High-speed stroboscopic photographs show the head of a 220g golf club is traveling at 49.9 m/s just before it struck a a 45.8g gold ball at rest on a tee. After the collision, the club head travels (in the same direction) at 33.9 m/s. Find the speed of the golf ball immediately after impact.
Please show your work and use this formula: m1v1+m2v2=m1v1f+m2v2f

depicts two negative charges balloons hanging from the ceiling via insulated cords. diagrams displaying the tension force in free bodies

Will there be a fee for this?

To demand payment from someone for a service you are providing for them or something you are offering to them is both intransitive and transitive. most clubs levie a fee for the privilege of using their tennis courts. You would be charged a little price for lodging and food. charge someone for something.

Which two categories of charges are there?

Positive charge, as shown by protons, and negative charge are the two different types of control (exhibited by electrons). The electromagnetic force becomes more complex as the charges move, according to Coulomb's law, which defines the electric forces among particles.

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The electric flux through the square is 2 * k * e.

The electric flux through the square is equal to the electric field passing through the surface multiplied by the area of the surface. Since the proton is located at a distance d/2 above the center of the square and the square is one face of a cube with edge length d, the electric field at the center of the square is equal to the electric field at the center of the cube.

The electric field at a point in space due to a point charge is given by Coulomb's law, which states that the electric field E at a distance r from a point charge q is given by: E = k * q / r^2 where

Given that the proton has a charge of +e and is located d/2 above the center of the square of side d, the magnitude of the electric field at the center of the square is: |E| = k * e / (d/2)^2

Since the area of the square is d^2, the electric flux passing through the square is:

electric flux = |E| * d^2

Therefore, the electric flux through the square is k * e * d^2 / (d/2)^2

= 2 * k * e.

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This is a measurement of relative air speed, also known as true airspeed.as the airplane flies, the probe measures relative air speed. what type of measurement is this.

What is airspeed?

Airspeed is the speed of an aircraft relative to the air through which it is moving. It is typically measured in knots, nautical miles per hour (knots), or kilometers per hour (kph).

Airspeed is important for pilots to know in order to safely and accurately navigate the airspace. An aircraft's airspeed has an effect on its performance, such as the rate of climb or descent, rate of turn, and stall speed. Airspeed is also important for aircraft designers, as it can affect the aerodynamic performance of the aircraft.

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The total random kinetic energy of all the molecules in 1 mol of hydrogen at a temperature of 300 K can be calculated using the equation for the internal energy of an ideal gas:

U = 3/2 * nRT

Where U is the internal energy, n is the number of moles, R is the ideal gas constant and T is the temperature in Kelvin.

Since hydrogen is a diatomic gas, the internal energy of 1 mol of hydrogen at 300 K is given by:

U = 3/2 * (1 mol) * (8.314 J/mol*K) * (300 K) = 1.50 x 10^4 J

The kinetic energy of a gas is related to its temperature by the following equation:

KE = 3/2 * nRT

So the total random kinetic energy of all the molecules in 1 mol of hydrogen at a temperature of 300 K is:

KE = 3/2 * (1 mol) * (8.314 J/mol*K) * (300 K) = 1.50 x 10^4 J

To find the velocity at which a mole of hydrogen would have to move so that the kinetic energy of the mass as a whole would be equal to the total random kinetic energy of its molecules, we need to use the formula for kinetic energy:

KE = (1/2) * m * v^2

The mass of 1 mole of hydrogen is given by the molar mass of hydrogen (2.016 g/mol), so the mass of a mole of hydrogen is 2.016 g.

So we can calculate the velocity as:

KE = (1/2) * m * v^2

v = sqrt(2* KE/m)

v = sqrt(2* 1.50 x 10^4 J / 2.016 g) = 3.41*10^3 m/s

Therefore, a mole of hydrogen would have to move at a velocity of approximately 3.41*10^3 m/s so that the kinetic energy of the mass as a whole would be equal to the total random kinetic energy of its molecules at a temperature of 300 K.

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A fraction of the free-fall  the acceleration due to gravity acceleration of the car is -0.64525g .

However, in the broader sense, gravity is indeed a force because it describes the resulting interaction between two masses. Gravitational effects are fundamentally caused by the warping of spacetime and the motion of objects through the warped spacetime. However, the end result is as if a force was applied.

Gravity is measured by the acceleration that it gives to freely falling objects. At Earth's surface the acceleration of gravity is about 9.8 metres (32 feet) per second per second. Thus, for every second an object is in free fall, its speed increases by about 9.8 metres per second.

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The constant force is exerted on the bullet while it is traveling down the 0.7m length of the barrel of the rifle is 2166.42N

Given the mass of bullet (m) = 10.9g = 10.9 x 10^-3kg

The speed of bullet (v) = 527.5m/s

Length of barrel of rifle (d) = 0.7m

From Newtons laws of motion we know that F = ma where F is the force and a is acceleration and also v = at where t is time

The distance travelled = d

d = 1/2at^2 = 1/2a(v/a)^2 = v^2/2a

a = v^2/2d

Then F = ma = mv^2/2d

F = 10.9 x 10^-3 x ( 527.5)^2 / 2 x 0.7 = 2166.42N

Hence the constant force that is exerted on the bullet is 2166.42N.

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OB. The new force will be 3 times more than the original. If the distance between the two objects is increased by a factor of 3, the distance between the two objects is increased by 3 times the original distance.

The inverse square law, which states that the force of attraction between two items is inversely proportional to the square of their distance, governs the interaction between two objects. This implies that the power of attraction between the two items weakens as their distance grows. In this case, there is a three-fold increase in the separation between the two items. The inverse square law states that the force of attraction between two objects will drop by a factor of nine if their separation grows by a factor of three. The formula for this is force = k/d2, where d is the separation between the two objects and k is a constant.

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The work done by resistive force from starting to return of the trip is -27.04KJ

The resistance to movement is caused when two objects rub against one another is called friction. Friction occurs whenever two items come into interaction with one another. Friction acts in the exact opposite direction from the motion and works against it. The two surfaces' respective materials have an impact on how much friction exists.

d1 = 5.2km east ; d2 = 5.2 Km west

f1 = 2.4N ; f2 = 2.8N

Work done = F.s => F scosФ

Ф => Angle between force and displacement

W1 = f1 d1 cosФ

    => 2.4 x 5200mx cos180

   => - 12.480KJ

W2= f2 d2 cosФ

    => 2.8 x 5200m x cos180

   => -14.56KJ

Total work done => W1 + W2 = - 12.480KJ + (-14.56KJ)

                           => -27.04KJ

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The ramp is not safe. Making the height up to 14.25 will make the ramp safe.

Given:

Incline angle = 85.5 degrees

Let's assume the steep angle is α. For a safe ramp, the angle should be:

Tanα = 15/95

Tanα = 3/19

Tanα = 0.158

α = Tan⁻¹(0.158)

α =  8.98°

Since the given angle is less than a steep angle,

8.98°  >  8.5°  

Hence, the ramp is not safe.

Dimensions for ramp to be safe:

Tan (8.5) = 0.15

Making the height up to 14.25 will make the ramp safe.

Hence, the ramp is not safe. Making the height up to 14.25 will make the ramp safe.

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A constant force applied to a 2.0 kg object at rest moves it 4.0 m in 2.0 seconds. The impulse of the force applied is 4kg m/s.

Impulse is a term which is used to describe or quantify the effect of force which is acting over time to change the momentum of an object. Impulse is represented by the symbol J and it is usually expressed in the SI unit as Newton-seconds or kg m/s.

Impulse = Change in momentum = ΔP

Momentum = m × v

ΔP = mv -mu

ΔP = 2.0 × 4/2 - 2.0 × 0

ΔP = 2.0 × 2 - 0

ΔP = 4kgm/s

The impulse of force applied is 4 kg m/s.

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The answer to this question depends on the type of thin lens being discussed and the position of the object.

Magnification is the process of enlarging an object or image beyond its normal size. Through magnification, objects can be seen with greater clarity and detail. It is often used in microscopes, telescopes, and magnifying glasses to allow for close examination of an object or image. Magnification can also be used to change the size of an image or object for a variety of applications.

Generally speaking, a thin lens that produces a positive magnification will produce an image that is real and inverted. This means that the image will be the same size as the object but will be inverted. This is because the rays of light being refracted by the lens are converging towards the same point and thus producing an image which is behind the lens and on the same side as the object. If the object is placed on the other side of the lens, this will result in a virtual and erect image.

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The image produced by a thin lens that produces a positive magnification is real and inverted. So correct option is a.

Positive magnification refers to the increase in size of an image produced by an optical system, such as a microscope or telescope. A positive magnification means that the image is larger than the object being viewed. A magnification of "x10" means that the image is ten times larger than the object being viewed.

A thin lens that produces a positive magnification will produce a real and inverted image.

When a lens has a positive magnification, it means that the image is larger than the object, and the image is on the same side of the lens as the object. Since the image is real, it means that it is formed by the actual convergence of light rays, and it can be projected on a screen. And since the image is inverted, it means that it is upside-down with respect to the object.

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By using Benoulli's principle the gauge pressure (P2) at a second point in the line is 1.62 × 10∧5 Pa.

The Bernoulli principle describes the conserve of mechanical work for all streamline which make up the flow and is primarily a statement on the energy conservation in a flowing fluid. When a vehicle goes quickly, it creates a low-pressure area, which causes dust to be pushed along in it.

Let pressure at at first point = P1

And, pressure at second point = P2

From Benoulli's principle -

P2 = P1 + 1/2 ρ(v1∧2 - v2∧2) + ρg (h1 - h2)

P2 = (5×10∧4 ) + 1/2 (1000) × ( (3 )∧2 - (0.75)∧2) + (1000) (9.8 ) × (11).

P2 = 1.62 × 10∧5 Pa

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the spacecraft is using xenon with a total spacecraft mass of 5 kg assumed. This simple formulation captured the interaction between propellant pressure and propellant tank volume.

A propellant (or propellent) is a mass that is expelled or expanded in order to produce a thrust or other motive force in accordance with Newton's third law of motion and "propel" a vehicle, projectile, or fluid payload. A reaction engine is the engine that expels the propellant in a vehicle. Although a propellant is technically the reaction mass used to generate thrust, the term "propellant" is commonly used to describe a substance that contains both the reaction mass and the fuel that stores the energy used to accelerate the reaction mass. For example, in chemical rocket design, the term "propellant" is frequently used to describe a combined fuel/propellant, although propellants should not be confused with fuel.

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The color of a galaxy can be used to determine something about what kinds of stars it contains by looking at the relative amounts of blue and red light.

The chemical composition of a galaxy is closely related to its color because the color of a galaxy is determined by the types of stars it contains. Galaxies that contain mostly young, hot, and blue stars will appear blue, while galaxies that contain mostly older, cooler, and red stars will appear red. The presence of elements such as hydrogen, helium, and oxygen can also affect a galaxy's color. For example, galaxies that contain high amounts of these elements tend to have more star formation, leading to a higher number of blue stars, and as a result, a bluer galaxy. The chemical composition also affects the brightness of the galaxy, with the galaxies that contain higher amounts of heavy elements tend to be brighter.

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For a 1.00 m (100 cm) crumple zone, about 200 kN of deformation is needed in order to keep the passengers safest.

Crumple zones, also known as crush zones or crash zones, are structural safety features used in vehicles, primarily in automobiles, to extend the time before a change in velocity and consequently momentum results from the impact during a collision by means of a controlled deformation.

In recent years, they have also been added to trains and railcars. As the average force delivered to occupants is inversely proportional to the time over which it is applied, crumple zones are intended to extend the duration over which the overall force from the change in momentum is applied to a person.

The equation for the impulse here is:

F Δt = m Δv

where, v is the velocity and m is the mass.

The survival rate of dummy experiments shows about 90% for a 1 m crumple zone. Hence, a deformation of 200-300 kN is needed to keep the passengers safest.

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The maximum distance the train can travel is 26.47 miles. If the train starts from rest and must come to a complete stop in 15 minutes, it can travel a maximum distance of 138600 ft.

The maximum distance a train can travel is affected by several factors such as the initial velocity of the train, the time spent accelerating, the cruising speed, the time spent cruising, the time spent decelerating and the deceleration rate. Additionally, the train's engine power, fuel capacity, and the weight of the train also affect the maximum distance it can travel. In this case, the train starts from rest and has a constant acceleration of 10ft/s^2, a cruising speed of 105mi/h and a time of 15min before decelerating.

The maximum distance the train can travel if it accelerates from rest until it reaches its cruising speed and then runs at that speed for 15 minutes can be found using the kinematic equation:

d = 1/2 x a x t^2 + v x t

Given,

a = 10 ft/s^2 (acceleration)

v = 105 mi/h = 150 ft/s (cruising speed)

t = 15 minutes = 900 seconds

d = 1/2 * 10 ft/s^2 * 900 seconds^2 + 150 ft/s * 900 seconds

d = 40,500 ft

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The angular acceleration as a function of time is found to be -2βt.

The instantaneous  angular acceleration is found to be -4.18rad/s².

The average angular acceleration is found to be -2.09rad/s².

The ratio of the change in angular velocity to the time it takes for the object to experience the change is known as the average angular acceleration, or avg., of an object. The limit of the average angular acceleration as time approaches zero is known as the instantaneous angular acceleration.

Given:

a)w = z(t)= γ − β×t²

By separating the two sides in terms of t, we obtain

α = z(t) = -2βt

b)Given:  γ = 4.65rad/s and β = 0.775 rad/s³

so, For t = 2.7 sec,

angular acceleration = -2 × 0.775× 2.7 = -4.18rad/s.

c) average angular acceleration α avg = ΔW₂(t)/Δt

 α avg = W₂ ×2.7 - W₂ ×0/2.7-0

 α avg = γ - β(2.7)² - [γ - β(0)²]

α avg = -β (2.7)²/2.7

α avg = β (2.7)

α avg = 0.775 (2.7)

α avg = -2.09rad/s².

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Potential difference of electron which is moving with speed of 5.00×105 m/s is 0.7109 V and Initial kinetic energy is 11.375 × 10∧-20 eV

Potential difference, also known as the external effort required to move a charge from one position to another in an electric field, is said to be the difference with in energy which electric charges have between 2 points in a circuit. Volts are used to measure it. Voltage is another name for potential difference (Pd. ), which is measured in volts (V).

Given -

Speed of electron = 5.00×105 m/s

We know that

K.E = e × V

Potential difference = K.E / e

= 11.375 × 10∧-20 / 1.6 × 10∧-19

= 0.7109 V

Initial kinetic energy = 1/2 ×m × v²

= 1/2 × 9.1×10∧-31 × (5×10∧5)∧2

= 11.375 × 10∧-20 eV

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The height of mercury in the tube decreases when  the atmospheric pressure decreases. Since, pressure s directly proportional to height change in barometer.

Since the two are inversely related, air pressure lowers as elevation rises. This is a result of the volume of air that is now surrounding you at your elevation. There is more air above you and therefore more pressure when you are at a lower level.

An instrument known as a barometer is used to measure atmospheric pressure, also known as barometric pressure. The air layers that surround Earth are known as the atmosphere. As gravity drags that air to Earth, it exerts pressure on everything it touches. This pressure is measured using barometers.

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(1) The primary different between Bill Nye's solar system model and the Second Life Model is the use of a realistic scale to depict the relative sizes and separations of the planets in Bill Nye's model.

(2) A project by designer and artist Josh Worth serves as an example. Its name, "If the moon were only one pixel," accurately describes what it does. The moon (3474.8 km) occupies the entire pixel, and the rest of the solar system is scaled down to fit. It turns out that most of the time, space is just that—space.  

All of the planets in Bill Nye's model are in a straight line, and it's quite realistic. Although Bill Nye's scale is more precise than this one, the second life model demonstrates how the planets orbit the sun, the spin of their axes, and other things. However, this model is not fully accurate.

"If the Moon Were 1 Pixel" is an infographic by designer Josh Worth. The interactive infographic precisely measures out our solar system using pixels and lets users scroll around space as if they were a spacecraft pushing its boundaries.

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a) We are assuming that the surface is frictionless, so when the pulling stops, the cart will continue to move at a constant speed in a straight line.

b) Illustration of description with motion diagrams, force diagrams, and position-versus-time and velocity-versus-time graphs is given in the attachment.

From Galileo Galilei's writings comes the idea of the frictionless surface. A formula for predicting the motion of an object moving down an inclined plane was provided by Galileo in his 1638 book The Two New Sciences. His formula was based on earlier work he had done with bodies that were falling freely.

Although his model was based on conceptual modelling of the forces acting upon the object, it was not based on experiments with objects moving down an inclined plane. Galileo understood the mechanics of the inclined plane as the union of the horizontal and vertical vectors; the outcome of gravity acting upon the object, diverted by the slope of the plane.

The cart accelerates until the pulling stops, at which point it will move at a constant speed(see attachment). Because of the constant acceleration that causes the velocity to increase with time, the first part of the function is a straight inclined line. The second part is a straight horizontal line because the cart moves at a constant velocity after the pulling stops because there are no horizontal forces acting on it.

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When body A slides down the inclined groove, it gains potential energy due to its height, which is converted into kinetic energy as the body moves down. The body will continue to gain kinetic energy as it slides down the half-circle due to the conservation of energy.

The velocity of the body at the highest point of its trajectory can be calculated by using the conservation of energy principle. The initial potential energy of the body at height h is converted into kinetic energy as the body moves down. At the highest point of its trajectory, the kinetic energy is equal to the initial potential energy.

Initial potential energy = mgh (where m is the mass of the body and g is the acceleration due to gravity)

Kinetic energy = 1/2 * m * v^2 (where v is the velocity of the body)

The velocity of the body at the highest point of its trajectory can be calculated by equating the initial potential energy and the kinetic energy, and solving for v:

mgh = 1/2 * m * v^2

v^2 = 2gh

v = √(2gh)

Therefore, the velocity of the body at the highest point of its trajectory is √(2gh).

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A ball is thrown directly up from a height of 0m with an initial speed of 2m/s. The height of the apex of the throw is 0.897 meters.

Initial speed refers to the velocity or rate of motion of an object at the beginning of a period or the start of a specific event. It is typically represented by the symbol "u" and is measured in units of distance per time, such as meters per second (m/s). The initial speed of an object can be determined by measuring its position at the beginning and end of a period and using the formula: speed = distance/time.

The height of the apex of the throw can be calculated using the following equation:

y = vi*t + (1/2)gt^2

where,

y = height of the apex (in meters)

vi = initial velocity (in m/s) = 2 m/s

t = time of flight (in seconds)

g = acceleration due to gravity (in m/s^2) = 9.8 m/s^2

Since the ball is thrown directly upwards and the initial velocity is given, we can use the following equation to calculate the time of flight:

t = 2*vi/g

Substituting the given values, we get:

t = 2*2/9.8 = 0.408 seconds

Now we can substitute the calculated value of t and the given value of vi into the first equation to get the height of the apex:

y = vit + (1/2)gt^2

y = 20.408 + (1/2)9.80.408^2

y = 0.816 + 0.081 = 0.897 meters

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D. Any height. Wave height is determined by the amount of energy that is present in the wave and the distance between the wave crests. As long as there is energy present in the wave, it can form regardless of its height.

Energy is a fundamental concept in physics, and is defined as the capacity for doing work. It can be transformed from one form to another, and is found in many forms such as thermal, kinetic, electrical, chemical, nuclear, and gravitational energy. Energy is found in the environment, in living things, and in the conversion of one form of energy to another. It is the driving force behind all physical, chemical, and biological processes. In the world of physics, energy is the ability to do work. It manifests itself in a variety of forms such as light, heat, electrical, gravitational, and chemical energy. Energy is never created or destroyed, but it can be converted from one form to another. The total amount of energy in the universe is constant and never changes, but it can be changed from one form to another. It is essential for life, as it is used to power everything from growth and development to communication and transportation.

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The wavelength of the light is rise to to 518 ×10⁻⁹ m. The recurrence of the shinning line is break even with to 5.79 × 10¹⁴ Hz. The color of light is yellow within the obvious range.

What are recurrence and wavelength?

The recurrence can be depicted as the number of motions of a wave in one moment and has S.I. units of per moment or Hertz.

The wavelength can be illustrated as the separate between the two adjoining focuses in stage w.r.t each other and includes a unit of meters.

The relationship between recurrence (ν), wavelength (λ), and speed of light (c) can be composed as follows: c = νλ

Given, the wavelength of the line, λ = 518 nm = 518 ×10⁻⁹ m

The speed of light is rise to to: c = 3 × 10⁸ m/s

The recurrence of the shinning line can decide from the above-mentioned relationship:

ν = c/λ = 3×10⁸/ 518 ×10⁻⁹ = 5.79 × 10¹⁴ Hz

Therefore, the recurrence of the shinning line is break even with to 5.79 × 10¹⁴ Hz. The color of light is yellow within the unmistakable spectrum.

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A)The strength of the electric field at the position (x,y)=(5.0cm,0cm) is [tex]3.6*10^{4}[/tex] N/C

B)The strength of the electric field at the position (x,y)=(−5.0cm,5.0cm) is [tex]1.78*10^4[/tex] N/C

C) The strength of the electric field at the position (x,y)=(−5.0cm,−5.0cm) is [tex]1.78*10^4[/tex] N/C

A)To determine the field strength at point A where (x,y)=(5.0cm,0.0cm),

notice that the distance from A to the origin is simply 5.0 units along the y-axis.

[tex]E=1/4\pi e_{o}*\frac{Q}{r^{2}}[/tex]

[tex]E=9*10^{9}*\frac{10*10^{-9}}{{5*10^{-2}}^{2}}[/tex]

[tex]E=3.6*10^{4}[/tex]N/C

B)To determine the field strength at point A where (x,y)=(-5.0cm,5.0cm),

use Pythagoras theorem,

[tex]r=\sqrt{5^2+5^2} \\r=7.1cm[/tex]

[tex]E=1/4\pi e_{o}*\frac{Q}{r^{2}}[/tex]

[tex]E=9*10^{9}*\frac{10*10^{-9}}{{7.1*10^{-2}}^{2}}[/tex]

[tex]E=1.78*10^4[/tex] N/C

C)To determine the field strength at point A where (x,y)=(-5.0cm,-5.0cm),

use Pythagoras theorem,

[tex]r=\sqrt{5^2+5^2} \\r=7.1cm[/tex]

[tex]E=1/4\pi e_{o}*\frac{Q}{r^{2}}[/tex]

[tex]E=9*10^{9}*\frac{10*10^{-9}}{{7.1*10^{-2}}^{2}}[/tex]

[tex]E=1.78*10^4[/tex] N/C

What is electric field strength?

Electric field strength is a quantitative expression of the intensity of an electric field at a particular location. The standard unit is the volt per meter (V/m or V·m-1). A field strength of 1 V/m represents a potential difference of 1 V between points separated by 1 meter.

How to measure electric field strength?

F=(k·Q·q)/d2

In this case, F again represents force, k equals the coulomb constant, Q refers to the source charge (in coulombs), q is the test charge (in coulombs) and d is the distance between Q and q.

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Out of all the instances described, a girl with more mass wearing shoes with higher tread will cause the most friction.

Which four forms of friction are there?

The force that prevents one solid item from moving across another is known as friction. Static friction, sliding friction, rolling friction, and fluid friction are the four main categories of friction.

What is frictional force, exactly?

Two surfaces that come into contact and slide against one another produce frictional force. The following variables impact the frictional force: Surface roughness and the amount of force pressing them together have the biggest an impact on these forces.

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By observing both boxes in a microgravity environment we can deduce which box has feathers and which one has sand.

What is microgravity?

Microgravity is a condition in which the gravitational force experienced by an object is much weaker than the gravitational force experienced on the Earth's surface. It is characterized by a very small or negligible acceleration due to gravity. Microgravity can be found in environments such as orbiting spacecraft, the International Space Station, or high-altitude balloons.

In an orbiting spacecraft, where there is no gravity, you can tell which box is filled with sand and which is filled with feathers by performing a simple experiment.

In a microgravity environment, both boxes will float in the air, but the box filled with sand will have more inertia and will tend to move less than the box filled with feathers due to their difference in mass. The box filled with feathers will have a lower mass and will be more affected by air resistance and other perturbations, thus moving more in the spacecraft.

Therefore, you can tell which box is filled with sand and which is filled with feathers by observing their motion in a microgravity environment without opening the boxes.

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The volume of a gas will decrease by half if the pressure is doubled while the temperature remains unchanged.

Boyle's Rule

The volume is inversely proportional to the pressure for a fixed mass of gas at a constant temperature.

That implies that, for instance, doubling the pressure will result in halving the volume. The volume will decrease ten times as quickly as the pressure does.

This can be mathematically stated as pV = constant.

The number of moles, n, remains constant since the mass of the gas is fixed.

The gas constant, R, is a constant that never changes.

The constant state of the temperature is required by Boyle's Law.

Boyle's Law, which we just stated is a result of, states that everything on the right-hand side of the equation pV = nRT is constant, and as a result, pV is constant.

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( 1) The speed of each seat is 6.73 m/s

( 2 ) The tension in the chain is 327.6 N.

The speed of each seat is determined by treating the system as a simple harmonic motion.

Apply the law of conservation of mechanical energy as shown below.

kinetic energy of each seat at the bottom = potential energy of each seat at the top

K.E = P.E

¹/₂mv² = mgh

v² = 2gh

v = √ ( 2gh )

where;

The vertical displacement of the seats is calculated from the length of the chain as follows;

h = L cos (24.4)

The speed of each seat is calculated as follows;

v = √ ( 2g L cos (24.4) )

v =  √ ( 2 x 9.8 x 2.54cos (24.4) )

v = 6.73 m/s

The tension in the chain is calculated by applying the formula for centripetal force as follows;

T = mv²/r

where;

T = ( 45.2 x 6.73² ) / ( 6.25 )

T = 327.6 N

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The complete question is below:

An amusement park ride consists of a rotating circular platform 12.5 m in diameter from which 10 kg seats are suspended at the end of 2.54 m massless chains. When the system rotates, the chains make an angle of 24.4° with the vertical. The acceleration of gravity is 9.8 m/s^2.

1. What is the speed of each seat? Answer in units of m/s.

2. If a child of mass 35.2 kg sits in a seat, what is the tension in the chain (for the same angle)? Answer in units of N.