what is the magnitude of the resultant force (in nano-newtons) on the 9 nc charge at the origin? the coulomb constant is 8.98755 × 109 n · m2 /c 2 . answer in units of nn. answer in units of nn.

The required natural frequency of the spring with certain elongation is calculated to be 5.3 hz.  

Spring is an object which can be elongate or compress by some external force to store or release energy when ever needed.The natural frequency of the spring is the frequency at which it tends to vibrate without any external force intended.

The elongation of the spring is given as x = 9 mm

g is the acceleration due to gravity

The expression for the natural frequency according to Rayleigh's method is known as,

f = 1/2π √(g/x)

f = 1/2π √[9.8/(9×10⁻³)] = 5.3 hz

Thus, the required natural frequency is calculated to be 5.3 hz.

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The starting temperature of the metals is -18ºc (or 0ºf) then

255.37222222 K is Celsius to Fahrenheit

-17.77777778ºc is Fahrenheit to Celsius

1. Fahrenheit to Celsius:

To convert from Fahrenheit to Celsius, subtract 32 from the Fahrenheit temperature, then divide by 1.8.

To convert from Celsius to Fahrenheit, you need to use the following formula:

F = (C x 1.8) + 32

To convert -18ºC to Fahrenheit:

F = (-18 x 1.8) + 32

F = 0ºF-18ºc = 0ºf

0ºf - 32 = -32

[tex]\frac{-32 }{ 1.8} = -17.77777778ºc[/tex]

-17.77777778ºc is the temperature of metal at  Fahrenheit to Celsius

2. Celsius to Kelvin:

To convert from Celsius to Kelvin, add 273.15 to the Celsius temperature.

[tex]-17.77777778ºc + 273.15 = 255.37222222 K[/tex]

255.37222222 K  is the temperature of metal at Celsius to Kelvin.

The temperature of metal varies depending on the type of metal in question. Most metals have a melting point between 1,000 and 1,500 degrees Fahrenheit (538 and 816 degrees Celsius).

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On December 3, 1999, the angle between the direction to the sun and the direction to Mars, as seen from the Earth, was approximately 26.6 degrees.

The angle between the direction to the Sun and the direction to Mars from the Earth is determined by the relative positions of Earth and Mars in their respective orbits. On December 3, 1999, Mars was at opposition, meaning that it was on the opposite side of the Sun from Earth. At this time, the angle between the two was approximately 26.6 degrees.

The angle between the two changes over time, depending on the relative positions of Earth and Mars. When the two planets are on the same side of the Sun, the angle between them is at a minimum, and when they are on opposite sides of the Sun, the angle between them is at a maximum. This is why the angle between the two is always changing and is never exactly the same.

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Exponential power refers to the power to which a base number (often represented as "e") is raised.

Exponential power is used to represent exponential functions, which describe growth or decay over time, among other things.

For example, the exponential power of d can be used to describe how a quantity changes with increasing d.

When the exponential power of a variable is negative, the quantity decreases with increasing the variable; when it's positive, the quantity increases.

Exponential functions can also be represented as exponential series, which are infinite sums of increasing powers of the base number e.

These series can be used to approximate functions that are otherwise difficult to solve exactly, or to represent functions with properties that are difficult to obtain using other methods.

Exponential powers are an important part of mathematics and are widely used across a range of scientific and engineering fields. Understanding exponential powers is essential for solving many problems and analyzing complex systems in a variety of disciplines.

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Number of revolutions the object make during the first 3.4 s is, 8.4.

The nature of the graph of the angular velocity vs time gives information about the angular acceleration of the body and the angular displacement of the body.

Revolutions is given by, the angular displacement divided by the total angular replacement in full circle.

Total angular replacement in full circle is 2π.

Looking at the graph, the angular displacement in time t is given by,

20 + (10 t)

The angular displacement in first 3.4 seconds.

20+ 10(3.4) = 54

Using the formula for number of revolutions,

Number of revolutions = 54/2π

Number of revolutions = 8.4

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Answer:

To find the final velocity of the cart, we can use the conservation of momentum principle. Momentum is defined as mass times velocity, and in an isolated system, the total momentum before an event equals the total momentum after the event.

Before the woman jumps off the cart, the total momentum of the system is (50 kg)(5 m/s) = 250 kg m/s. After the woman jumps off, the total momentum of the cart is (10 kg)(v), where v is the final velocity of the cart.

Using the conservation of momentum principle, we can write the following equation:

(50 kg)(5 m/s) = (10 kg)(v) + (50 kg)(7 m/s)

Solving for v, we get:

v = (250 kg m/s - (50 kg)(7 m/s)) / 10 kg

v = -25/10

v = -2.5 m/s

So the final velocity of the cart is -2.5 m/s (westward direction)

According to the question of force, the y-component of F3 is -2.719 N.

What is force?

Force is a fundamental concept in physics that describes the interaction between two objects or systems. It is a vector quantity, meaning it has both magnitude and direction, and can be described mathematically. Force is a push or pull that can cause an object to accelerate, change its direction, or change its shape. Force is a function of mass and acceleration, as described by Newton's second law of motion.

The y-component of F3 can be calculated using the equation F3y = F1y + F2y. Since F1 is at a 180° angle, its y-component is 0. The y-component of F2 can be calculated using the equation F2y = F2 × sin(θ), where θ is the angle of F2. In this case, θ is 2430°, so the y-component of F2 is 8.90 × sin(2430°) = 8.90 × -0.3105 = -2.719 N. Therefore, the y-component of F3 is -2.719 N.

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The correct statements are;

Electrical resistance is the measure of a material's opposition to the flow of electric current, resulting in energy loss as heat.

We have to note that the resistance of the object would determine the magnitude of the electrical current that can be able to pass through the material.

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One second apart, two bodies start free falling from the same height after coming to rest. When the two bodies are 10 m apart, the first body will start to fall, taking 1.73 seconds.

To solve this problem, we will use the equation for the acceleration due to gravity, which is a = g = 9.8 m/s2. We can use this equation to calculate the time it will take for the first body to fall 10 m, starting from rest.

The equation for distance travelled (s) due to a constant acceleration (a) is

s = ut + 0.5at2

Where u is the initial velocity (in this case, 0 m/s) and t is the time taken.

Putting values, we get

10 = 0 + 0.5 x 9.8 x t2

Solving for t, we get

t = √(20/9.8) = 1.73 s

Therefore, it will take 1.73 seconds for the first body to fall from a height 10 m, starting from rest.

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The image where the rod is held near to the left side of the sphere on the stand, making the left side of the sphere become positively charged, best represents the resulting charge distribution on the conducting sphere.

Since the rod is too far away to contact the remaining portion of the sphere, it will remain neutral. The electrons in the sphere's substance will be drawn away from the positive charge on the left side of the sphere, leaving a region of positive charge there. The electrons will stay put on the right side of the sphere, creating a neutral charge there.

The image is provided below

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Row operation 22R6 + R2 R2 changes the matrix by adding row 6 to row 2 twice. To reverse this procedure and restore the matrix to its original shape, subtract row.

6 twice from row 2. This can be written as: -22R6 + R2 ⇒ R2 As a result, the row operation that will return the matrix to its original form is: -22R6 + R2 ⇒ R2 This procedure can be used to reverse the results of the previous operation and restore the matrix to its original state. 22r6 r2⇒r2 is used to transform a matrix. determine the row operation that will transform the matrix back to its original form. use r1, r2, etc. to represent the rows r1, r2, etc. Row operation 22R6 + R2 R2 changes the matrix by adding row 6 to row 2 twice. To reverse this procedure and restore the matrix to its original shape, subtract row.

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EA is the electric flux at the surface. because the electric flux is calculated by multiplying the electric field by the surface area it covers.

Because the surface area is known and the electric field intensity is constant, the electric flux can be computed as EA. The strength of an electric field flowing through a particular surface is measured by the electric flux. The strength of the electric field divided by the surface area through which it passes is used to compute it. The electric flux can be determined by by multiplying these two quantities if the surface area is known and the electric field magnitude is constant. Any closed surface surrounding a zero net charge has zero net electric flux. As a result, if we are aware of the net flux over a closed surface, we are also aware of the net charge contained.

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As Column A gets heated, the balI moves left along the beam. The solid ball cannot fit through the ring because it grows larger and expands when heated.

Heat causes a substance's molecules and atoms to vibrate more quickly. Atoms that vibrate more swiftly separate themselves from one another. The state of matter of a substance is determined by the velocity and spacing of the particles. The thing finally grows and takes up more space as a result of increased molecular mobility. Heat causes the molecules in the thermometer's red liquid to flow more swiftly. This movement causes the molecules to spread out a little bit further, which competes with their mutual attractions. They can only get out by climbing the tube.

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A) centre of mass will be 3.843 x 10⁸ m from the centre of moon

B) r₁ = 3.843 x 10⁸m  

r₂ = 0.047 x 10⁸ m

C) Ve /Vm = 0.01226

A) Let the centre of moon be considered as point of origin.

therefore centre of mass = Mm x 0 + Me x 3.89x 10⁸/ Mm + Me

Mm = mass of moon

Me = mass of earth

Mm = 0.0123 Me

Centre of mass = 3.89 x 10⁸ / 1.0123 m

So centre of mass will be 3.843 x 10⁸ m from the centre of moon or it will be at a distance of 0.00256 Au from the centre of the moon.

B) For moon  G Mm Me /r² = Mm Vm² /r²

For earth  G Mm Me / r² = Me Ve² / r₂²

r₁ = 3.843 x 10⁸m  

r₂ = 0.047 x 10⁸ m

C) Mm Vm² / r₁ = Me Ve² / r₂

(Ve/Vm)² = Mm r₂ / Me r₁

Ve/Vm =√ 0.047 x 0.0123/ 3.843

Thus Ve /Vm = 0.01226

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A) centre of mass will be 3.843 x 10⁸ m from the centre of moon B) r₁ = 3.843 x 10⁸m   r₂ = 0.047 x 10⁸ m C) Ve /Vm = 0.01226 A) Let the centre of moon be considered as point of origin.

therefore centre of mass = Mm x 0 + Me x 3.89x 10⁸/ Mm + Me Mm = mass of moon Me = mass of earth Mm = 0.0123 Me Centre of mass = 3.89 x 10⁸ / 1.0123 m So centre of mass will be 3.843 x 10⁸ m from the centre of moon or it will be at a distance of 0.00256 Au from the centre of the moon. B) For moon  G Mm Me /r² = Mm Vm² /r² For earth  G Mm Me / r² = Me Ve² / r₂² r₁ = 3.843 x 10⁸m   r₂ = 0.047 x 10⁸ m C) Mm Vm² / r₁ = Me Ve² / r₂ (Ve/Vm)² = Mm r₂ / Me r₁ Ve/Vm =√ 0.047 x 0.0123/ 3.843 Thus Ve /Vm = 0.01226 The center of the moon is 0.0026 AU (3.890 x 10⁸ m ) from the center of the Earth and has a relative mass of 0.0123. (a) Locate the cm of the Earth-Moon system with respect to the center of the Earth. (b) With respect to the center of the Moon. (c) Find the ratio of orbital velocities of the Earth and Moon about the cm of the system. (d) If the orbital velocity of the Moon is 1012 m/s , what is the approximate orbital velocity of the Earth about the cm of the Earth-Moon system

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We need a force of  7500 in the opposite direction of the motion of the truck.

According to the first equation of motion

V= U  + a t

t = time taken

V= final velocity =0 (as truck will come to rest)

U = initial velocity = 90 km/hr = 25 m/sec

a = acceleration

a=  V- U / t

a =  0- 25 / 8

a =  - 3.125 m/[tex]sec^{2}[/tex]

According newtons second law

F= m a

F =  2400  (- 3.125 m/[tex]sec^{2}[/tex])

F=  - 7500 Newton

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The RMS current in an RL circuit when 50 hertz 120 volts RMS ac voltage is applied is 82.68 mA

RMS or root mean square current/voltage of the alternating current/voltage represents the d.c. current/voltage that dissipates the same amount of power as the average power dissipated by the alternating current/voltage. For sinusoidal oscillations, the RMS value equals peak value divided by the square root of 2.

Inductive reactance

XL= 2xpixfxL

    =2pix50x0.37

XL=116.24 ohms

Impedance

Z= √[R^2+XL^2] =√[2900^2+116.24^2]

Z=2902.35 ohms

Rms current

I,rms=V,rms/Z

=240/2902.35

I,rms=0.08268 A or 82.68 mA.

Therefore , The RMS current in an RL circuit when 50 hertz 120 volts RMS ac voltage is applied is 82.68 mA

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(a) When the swimmer steps off the diving board, his initial PE is 5800 J and his initial KE is zero.

(b) At the instant he is half way to the water just before he hits the water, then PE = KE = 0.5 * 5800 J = 2900 J.

The conservation of energy principle states that the initial potential energy (PE) plus the initial kinetic energy (KE) is equal to the final PE plus the final KE. When the swimmer steps off the diving board, his initial PE is 5800 J and his initial KE is zero.

As he falls towards the water, some of his potential energy is converted into kinetic energy (KE = 1/2 mv²). At the instant he is half way to the water just before he hits the water, half of his initial PE has been converted into KE, so his PE and KE are both equal to half of his initial PE:

PE = KE = 0.5 × 5800 J = 2900 J

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The answers include the following:

This is referred to as quantities that are fully described by a magnitude (or numerical value) alone while on the other hand vector quantity is described by both magnitude and direction.

Reference point is referred to as the set of points or objects used to determine relative movement.

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The angle formed by the vector and the positive or counterclockwise of x-axis is 40.91°

The term "vector" is used informally to describe constituents of particular vector spaces or some values that cannot be described by a single integer.

A quantity or phenomena with independent qualities for both size and direction is called a vector. The word can also refer to a quantity's mathematical or geometrical representation. Velocity, momentum, force, electromagnetic fields, and weight are a few examples of vectors in nature.

Any vector with a two-dimensional direction may be conceived of as having two distinct parts. The impact of a single vector in a certain direction is described by its component.

The components are

Aₓ = 1.50

Ay = 1.30

We can find the angle of the vector by using the formula

[tex]tan\theta = \frac{A_{y} }{A_{x} }[/tex] = [tex]\frac{1.30}{1.50} =[/tex]

⇒[tex]\theta = tan\x^{-1}(1.3/1.5)[/tex]

⇒θ = 40.91°

The angle formed by the vector and the positive or counterclockwise of x-axis is 40.91°

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insufficient data or simulation software constraints If the medium is heterogeneous or anisotropic, the wave's speed can change with harmonic number to produce the first harmonic in a simulation.

Numerous factors, such as improper simulation settings, software restrictions, or insufficient data, could prevent a simulation from producing the first harmonic. The simulation settings must be configured to accurately resolve the first harmonic frequency in order to produce the first harmonic in a simulation. This can be accomplished by changing parameters like the simulation's time step size, frequency range, or number of harmonics.

The medium through which the wave is propagated determines the wave's speed. travelling as well as the characteristics of that medium, such as its elastic modulus and density. The wave's speed is constant for each harmonic if the medium is homogeneous and isotropic. However, the wave's speed can vary with harmonic number if the medium is heterogeneous or anisotropic. In order to calculate the speed using the equation v = f,

where v is the speed, f is the frequency, and is the wavelength, the frequency and wavelength of the wave in Parts A and B must be measured.

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The required time period of the mass suspended from the spring is calculated to be 0.446 s.

The spring is said to be stretched by 0.050 m (x).

The mass suspended from the spring is 1 kg (m).

The suspended mass oscillates in simple harmonic motion.

Its time period T =?.

Let us find out the force constant of the spring.

k = F/x = m g/x = (1× 10)/0.050 = 200 N/m

Now, if the mass of 1 kg is suspended by the spring, then the period of oscillation, we know the formula,

T = 2π√(m/k)

where, m is mass

k is spring constant

Putting in the values,

T = 2π√(m/k) = 2π√(1/200) = 2π × 0.071 = 0.446 s

Thus, the required time period is calculated to be 0.446 s.

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When a point charge of 8.00×10−12 c is located at the center of a cubical gaussian surface, 143.84 x 10^3 is the electric flux φface through each face of the cube.

The electric flux through a face of a cube is given by the product of the electric field and the area of the face. The electric field due to a point charge can be calculated using Coulomb's law:

=> E = k x Q / r^2

here,

E is electric field,

k is C constant (8.99 x 10^9),

Q is charge,

r is distance from the point charge to the surface,

In this case, the charge is

= 8.00 x 10^-12 C

and the distance from the point charge to the surface is equal to half the length of one side of the cube,

So, r = a/2

here,

a is length of a side of the cube.

The area of one face of the cube is a^2,

The electric flux of face is:

=> φface

= E x a^2

= k x Q / (a/2)^2 x a^2

= 2k x Q / a^2

Since there are six faces of the cube in the total electric flux is:-

=> φtotal

= 6 x φface

= 6 x 2k x Q / a^2

adding values, we get:

=> φtotal

= 6x2x8.99 x 10^9 Nm^2/C^2 x 8.00 x 10^-12 C / (a/2)^2

The electric flux of each face is :-

=> φface

= φtotal / 6

= 2 x 8.99 x 10^9 Nm^2/C^2 x 8.00 x 10^-12 C / a^2

= 143.84 x 10^3

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The difference between the inner and external pressures is measured by the pressure gauge on a reservoir. When the oxygen (O2) tank is full, it holds 12.0 kg of the gas at a gauge pressure of 40 atm.

The oxygen (O2) tank holds 12.0 kg of the gas at a gauge pressure of 40 atm when it is fully filled. Gauge pressure is the common name for this type of reading since the gauges measure pressure in relation to atmospheric pressure, which serves as the zero point. However, anything that is not a complete vacuum is considered to be under some type of pressure. In daily life, gauge pressure is frequently utilized. Tire pressure, for instance, is assessed in relation to atmospheric pressure. When an automobile ascends a mountain, the gauge pressure rises as the air pressure falls, but it is assumed that the tire's absolute pressure stays constant.

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(a) 9.8 m/s^2 is acceleration due to gravity. (b) force is 607.6 N (c) Pressure on the ice from the person can be expressed as P = F/A (d) P is 147,757 Pa.

a) The force that the person exerts on the ice is given by:

F = m x g

where m = 62 kg is the mass of the person and g = 9.8 m/s^2 is the acceleration due to gravity. This is the force the person exerts on the ice due to her weight.

b) Numerical value of F can be calculated by multiplying the mass of the person by the acceleration due to gravity:

F = m x g = 62 kg x 9.8 m/s^2 = 607.6 N

c) Pressure on the ice from the person can be expressed as the force per unit area, or

P = F/A

where A = 0.0041 m^2 is the contact area between the skate and the ice.

d) Numerical value of P can be calculated by dividing the force by the area:

P = F/A = 607.6 N / 0.0041 m^2 = 147,757 Pa

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If you gained weight, your mass increased. The ratio of your weight to your mass would have increased as well, since weight is directly proportional to mass.

Weight is the force of gravity on an object, and is equal to the mass of an object multiplied by the acceleration due to gravity. Therefore, if the mass of the object increases, the weight of the object increases as well.

Additionally, the ratio of weight to mass will increase as the mass increases. Since weight is directly proportional to mass, as the mass increases, the ratio of weight to mass will increase as well. This is because when the mass is larger, the weight of the object will be greater compared to its mass.

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The system has grown more stable when the potential energy drops. Remember that negative numbers are more negative and have a lower value when their absolute values are larger than when they are less.

Electric potential V is given as potential energy per charge.

Mathematically, V = PE/q

where, q is charge

PE is potential energy

The work done on q by the electrostatic or Coulomb force is independent of the direction taken because it is a conservative force. The gravitational force in the absence of dissipative forces like friction is exactly identical to this. When a force is conservative, it is possible to define a potential energy that goes along with the force. Because the potential energy varies solely on position, managing it is typically simpler than calculating the work directly.

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The magnetic field is 228π x 10⁻¹⁰ T.

To calculate the magnetic field at the center of each turn of the toroid, we can use the formula for magnetic field produced by a solenoid:

B = μ x n x I / L

where:

B is the magnetic field

μ is the magnetic constant

n is the number of turns per unit length of the solenoid

I is the current flowing through the solenoid

L is the length of the solenoid

For the toroid, we need to find the magnetic field at the center of each turn. We can assume that the number of turns per unit length is equal to the number of turns per centimeter of the original solenoid.

So, substituting the given values:

B = (4π x 10⁻⁷) x 21 turns/cm x 57 x 10⁻³ A / 1 cm = 228π x 10⁻¹⁰ T.

Magnetic field is a field that surrounds a magnetic object and influences the behavior of moving charges within it. It is characterized by its direction and magnitude, and it can be represented by magnetic field lines. The magnetic field is proportional to the amount of current flowing through a conductor or a wire, and it can also be created by moving charged particles.

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Provided that the concave mirror's given focal length is 20 cm long.The object is 40 cm away, which indicates that it is at the center of the curve.

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Air bubbles move up in the capillary tube due to the upward buoyant force applied by the water on bubbles.

According to the Archimedes' principle, when an object floats in a liquid, it experiences an upward exerted by the liquid. This force is equal to the weight of the liquid displaced by the volume of the floating or sinking object.

When air bubbles are present in capillary tube, then the upward force exerted by the water on bubbles is more than the weight of the air bubbles, as the density of the air is very less than that of the water. That's why the air bubbles move up in capillary tube.

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Answer:

Explanation:

Ths question is about conservation of momentum.  The momentum of the camper on the dock is the same as the momentum of the other camper and the canoe.

[tex]m_1v_1=m_2 v_2[/tex]

[tex]80 kg . 4.0 m/s = 110 kg . v_2[/tex]

[tex]v_2 = \frac{320 kgm/s}{110 kg}[/tex]

[tex]v_2 = 2.9 m/s[/tex]

The canoe will move backward (away from the dock) at 2.9 m/s