moment of inertia for a point mass is just the mass times the square of the distance perpendicular to the axis of rotation. This is an extensive (additive) property.

Find the attachment of answer

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According to the given photon energy formula and with the two emission lines mentioned, it can be concluded that the emission line at 627 nm represents a lower transition energy than the emission line at 450 nm.

It is given to us that -

Element C has a strong emission line around 450 nm.

There is also another emission line at 627 nm.

We have to find out the emission line that has a lower energy or higher energy transition.

We know that Transition energy is the energy required for electrons in the sample to move from one quantum state to another.

Emission spectra measure energy in the form of light emitted when energy is added to a molecule to excite it, support this electronic transition, and move from the excited quantum state to the ground state or the basic state that they were in initially.

This transition energy depends on the wavelength of the emitted radiation which can be represented as a photon energy formula such as -

E = h c / λ

Therefore, from the given photon energy formula and with the two emission lines mentioned, it can be concluded that the emission line at 627 nm represents a lower transition energy than the emission line at 450 nm.

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If we were to move a detector along the x-axis starting at S1, it would have to be moved 11.6m far before it detects no sound at all.

A sound wave is what?

A sound wave is a pressure wave, which may be conceptualized as variations in pressure over time. Transverse waves include sound waves. The tines of a tuning fork must transfer air from the fork to one's ear in order for one to hear the sound of the fork. The majority of sound waves, although not all of them, are produced by some sort of vibrating object.

What two forms of sound waves are there?

The characteristics of sound waves should be the starting point for studying sound. Transverse and longitudinal waves are the two fundamental forms of waves, and they are distinguished by how they move through space.

Given,

The two sources, [tex]S_{1}[/tex] and [tex]S_{2}[/tex] separated by a distance is d = 2.0m

[tex]S_{2}P = \sqrt{x^{2} +2.0^{2} }[/tex]

       = [tex]\sqrt{x^{2} +4}[/tex]

For destructive interference

[tex]S_{2}P - S_{1}P[/tex] = λ/2                                                    

 λ=ν/f

Given:

frequency  f = 1000hz

speed of sound ν = 343m/s

   =[tex]\frac{343}{1000} = 0.343m[/tex]

[tex]\sqrt{x^{2} +4} -x[/tex] = [tex]\frac{0.343}{2}[/tex] = 0.1715

⇒ [tex]\sqrt{x^{2} +4}[/tex] = 0.1715 + x

⇒ [tex]x^{2}[/tex]+4 = [tex](0.1715+x)^{2}[/tex]

           =      [tex](0.1715)^{2} + x^{2} + 2(0.1715)(x)[/tex]

⇒ 4 = [tex](0.1715)^{2}[/tex]+ 0.343 [tex]x[/tex]

⇒ [tex]x = \frac{4-0.1715^{2} }{0.343}[/tex]

       = 11.6m

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Due to her location within it, this is not possible. It can only be seen if the sky is clear and there is little to no light pollution, and as a result, environmental changes occur.

The Milky Way is crammed with anything between 100 billion and 400 billion more stars, many of which have their own planets. The Milky Way is so named because it appears from Earth like a streak of milk that has been spilled across the sky.

A galaxy is a sizable group of stars gathered in one place in the universe. The Milky Way galaxy, which contains the sun, Earth, and seven other planets, is where our solar system is located. Similar to our sun, the Milky Way is home to hundreds of billions of stars.

The Milky Way makes it possible to examine a medium-sized spiral galaxy's functioning in great detail.

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During the day, the Sun appears to move across the sky from Earth and disappears at night. As a result of the Earth's eastward rotation, this has occurred.

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Speed can be calculated using Kinetic energy and Potential energy. Kinetic energy is directly proportional to the mass of the object and to the square of its velocity: K.E. = 1/2 m v2.

How to calculate speed using Kinetic energy and Potential energy?

We know

Mass of the car = 300kg

G=9.8

Height = 16m

Thus, potential energy U =mgh and kinetic energy is 1/2mv²

0.5*m*v2 = m*g*h

v = √(2*g*h) = √(2*9.81*16)

v=17.71 m/s

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The Energy of the Infrared photon is  45.678* [tex]10^{-21}[/tex] J

The parameters are :

Frequency (f) = [tex]6.9 * 10^{13}[/tex] Hz

Energy is given by E = hf

where h is the Planck's constant = h = 6.62* [tex]10^{26}[/tex]

Putting these values in the formula for energy,

We evaluate the energy of the infrared photon as,

E = hf

E = [tex]6.62 *10^{-34} * 6.9 *10^{13}[/tex] = 45.678* [tex]10^{-21}[/tex]

IR emissions from materials are measured using infrared spectroscopy at certain wavelengths. As photons (light particles) are absorbed or released by electrons in molecules as the electrons pass between orbits, or energy levels, the IR spectrum of a material will exhibit distinctive dips and peaks.

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Answer:

0.612 kilograms.

Explanation:

To solve this problem, we need to use the definition of work as the product of force and displacement.

(a) The work done on the book is the force applied to it multiplied by the distance through which it is moved. In this case, the force applied to the book is its weight, which is 6 newtons. The displacement of the book is 2 meters, because it is moved from one shelf to another shelf that is 2 meters higher. Therefore, the work done on the book is 6 newtons * 2 meters = 12 joules.

(b) The next person to take the book from the shelf accidentally drops it. When an object is dropped, it accelerates due to the force of gravity, which is 9.8 m/s². Since the force of gravity is the same for all objects, we can use the acceleration of the book to calculate its mass. Specifically, we can use the formula F = ma, where F is the force acting on the object (in this case, the force of gravity), m is the mass of the object, and a is its acceleration.

In this case, the force acting on the book is its weight, which is 6 newtons. The acceleration of the book is 9.8 m/s². Therefore, we can solve for the mass of the book using the formula F = ma: 6 newtons = m * 9.8 m/s². This simplifies to m = 6 newtons / 9.8 m/s² = 0.612 kilograms.

In summary, the work done on the book when it is picked up and moved to a higher shelf is 12 joules, and the mass of the book is 0.612 kilograms.

Neptune and Uranus are similar in terms of size, mass, composition, and internal structure. The largest moon of Neptune, Triton, appears to have been captured because of its retrograde orbit.

Triton has a thin atmosphere and could be experiencing geological activity. Neptune's location was anticipated before it was ever discovered. Neptune is one of just two ice giants in the outer solar system (the other is Uranus). The planet's bulk, which is composed of a hot, dense fluid floating atop a tiny, rocky core, is primarily made up of water, methane, and ammonia (80% or more). Uranus is Neptune's identical twin. Their mass and chemical contents are equivalent. They are composed of an exterior layer of rocks and a mantle that is a mixture of water, ammonia, and methane ices. A physical body's mass is its total amount of matter. Inertia, or the body's resistance to acceleration (change of velocity) when a net force is applied, is also measured by this property. The gravitational pull an object has on other bodies is also influenced by its mass. The kilograms is the fundamental mass unit of SI (kg).

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The first and second overtones are 400hz and 600hz respectively

When a string vibrates in section, it produces overtones. The lowest frequency produced from a plucked string when the string vibrates in one loop is called fundamental frequency. But when it vibrates in multiple loops it is called overtone. Overtones are also called Harmonics of the fundamental frequency.

The first , second and third overtones in a string is 2fo , 3fo and 4fo , where fo is the fundamental frequency.

Therefore if the fundamental frequency is 200hz, the first overtone is 2×200 = 400hz and the second overtone is 3×200 = 600hz.

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The required angled is[tex]$\theta=33.4^{\circ}$[/tex].

What is angle is the first minimum?

The first minimum is going to be theta one is the inverse sine of one times 550 times ten to the minus nine meters divided by one times ten to the minus six meters giving an angle of 33.4 degrees

[tex]\begin{aligned}& \lambda=550 \mathrm{~nm} \\& D=1.00 \mathrm{~nm}\end{aligned}[/tex]

[tex]D \sin \theta=m \lambda, m=1,-1,2,-2, \ldots$$[/tex]

a) [tex]$\theta=\sin ^{-1}\left(\frac{m \lambda}{D}\right)$[/tex]

[tex]\theta_1=\sin ^{-1}\left(\frac{(1)\left(550 \times 10^{-9} \mathrm{~m}\right)}{1.00 \times 10^{-6} \mathrm{~m}}\right)=33.4^{\circ}[/tex]

b)The value of sine function can never be greater than 1, so second minimum does not exists for given wavelength of light and width of slit.

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The percentage of mechanical energy of the oscillator lost in each cycle is 5.91%.

The difference between mean or equilibrium position and either extreme is the oscillation's amplitude. The particle oscillates completely back and forth from its mean position.

The mechanical energy is the sum of both elastic potential energy and kinetic energy.

The mechanical energy of any oscillator is given by the formula,

E = 1/2 K*A²

When amplitude A decreases by 3%, then

(E₂ - E₁)/ E₁ = [1/2 K( A₂²/A₁²)]/(1/2 K*A₁²)

⇒ [(A₂²- A₁²)/(A₁²)]

⇒ (97² - 100²)/100²

⇒ 5.91% of the mechanical energy is lost in each cycle

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In our bobsleds, the bobsled's potential energy on the ramp was converted into kinetic energy as it descended the ramp, and then thermal energy as friction as it came to a stop.

The term "potential energy" describes the energy that is held within an object due to the object's position, state, and arrangement. It is one of the two essential types of energy; the other is energy. The object's position, status, or configuration changes, releasing the stored energy.

Due to its position, an object might accumulate energy. If a demolition machine's heavy ball is held in an elevated position, for instance, it can store energy. Potential energy is the name for this kinetic energy that is held in a position. As a result of its location, a drawn bow can also store energy.

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They are terrestrial or Jovian and can have specifics of energy level.

Jovian Planets:-

Terrestrial Planets:-

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