nitialize the tuple team names with the strings 'rockets', 'raptors', 'warriors', and 'celtics' (the top-4 2018 nba teams at the end of the regular season in order). sample output for the given program:

The time it takes the ball to roll down without slipping 1.7 mm down an incline is 0.046 s.

The ball rolling without slip means that the ball experiences translational kinetic energy and rotational kinetic energy. The formula for the energy

PE = m × g × h

KE = 0.5 × m × v²

ME = PE + KE

RKE = 0.5 × I × ω²

ω = v/R

At the top

At the bottom

According to the law of conservation of energy

ME₁ = ME₂

PE₁  + KE₁ + RKE₁ = PE₂ + KE₂ + RKE₂

1.67 × 10⁻² × m + 0 + 0 = 0 + 0.5 × m × v² + 0.5 × I × ω²

1.67 × 10⁻² × m = 0.5 × m × v² + (1/2) × (2/3)mR² × (v/R)²
1.67 × 10⁻² = (1/2) × v² + (1/3)R² × v²/R²

1.67 × 10⁻² = (3/6)v² + (2/6)v²

1.67 × 10⁻² = (5/6)v²

v² = 1.67 × 10⁻² × (6/5)

v² = 2.0 × 10⁻²

[tex]v \:=\: \sqrt{2.0 \times 10^{- 2}[/tex]

v = 0.14 m/s

According to non-uniform motion

v² = u² + 2ad

v = u + at

Calculate the acceleration

v² = u² + 2ad

0.14² = 0² + (2 × a × 0.0032)

0.0196 = 0.0064a

a = 0.00196 ÷ 0.0064

a = 3.06 m/s²

Time traveled

v = u + at
0.14 = 0 + 3.06t

t = 0.14 ÷ 3.06

t = 0.046 s

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If an airplane is  is accelerating down a runway at 2.5 m/s². It's velocity changes 2.5 m/s in each second.

Acceleration is the rate at which speed and direction of velocity vary over time. A point or object going straight ahead is accelerated when it accelerates or decelerates.

Even if the speed is constant, motion on a circle accelerates because the direction is always shifting. Both effects contribute to the acceleration for all other motions.

Hence, the velocity of the airplane changes 2.5 m/s in each second  when it  is accelerating down a runway at 2.5 m/s².

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a) The Cartesian components of tension TnA for unit vector by the magnitude of tension is (-87.89, -74.59, 47.44), i lb, j lb, k lb.

b) The tension in cable DC is TnC = 74.59 lb.

Part A: Determining Cartesian components of force

To find the Cartesian components of the tension TnA, we need to determine the direction of the tension from point D to point A. The direction can be expressed in terms of unit vectors i, j, and k.

The direction from point D to point A can be expressed as the vector (AXD) = (-4.50,-3.80,2.80) ft - (0,0,0) ft = (-4.50,-3.80,2.80) ft.

To convert the direction vector into a unit vector, we divide each component by the magnitude of the vector:

AXD = (-4.50,-3.80,2.80)/√((-4.50)² + (-3.80)² + (2.80)²) = (-8.158, -6.889, 4.532)

Finally, the Cartesian components of tension TnA can be found by multiplying the unit vector by the magnitude of tension:

TnA = 10.6 lb × (-8.158, -6.889, 4.532) = (-87.89, -74.59, 47.44), i lb, j lb, k lb

Part B: Determining an unknown force

To find the tension in cable DC, we need to find the net force acting on the ball. The net force can be expressed in terms of its Cartesian components, which can be calculated as the sum of the tensions in cables DA, DB, and DC.

Let's call the tension in cable DC TnC. The net force in the x-direction is equal to the sum of the x-components of the tensions, which is:

-87.89 + TnC = 0

TnC = 87.89 lb

Similarly, the net force in the y-direction is equal to the sum of the y-components of the tensions, which is:

-74.59 + TnC = 0

TnC = 74.59 lb

Since the net force must be zero, TnC must be equal in both the x-direction and the y-direction. Therefore, TnC = 87.89 lb = 74.59 lb.

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The question is -

To determine Cartesian force components from the magnitude and determine the position and resultant vectors by summing Cartesian components. Part A- Determining Cartesian components of force As shown, a 3.3-lb ball is suspended at point D inside a box with dimensions w = 8.90 ft, d 6.40 ft, and h = 4.50 ft.

The ball is held in place by three cables anchored at points A, B, and C on the surface of the box. The tension in cable DA has a magnitude of TnA = 10.6 1b. Find the Cartesian components of tension TnA which is directed from D to A.

D is the origin of the Cartesian coordinate system, point A is located at (-4.50,-3.80,2.80) ft, point B is located at (1.90,-3.80,1.80) ft, and point C is located at (1.90, 5.10, -1.70) ft.

Part B- Determining an unknown force If the tensions in cables DA and DB are Tpa = 10.6 lb and TDB 6.98 lb, respectively, what is the tension in cable DC? Express your answer to three significant figures and include the appropriate units.

He possesses an extra electron at the same energy level as H and a higher nuclear charge than H.

Photoelectron Spectroscopy (PES):

PES (photoelectron spectroscopy) is a technique for determining the relative energy levels of electrons in atoms and molecules. Scientists typically employ PES to investigate molecular bonding or to identify the constituent constituents of a substance.

Photoelectron spectroscopy (PES) is a method that determines the composition and electronic state of a sample's surface area by ionising it and analysing the kinetic energy distribution of the emitted photoelectrons.

It is feasible to analyse the electronic structure of molecules by determining the binding energy, intensity, and angular distributions of photoelectrons by measuring their kinetic energy. It differs from conventional spectroscopy in that it investigates the electrical structure of a substance by detecting electrons rather than photons.

Photoelectron spectroscopy allows one to determine the relative energy of electrons in atoms and molecules (PES).

A graph of the photoelectron count against binding energy is a PES spectrum.

PES peaks represent the electrons in the different subshells of an atom. Core electrons are represented by the peaks with the highest binding energies, while valence electrons are represented by the peaks with the lowest binding energies.

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The power which allows courts to help parties determine their rights and duties even though neither may yet have been harmed, so long as there is a real case or controversy between them is called "judicial review."

Judiacial review power allows courts to interpret and apply the law in order to resolve disputes and determine the constitutionality of laws and government actions.

In the United States, judicial review is exercised by the Supreme Court, which has the power to declare laws and executive actions unconstitutional. This power helps to ensure that the government acts within the limits set by the Constitution and that individuals' rights are protected.

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A social event must be painstakingly planned and the budget developed.

The steps that can be taken in planning a social event are;

Define the purpose and goals of the event: Determine what you want to achieve with the event, who the target audience is, and what kind of atmosphere you want to create.

Set a budget: Determine how much you can spend on the event and allocate funds for different expenses, such as venue rental, food and drinks, decorations, and entertainment.

Choose a date and location: Select a date that is convenient for your guests and a location that is suitable for the type of event you are planning.

Invite guests: Create a list of guests to invite and send out invitations, either by mail or email. Consider the size of the venue and the number of guests you would like to attend.

Plan the event details: Choose a theme or decor for the event, decide on the food and drink menu, and arrange for entertainment, such as music or games.

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Because Loeffler medium enhances primary and secondary isolation and cultivation of fastidious pathogenic microorganisms especially from nose and throat. It also restores virulence and other identifying properties.

Loeffler medium enhances primary and secondary isolation and cultivation of fastidious pathogenic microorganisms especially from nose and throat. It also restores virulence and other identifying properties (microscopic and colonial) after they have been lost due to prolonged incubation or repeated subculturing.Ions are supplied by sodium chloride. Dextrose is a fermentable carbohydrate source. During the sterilising process, the eggs and beef serum cause the medium to coagulate and are sources of protein that the coynebacteria and other organisms utilise for metabolism.

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The correct option is C, the area of R is the area of the large triangle minus the area of the small triangle minus the area of the circle, which is [tex]$\frac{14^2}{2}-\frac{4^2}{2}-(\frac{5\sqrt{2}}{2})^2\pi=98-8-\frac{25\pi}{2}$[/tex] ,which is approximately 51.

Area is a mathematical concept that represents the size or extent of a two-dimensional region or surface. It is expressed in square units, such as square meters, square centimeters, or square miles. The area of a shape is determined by multiplying its length by its width.

Area is an important concept in various fields, such as architecture, construction, engineering, and physics. In architecture, for example, the area of a room or a building is used to determine its capacity, as well as its heating and cooling needs. In construction, the area of a plot of land is used to determine its value, and the area of a building’s roof is used to determine the amount of materials required for its construction.

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Complete Question: -

Let A(2,2) and B(7,7) be points in the plane. Define R as the region in the first quadrant consisting of those points C such that triangle ABC is an acute triangle. What is the closest integer to the area of the region R?

(A )25     (B) 39    (C) 51     (D) 60    (E) 80

The distance between the origin and the destination is the length of the path that was traveled.

The displacement is always less than or equal to the distance since it is calculated along the shortest path between two places. While distance refers to "how much land an object has traversed throughout its journey," displacement measures "how far an object is out of place." Distance travelled, on the other hand, is the actual length the body travels, whereas displacement is the straight path between the initial and final places. While displacement is a vector quantity, distance is a scalar quantity. The final position less the starting position is known as displacement.

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complete question: distance and displacement lab activity answer key place a piece of tape where you will begin your walk outside. this tag marks the origin. What is the distance between the origin and your destination?

Because the tank's volume is fixed (it's rigid), the pressure must rise when additional gas is supplied.

The force per unit area on an item in the fluid or on the surface of a closed container is measured as fluid pressure. Gravity, acceleration, or forces outside a closed container can all create this pressure. Because a fluid has no fixed structure, its pressure is applied in all directions. Pressure is defined as the force applied perpendicular to the surface of an item per unit area across which that force is dispersed. Pressure is defined as the amount of force exerted perpendicular to an object's surface per unit area.

Here,

When more oxygen is supplied to a rigid metal tank containing oxygen gas at a fixed temperature, the gas pressure rises. At constant temperature, the pressure and volume of a gas are inversely related, according to Boyle's Law. Because the tank's volume is fixed (it's rigid), the pressure must rise when additional gas is supplied.

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To determine the tension in cable AC, we need to use the equation of equilibrium: the sum of the forces in the horizontal direction (Fx) must be equal to zero. The forces in the horizontal direction are the load P, the tension TAB in cable AB and the tension TAC in cable AC.

Fx = P - TAB + TAC = 0

Therefore, TAC = P + TAB

Substituting the known values, we get

TAC = P + TAB = 288 lb

Therefore, the tension in cable AC is 288 lb.

Tension force is a force experienced by a rope, string, or cable when it is pulled from the opposite end. It acts along the length of the rope, string, or cable, and is the result of the electromagnetic forces which hold the rope together as something tries to stretch it. The amount of force that gets transmitted depends on the tension in the rope, string, or cable, which can be increased by increasing the amount of force applied to it.

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The phase velocity in a printed circuit board with a relative dielectric constant (εr) of 4.6 can be calculated using the formula, so the final answer will be [tex]2.36 \times 10^{8} m/s.[/tex]

The symbol for it is r. It is a substance's capacity to permit the passage of an electric current. the capacity of empty space to permit the passage of an electric current the proportion of a substance's permittivity to the permittivity of empty space It is influenced by frequency.

The relative permittivity was once known as the dielectric constant and represented by the Greek letter kappa: = 0; r = 0; Since we frequently use the same units, F/m, for both and 0, r is a dimensionless number. Air and vacuum. A vacuum has a relative permittivity of 1 by definition.

vp = c / √εr

vp = 3 x 10^8 m/s / √4.6

vp = 2.36 x 10^8 m/s

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The speed of the electron at point B is 4.51 x 10⁵ m/s.

The speed of the proton at point B is 1.913 × 10⁴ m/s.

Part A: The electric field will exert a force on the electron in the opposite direction of its motion. The magnitude of the force is given by the product of the electric field strength (1.51 N/C) and the charge of the electron (-1.60 x 10⁻¹⁹C). The acceleration of the electron due to this force is given by the force divided by its mass (9.11 x 10⁻³¹ kg). The velocity of the electron after a time t can be calculated using the kinematic equation v = v₀ + at, where v₀ is the initial velocity and a is the acceleration.

The time t can be calculated from the distance the electron moves in the electric field (0.380 m) and its initial velocity: t = x / v₀

Finally, the speed of the electron at point B can be calculated as the magnitude of its velocity.

Putting everything together, we get:

F = qE = -1.60 x 10⁻¹⁹ C x 1.51 N/C = -2.42 x 10⁻¹⁸ N

a = F / m = -2.42 x 10⁻¹⁸ N / 9.11 x 10⁻³¹ kg = -2.65 x 10¹² m/s²

t = x / v₀ = 0.380 m / 4.51 x 10⁵ m/s = 8.38 x 10⁻⁷ s

v = v₀ + at = 4.51 x 10⁵ m/s - 2.65 x 10¹² m/s² x 8.38 x 10⁻⁷ s = 4.51 x 10⁵ m/s - 0.22 m/s

The speed of the electron at point B is approximately 4.51 x 10⁵ m/s - 0.22 m/s = 4.51 x 10⁵ m/s.

Part B: The velocity of a charged particle moving in a uniform electric field is given by v = v₀ + at, where v₀ is the initial velocity, a is the acceleration, and t is the time elapsed.

In this case, the electric field acts on the proton, which has a positive charge, and thus the direction of acceleration is to the west. The magnitude of the acceleration is given by a = qE/m, where q is the charge of the proton and m is its mass.

Since the electric field is uniform, we can use the equation x = v₀t + 0.5at², where x is the displacement of the proton, to find the time elapsed.

Plugging in the given values, we have:

x = 0.380 m

v₀ = 1.91 × 10⁴ m/s

q = 1.6 × 10⁻¹⁹ C (charge of a proton)

E = 1.51 N/C

m = 1.67 × 10⁻²⁷ kg (mass of a proton)

Solving for t, we find that t = 4.40 × 10⁻⁷ s.

Substituting this value back into the equation for v, we find that the speed of the proton at point B is 1.913 × 10⁴ m/s.

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The mechanical or chemical degradation of rocks is known as weathering. rock fragments being transported via water, ice, or wind. When the energy of the transported materials declines, deposition takes place.

Crystallization, metamorphism, and erosion and sedimentation are the three processes responsible for transforming one rock into another. By going through one or more of these processes, every rock can change into any other rock. The rock cycle is thus produced.

The "rock cycle" is a key concept that highlights the differences between the three main rock kinds (metamorphic, igneous and sedimentary). The different kinds of rocks found in the Earth's crust are created and altered by a number of processes, to put it simply.

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Elliptical galaxies make up both the largest and smallest galaxies in the cosmos. One trillion or more stars can be found in giant elliptical galaxies. Dwarf ellipticals have less than 10 million stars.

The solar system is a very large area compared to your neighbourhood , your nation, or even planet Earth. However, there are much larger systems—groups of two, two hundred, or two billion stars—in the cosmos. Star clusters are somewhat bigger groups of stars than star systems, which are smaller groups of stars.

The nucleus, a central bulge, a disc, spiral arms, and a large halo are the four main structural divisions of this structure.

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The model to show changes in the nucleus of an atom during nuclear fission and fusion is given in the images attached.

Alpha decay is a type of radioactive decay where the parent nucleus loses an alpha particle, which is made up of two protons and two neutrons. This results in the formation of a smaller nucleus. Alpha particles have a high amount of kinetic energy and can cause harm to skin and living tissue if not shielded properly. However, they are relatively easy to shield against as they can be stopped by simple materials such as paper or fabric.

Therefore, To compare the amounts of energy released in alpha decay to other events, one could look at the half-life of the radioactive material and the energy released during each decay event. For example, gamma decay releases a large amount of energy in the form of high-energy photons, which are much more difficult to shield against compared to alpha particles. Similarly, beta decay releases high-energy electrons, which can also cause harm to living tissue if not shielded against properly.

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From this equilibrium position, a pendulum is drawn down an additional 0.15 m but then released after being pulled apart 13.0 cm.

Its gravitational energy is at its peak near the height of the swing. Gravitational energy declines and is converted to kinetic energy even as pendulum swings downward. It possesses the most kinetic energy and the least gravitational energy somewhere at bottom of its swing.

Energy may be found OR transferred easily, for instance The pendulum possesses kinetic energy when it is in motion. It also has gravitational force due to its height at the end of the swing. As the pendulum swings, heat is lost to the atmosphere, and kinetic energy transforms into potential energy, or KE to PE.

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The mean of the given data is  1.0297 and median is 1.009.

Sum of terms=.736+.863+.865+.913+.915+1.394 = 16.475

Number of terms = 16

Mean=[tex]\frac{Sum of terma}{Number of terms}[/tex]

In statistics, in addition to the mode and median, the mean is one of the measures of central tendency. Simply put, the mean is the average of the values in the given set. It indicates that values in a particular data set are distributed equally. The three most frequently employed measures of central tendency are the mean, median, and mode. The total values provided in a datasheet must be added, and the sum must be divided by the total number of values in order to determine the mean. When all of the values are organised in ascending order, the Median is the median value of the given data. While the number in the list that is repeated a maximum of times is the mode.

Mean=[tex]\frac{16.475}{16}[/tex]

On solving we get,

Mean ≈ 1.0297

The middle value in a sorted list of numbers is known as the median. The middle number must be found after sorting the numbers according to value in order to get the median.

When the data are arranged from least to largest, we obtain:

.736 .863 .865 .913 .915 .937 .983 1.007 1.011 1.064 1.109 1.132 1.140 1.153 1.253 1.394

The median is the average of these two values since, as you can see, we have two middle numbers rather than simply one:

Median=[tex]\frac{1.007 +1.011}{2}[/tex]

= 1.009

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Drag in fluid dynamics is a force that opposes an object's relative motion to the fluid it is moving relative to.

Why Air Resistance Exists A force produced by air is known as "air resistance," sometimes known as "drag." An item slows down when air particles hit its front. As surface area grows, more air particles will hit the object, raising resistance overall.

Form drag or skin drag are two different categories of drag force. Form drag is brought on by a fluid's (liquids or gases) reluctance to being pushed aside by an item moving through it.

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The correct question is

A cyclist is coasting at 15 m/s when she starts down a 450 m long slope that is 30 m high. The cyclist and her bicycle have a combined mass of 70 kg. A steady 12 N drag force due to air resistance acts on her as she coasts all the way to the bottom.

What is her speed at the bottom of the slope?

The specific heat capacity of the metal  is 0.5744 J/kg/K

Specific heat capacity is described as the amount of heat energy required to raise the temperature of a substance per unit of mass.

To calculate

Q = m_Metal * c_Metal * ΔT_Metal = -m_ Water * c_ Water * ΔT_ Water

The final temperature of the mixture is 25°C, the change in temperature of the water is:

ΔT_Water = 25°C - 15°C = 10°C

The heat transfer between the metal and the water is equal to the heat absorbed by the water, which can be calculated as:

Q = m_Water * c_Water * ΔT_Water = 0.5 kg * 20 J/kg/K * 10 K = 100 J

ΔT_Metal = Q / (m_Metal * c_Metal) = 100 J / (0.5 kg * c_Metal)

c_Metal = Q / (m_Metal * ΔT_Metal) = 100 J / (0.5 kg * (100°C - 25°C))

The specific heat capacity of the metal  is 0.5744 J/kg/K

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The impulse imparted by the platform on the ball is 15 Ns, which is equal to option (A). We need to use the law of

To calculate the impulse imparted by the platform on the ball, we need to consider the law of conservation of momentum. According to this law, the total momentum of a system of objects remains constant if no external forces act on it. In the case of the ball striking the platform, the total momentum of the system is equal to the momentum of the ball just before the collision plus the momentum of the platform.

At the moment of impact, the ball's momentum was 10 m/s downward and the platform's momentum was 0. The ball is then sent back upward with a velocity of 5 m/s, so its final momentum is 5 m/s upward.

The impulse imparted by the platform on the ball is equal to the change in momentum of the ball, which can be calculated as:

Impulse = Final momentum - Initial momentum = (1 kg)(5 m/s) - (1 kg)(-10 m/s) = 15 Ns

Therefore, the impulse imparted by the platform on the ball is 15 Ns, which is equal to option (A).

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The tension in a horizontal strand of a spiderweb cannot be accurately determined without knowing additional information such as the mass of the spider, the size of the spiderweb, and the material properties of the spider silk. These factors all affect the tension in the strand.

The definition of web crawlers-or often also called Spiderweb-is a tool for indexing and downloading content from the internet, then storing it in a search engine database. So that when someone is looking for some information, the search engine will immediately display relevant results from the database.

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In Edgar Allan Poe's "The Narrative of Arthur Gordon Pym of Nantucket," the narrator refers to the shore of the River Styx as "Pluto."

This allusion serves a symbolic purpose in the narrative. The River Styx was believed in Greek mythology to separate the land of the living from the land of the dead, with the ferryman Charon transporting souls across the river. By using the allusion of the River Styx, Poe creates a sense of foreboding and the idea that the narrator and the crew are crossing a threshold into an unknown and dangerous territory. This metaphor further emphasizes the theme of death and the unknown that runs throughout the narrative, heightening the suspense and eerie atmosphere of the story. By making this allusion, Poe effectively sets the stage for the events that are to come, suggesting that the narrator and crew are embarking on a journey into the unknown and possibly even the afterlife.

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Convolution is the technique of altering an image in image processing by applying a kernel to each pixel and its nearby pixels over the whole picture.

Convolution is the process of adding each picture component to its nearby neighbours while using the kernel's weighting. This is connected to a certain kind of convolution in mathematics. Despite being similarly indicated by the symbol *, the matrix operation being carried out—convolution—is not conventional matrix multiplication.

Conv2 can produce one of the following outcomes: full: larger than the original image, accounting for all pixels that the convolution kernel can calculate, even if their centres are outside of the image. This is the function's default option.

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The current density vector is 0.318Amps/m^2, The volume charge density ρv0 inside the electron beam is 5.2488 × 10^13 C/m^3 and  the spacing between the electrons is 0.0018m.

Given the radius of cylinder (a) = 1mm

The velocity of charge (v) = 0.1c = 0.1 x 3 x 10^8m/s

The current in the cylinder (I) = 1A

(a) J = I/A, where I is the current in the beam and A is the cylinder's cross-sectional area, yields the current density vector. A = πa^2 calculates the cylinder's cross-sectional area.

Therefore, the current density vector is [tex]J = 1/(π*1^2)[/tex] = 0.318Amps/m^2.

(b) The volume charge density ρv0 inside the electron beam

ρv0 = [tex](1 Amp)/(2πa^2v)[/tex]

[tex]ρv0 = (1 Amp)/(2π(1 mm)^2*(0.1c*2.99792458×10^8 m/s))[/tex]

ρv0 = 5.2488 × 10^13 C/m^3

(c) Average charge density = [tex]1 Amp/(0.1c x π xa^2)[/tex] = 1.5708*10^16 C/m^3

Since the electron is arranged on a cubical lattice, the charge in each cube is [tex](1.5708*10^16 C/m^3) * (∆^3) C.[/tex]

Therefore, the spacing between electrons is [tex]∆ = (1/1.5708*10^(16))^(1/3)[/tex] = 0.0018 m.

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complete question: An electron beam coming from an electron gun (shown below) consists of electrons that are uniformly distributed within a cylindrical region of space having a radius a = 1 [mm]. The axis of the cylinder is along the z axis, and the electrons are moving with a velocity vector v in the positive z direction. The velocity of the electrons is 0.1c where c is the speed of light (2.99792458 × 10^8 [m/s]). The magnitude of the current in the beam is 1 Amp.

a) Calculate the current density vector.

b) Calculate the volume charge density ρv0 inside the electron beam.

c) Calculate the spacing between the electrons, assuming that they are arranged on a cubical lattice, with spacing ∆ between the centers of adjacent electrons in the x, y, and z directions. (Hint: Think of one electron being at the center of each cube of length ∆ in the lattice. The average charge density can be found from considering how much charge is inside each cube.)

The convertion between minutes to second can be calculated by:

[tex]8\frac{1}{3} minutes = 8\frac{1}{3} . 60s =500s[/tex]

The convertion between km to meter can be calculated by:

150,000,000 km = 150,000,000 x 1,000 = [tex]1.5x10^{11}[/tex]m

The, the speed of light in m/s is [tex]\frac{1,5x10^{11} }{500}= 3x10^{8}[/tex] m/s

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The magnitude of vector A is determined as 3.52 m.

The value of vector A is calculated by applying the principle of vector addition.

R² = A²  + B²

where;

The resultant vector is given as 2 times vector A.

( 2A)² = A² + ( 6.1 )²

4A² = A² + 37.21

3A² = 37.21

A² = 37.21 / 3

A² = 12.4

A = √ ( 12.4 )

A = 3.52 m

Thus, the value of vector is determined from vector addition of A and B.

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By the use of Coulomb's law The value of charge is q = 89.7 nC

Coulomb's law is the mathematical expression describing how these three factors affect electric force. According to Coulomb's law, the electrical force between two charged items is inversely proportional to the square of the separation distance between the two objects and directly proportional to the product of the quantity of charge on the objects. When two items behave as point charges, the force between them can be accurately described by the Coulomb's law equation. When interacting with other charged objects, a charged conducting sphere behaves as though its whole charge were concentrated in its centre. Although the charge is evenly distributed around the sphere's surface, the centre of charge can be thought of as the sphere's centre.

m = 1.4g = 0.0014 kg is the mass of each sphere

r = 2.1 cm =m is the distance between the spheres

a = 130m[tex]s^{-2}[/tex] is the acceleration of the spheres

Let us assume that the spheres accelerate away from one another. This would tell us that the charges have the same sign. So here we can get the force from the mass and acceleration:

F = ma

Now this force is also equal to Coulomb's law since the charges are the only source of force here. We can thus equate:

ma = [tex]\frac{k \times q ^ 2}{r ^ 2}[/tex]

We isolate the charge q:

q = [tex]\sqrt\frac{m\times a \times r ^ 2}{k}[/tex]

We substitute:

q= [tex]\sqrt\frac{0.0014\times 130\times (0.021 ) ^ 2}{9\times10^9}[/tex]

We thus get:

q = [tex]8.918\times10^{-7}[/tex]

q= [tex]8.918\times10^{-7}[/tex] x  [tex]\frac{1 nC}{1 \times 10^{-9}}[/tex]

q = 89.7 nC

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