how long would a day be if the earth were rotating so fast that objects at the equator were apparently weightless?

To double the speed of a wave in a string, you must increase the tension in the string by a factor of four.

The speed of a wave in a string is given by the equation \(v = \sqrt{T/u}\), where v represents the wave speed, T is the tension in the string, and μ is the linear mass density of the string. To double the wave speed, we need to find the factor by which the tension must be increased.

Let's assume the initial tension in the string is T₁, and the resulting tension required to double the wave speed is T₂. According to the equation, we have \(v_{1} =\sqrt{T_{1}/u }\) and\(v_{2} =\sqrt{T_{2/u }\), where v₁ is the initial wave speed and v₂ is the desired doubled wave speed.

To find the factor by which the tension must be increased, we can set up the following equation: v₂ = 2v₁ = √(T₂/μ). Simplifying this equation, we get \(T_{2} /u= (2v_{1} )^{2} = 4v_{1} ^{2}\)

Since we want to double the wave speed, v₂ = 2v₁, we substitute the value of v₁ into the equation above and find \(T_{2} /u= 4(v_{2} /2)^{2} = 4(v_{2} ^{2} /4) =v_{2} ^{2}\)

Therefore, to double the speed of the wave in the string, the tension in the string must be increased by a factor of four, as \(T_{2} /u =v_{2} ^{2}\)

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Question 1

T=2*pi*sqrt(m/k) 

dimension of T=sec

dimension of 2*pi=nil(dimensionless)

dimension of m=kg

equation dimension

sec=sqrt(kg/k)

sec^2=kg/k

k=kg/sec^2

so dimension of k will be 

MT^(-2) 

dimension of N/m=kgms^(-2)/m=kgs^(-2) so it is same 

Question 2

F=Gm1*m2/r^2

Dimension of F=MLT^(-2)

MLT^(-2)=G*M*M/L^2

G=ML^3T^(-2)/M^2=M^(-1)L^(3)T^(-2)

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An item obtains mechanical energy when an external force applies positive work to it.

The object experiences negative work when the force and displacement are in the opposite directions; as a result, the item loses mechanical energy.

The power needed, which is defined as energy per unit of time, depends on the velocity.

More power is needed to move a certain distance quickly, thus you must provide the same quantity of energy over a shorter period of time.

Work is defined as the energy transferred while exerting force to move an item across a distance. It is the result of distance and force.

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Answer:

Resistance is measured in ohms

Answer:

visual art in which one uses to mark drawing and express feelings

Explanation:

In my own opinion. Hope it helps.

No resistors are connected in series.

A resistor is a passive two-terminal electrical component used in circuits to implement electrical resistance.

A resistor is an electrical component that controls or restricts how much electrical current can pass across a circuit in an electronic device. Additionally, resistors can be used to supply a particular voltage to an active device like a transistor.

A passive electrical component called a resistor prevents the flow of electric current by introducing resistance. They are present in practically all electrical networks and electronic circuits. Ohms are used to measuring resistance.

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The walker is walking at a uniform speed that is constant speed.

An object is considered to be moving with uniform speed when it covers the same distance in the same amount of time, as opposed to non-uniform speed when it covers different distances in the same amount of time. The distance-time graph has a steady slope. As a result, it demonstrates that the rate at which distance changes is constant. Thus, it depicts a constant speed. We refer to an object as travelling at a constant speed when its speed is constant and neither rises nor falls.

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The angle of refraction when a ray of light passes from air into water at an angle of 50.0° to the surface of the water is approximately 34.4°, and the speed of light in water is about 2.26 x 10⁸ m/s.

When light passes from one medium to another, it undergoes refraction, which involves a change in direction and speed. The angle of refraction is determined by Snell's law, which states that the ratio of the sines of the angles of incidence and refraction is equal to the ratio of the speeds of light in the two media.

In this case, the angle of incidence is 50.0° and the medium changes from air to water. By applying Snell's law, we can calculate the angle of refraction to be approximately 34.4°.

The speed of light in a medium is determined by the refractive index, which is the ratio of the speed of light in vacuum to the speed of light in the medium. The refractive index of water is approximately 1.33.

Therefore, the speed of light in water can be found by dividing the speed of light in vacuum (approximately 3 x 10⁸ m/s) by the refractive index, resulting in approximately 2.26 x 10⁸ m/s.

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The magnitude of the force, F, between an ion and a molecule with polarizability α can be expressed as:
F = (q² * α) / (4πε₀r⁶)
Here, q represents the charge of the ion, α represents the polarizability of the molecule, r represents the distance between the ion and the molecule, ε₀ represents the permittivity of free space, and π is a mathematical constant.

The force between an ion and a molecule with a permanent dipole moment is known as an ion-dipole interaction. This force arises due to the attraction between the ion and the partial charges of the dipole. In the case of an ion and a molecule with polarizability, the force is known as an ion-induced dipole interaction.

The force between the ion and the polarizable molecule is inversely proportional to the sixth power of the distance, r. This means that as the distance between the ion and the molecule increases, the force decreases rapidly.

The force is also directly proportional to the square of the charge, q, and the polarizability, α. A larger charge or polarizability will result in a stronger force between the ion and the molecule.

Overall, the expression for the magnitude of the force, F, between an ion and a molecule with polarizability α is given by:
F = (q² * α) / (4πε₀r⁶)

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Answer:

since the cannon ball has much less mass it will have a smaller momentum.

The system's total momentum was zero before the cannon was fired, the momentum of the cannonball and the cannon must be equal and opposing. Since the cannon has much more mass, it will have a smaller velocity.

The combination of a particle's mass and velocity produces momentum. Momentum has both a direction. The force exerted on a particle is equated to the time rate of change of momentum by Isaac Newton's second equation of motion.

Since there is no external force acting on the system, momentum ought to be conserved in accordance with the law of conservation of momentum.

Since we are aware that momentum is determined by a formula

M = \(mass * velocity\)

Here M is the momentum.

Since the system's total momentum was zero before the cannon was fired, the momentum of the cannonball and the cannon must be equal and opposing. The cannon will have a lower velocity because it has a lot greater mass.

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The time taken to accelerate from 15 m/s to 21 m/s by a rate of 3 m/s is 2 seconds. Then, the distance travelled by the motorcyclist while accelerating is 36 m.

Acceleration is the rate of change in velocity of an object. Like velocity, it is a vector quantity. As the magnitude or direction or both of the velocity changes the object is said to have an acceleration.

Given v1 = 15 m/s

v2 = 21 m/s

a = 3 m/s²

then t = v2- v1/ a

t = 21 m/s - 15 m/s /3 m/s² = 2 seconds.

Now, the distance travelled while accelerating is calculated as follows:

s = v1 t + 1/2 at²

  = 15 m/s × 1/2 3m/s² × 2 s = 36 m

Therefore, the motorcyclist will travel up to a distance of 36 m.

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The wavelength of the laser is 0.4464 mm.

The equation for the diffraction grating is given as:

dsinθ = mλ

where d is the distance between the slits (in meters), θ is the angle between the central maximum and the mth bright fringe (in radians), m is the order of the bright fringe, and λ is the wavelength of the light (in meters).

The equation to calculate the wavelength of a laser is λ = d × sin θ/m, where d is the distance between two adjacent slits on the diffraction grating (in this case, 1000 slits/mm, which is equivalent to 1 mm), θ is the angle of the fringe relative to the central axis (in this case, 26 degrees), and m is the order of the fringe (in this case, m=1). Therefore, plugging in the values:

λ = 1 mm × sin 26°/1 = 0.4464 mm

The wavelength of the laser is 0.4464 mm.

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The speed of sound is approximately 350.87 m/s on a day when a 1523 Hz frequency has a wavelength of 0.229 m.


The formula to calculate the speed of sound is v = fλ, where v is the speed of sound, f is the frequency, and λ is the wavelength.
Substituting the given values, we get:
v = 1523 Hz x 0.229 m = 348.47 m/s
However, the speed of sound varies with temperature, humidity, and air pressure. At standard temperature and pressure (STP), which is 0 °C and 1 atm, the speed of sound is 331.3 m/s. Assuming STP conditions, we can use the following formula to find the speed of sound:
v = 331.3 m/s x √(1 + (T/273.15))
where T is the temperature in Celsius. If we assume a temperature of 20 °C, we get:
v = 331.3 m/s x √(1 + (20/273.15)) = 350.87 m/s
Therefore, the speed of sound is approximately 350.87 m/s on a day when a 1523 Hz frequency has a wavelength of 0.229 m, assuming standard temperature and pressure conditions.

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Answer:

F=200 N

a=10m/s2

F=ma

m=F/a=200/10=20m

Explanation:

Answer:

a) k=50N/m

b) m=0.025kg or 25g

Explanation:

a) F=ma

but m=100g-0.1kg

a=10m/s²

F = 10×0.1

=1N

k=F/e

but e=2cm-0.02m

k=1/0.02

k=50N/m

b) F=ke

e=0.5cm

=0.005m

Recall;k=50N/m

F=50×0.005

F=0.25N

but F=ma

m=F/a

= 0.25/10

m = 0.025kg or 25g

【Answer】Therefore, the mass in said substance is 375 kilograms.

                               \(\red{ {\hspace{50 pt}\above 1.2pt}\boldsymbol{\mathsf{Procedure}}{\hspace{50pt}\above 1.2pt}}\)

This is an exercise on fluids and their fundamental characteristics.

We start to solve, obtaining the data:

                                   Conversion from liters to m³

                                      \(\boldsymbol{1500\not{l}*\dfrac{1 \ m^{3} }{1000\not{l} }=1.5 \ m^{3} }\)

To calculate mass: multiply density by volume.

                                       \(\boldsymbol{m=d*v \ \ \to \ \ \ Formula}\)

We clear our data in the formula:

                                       \(\boldsymbol{m=250\dfrac{kg}{\not{m^{3}}}*1.5\not{m^{3}} }\)

                                        \(\boldsymbol{m=375 \ kg}\)

The period of oscillation is 1.10 s. (option b).

We can use the formula for the period of oscillation of a spring-mass system, which is:

T = 2π√(m/k)

where T is the period, m is the mass, and k is the spring constant.

In this case, we have:

m = 2.50 kg
k = 3 N/m
Δx = 0.065 m

To find the period, we need to first calculate the effective spring constant, which takes into account the initial displacement of the mass. This is given by:
acceleration
k' = k(mg)/(mg - kΔx)

where g is due to gravity (9.81 m/s^2).

Plugging in the values, we get:

k' = (3)(2.50)(9.81)/(2.50)(9.81 - (3)(0.065)) = 2.87 N/m

Now we can find the period using the formula:

T = 2π√(m/k')

Plugging in the values, we get:

T = 2π√(2.50/2.87) = 1.10 s

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Answer:

There will be a force of gravity and a normal force coming from the track itself.

Explanation:

Assuming this is a continuation of an earlier question [20398149], the crate starts at rest and is allowed to slide down the ramp with acceleration a = 2.35 m/s², so the block will have some speed as it reaches the bottom of the ramp and it will continue to slide some distance along the flat part.

If the flat part is made of the same material as the ramp, then in addition to its own weight and the normal force, the crate will also feel some friction that slows down its leftward slide.

• The crate's weight and the normal force act vertically, so that

∑ F = n - w = 0

n = w = mg = (100 kg) (9.8 m/s²) = 980 N

(where ∑ F = net force, n = magnitude of normal force, w = crate weight, m = crate mass, g = mag. of gravitational acceleration)

• The friction acts horizontally, so

∑ F = -f = m a

(where f = mag. of friction and a = crate acceleration)

The surface has a coefficient of kinetic friction of µ = 0.3, so

f = µ n = 0.3 (980 N) = 294 N

So at the bottom of the ramp, there are 3 forces exerted on the crate:

• its weight of 980 N pointing downward

• the normal force of the surface pushing upward on the crate, also of 980 N

• friction of 294 N, pointing to the right

and the two vertical forces cancel each other.

=========================================================

Explanation:

amu = atomic mass unit

If the amu is 61, and we have 33 neutrons, then there are 61-33 = 28 protons. The number of protons directly determines the element. Use the periodic table to find that the element Nickel (symbol "Ni") has 28 protons. The number up top shows the number of protons. For some periodic tables, the number down below (some decimal value) represents the atomic mass. This is usually the average atomic mass when considering all varieties of isotopes.

Nickel is a transition metal found in the middle portion of the periodic table, in the top-most row. It has Cobalt (Co) on the left side, Copper (Cu) on the right side, and Palladium (Pd) below it. See the diagram below.

Answer:

Explanation:

Considering the fact that we ave been given an angle of inclination here, we best use it! That means that the velocity of 23 m/s is actually NOT the velocity we need; I tell my students that it is a "blanket" velocity but is not accurate in either the x or the y dimension of parabolic motion. In order to find the actual velocity in the dimension in which we are working, which is the y-dimension, we use the formula:

\(v_{0y}=v_0sin\theta\) and filling in:

\(v_{0y}=23sin(25)\) which gives us an upwards velocity of 9.7 m/s. So here's what we have to work with in its entirety:

\(v_{0y}=9.7m/s\)

a = -9.8 m/s/s

t = 2.8 seconds

Δx = ?? m

The one-dimensional motion equation that utilizes all of these variables is

Δx = \(v_0t+\frac{1}{2}at^2\) and filling in:

Δx = \(9.7(2.8)+\frac{1}{2}(-9.8)(2.8)^2\) I am going to do the math according to the correct rules of significant digits, so to the left of the + sign and to 2 sig fig, we have

Δx = 27 + \(\frac{1}{2}(-9.8)(2.8)^2\) and then to the right of the + sign and to 2 significant digits we have

Δx = 27 - 38 so

Δx = -11 meters. Now, we all know that distance is not a negative value, but what this negative number tells us is that the ball fell 11 meters BELOW the point from which it was kicked, which is the same thing as being kicked from a building that is 11 meters high.

Light photons always travel at a constant speed (the speed of light) regardless of their energy, while the velocity of electrons is not constant and can vary with their energy.

Light photons and energetic electrons do not have constant velocities independent of energy. Light photons, which are particles of electromagnetic radiation, travel at a constant speed in a vacuum, which is approximately 299,792 kilometers per second (or about 186,282 miles per second) in a vacuum, denoted as the speed of light (c). This speed is a fundamental constant of nature and remains constant regardless of the energy of the photons. In other words, all photons, regardless of their energy, travel at the same speed in a vacuum.

On the other hand, energetic electrons do not have a constant velocity independent of their energy. According to classical physics, the velocity of an electron can vary depending on its energy. In classical mechanics, the kinetic energy of an object is related to its velocity. However, in the microscopic world of quantum mechanics, the behavior of particles such as electrons is described differently.

In quantum mechanics, the concept of particle velocity becomes less straightforward. Instead of velocity, quantum particles are described by wavefunctions, which represent the probability distribution of finding the particle at a certain location. The wavefunction of an electron evolves over time according to the Schrödinger equation, and it does not directly correspond to a well-defined classical velocity.

However, in certain situations, such as in electron beams or particle accelerators, electrons can be accelerated to high energies. In these cases, the energy of the electrons is related to their speed, but it is not a constant relationship. As the energy of the electrons increases, their speed can also increase, but it is not independent of their energy.

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Freeman Alphonsa Hrabowski is an American educator, advocate, and mathematician.

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Answer:

27,32 dia

Explanation:

Based on the calculations, the radius of a tantalum (Ta) atom is equal to 0.143 nm.

Given the following data:

Density of tantalum (Ta) = 16.6 g/cm³.

Atomic weight of tantalum (Ta) = 180.9 g/mol.

Density can be defined as a ratio of mass to the volume of a physical object such as a tennis ball. Mathematically, the density of a physical object can be calculated by using this formula:

Density = Mass/Volume

For the mass of this unit cell, we have:

Mass = 2 atoms/unit-cell  × 180.9 g/mol × 1  mol /6.022 x 10²³ atoms/mol

Mass = 6.01  x 10⁻²² g/unit-cell

Next, we would determine the volume and edge length of the cube:

Volume, V = 6.01 x 10⁻²²/16.6

Volume, V = 3.62 x 10⁻²³ cm³

For the edge length, we have:

V = a³

a = ∛V

a = ∛3.62 x 10⁻²³ cm

Edge length, a = 3.31 x 10⁻⁸ cm

Mathematically, the edge length of a body-centered cubic unit cell is given by this formula:

a = 4r/√3

r = a × √3/4

r =  3.31 x 10⁻⁸ × √3/4

Radius, r = 1.43 × 10⁻⁸ cm

Lastly, we would convert the value in cm to nm:

Radius, r = 1.43 × 10⁻⁸ × 1/100 × 1 × 10⁹

Radius, r = 0.143 nm.

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Answer:-L/4

Explanation:

Sum the masses for the starting position and the center of the raft:

3M(0)+M(1/2L)

Find the distance the person moves

3M(L-d) + M(1/2L-d)

d=3/4L

Subtract

x = 1/2L -3/4L = -1/4L

Answer:

At \(t = (70 / 3) \; {\rm s}\) (approximately \(23.3 \; {\rm s}\).)

Explanation:

Note that the acceleration of the car between \(t = 0\; {\rm s}\) and \(t = 20\; {\rm s}\) (\(\Delta t = 20\; {\rm s}\)) is constant. Initial velocity of the car was \(v_{0} = 0\; {\rm m\cdot s^{-1}}\), whereas \(v_{1} = 35\; {\rm m\cdot s^{-1}}\) at \(t = 20\; {\rm s}\!\). Hence, at \(t = 20\; {\rm s}\!\!\), this car would have travelled a distance of:

\(\begin{aligned}x &= \frac{(v_{1} - v_{0})\, \Delta t}{2} \\ &= \frac{(35\; {\rm m\cdot s^{-1}} - 0\; {\rm m\cdot s^{-1}}) \times (20\; {\rm s})}{2} \\ &= 350\; {\rm m}\end{aligned}\).

At \(t = 20\; {\rm s}\), the truck would have travelled a distance of \(x = v\, t = 20\; {\rm m\cdot s^{-1}} \times 20\; {\rm s} = 400\; {\rm m}\).

In other words, at \(t = 20\; {\rm s}\), the truck was \(400\; {\rm m} - 350\; {\rm m} = 50\; {\rm m}\) ahead of the car. The velocity of the car is greater than that of the truck by \(35\; {\rm m\cdot s^{-1}} - 20\; {\rm m\cdot s^{-1}} = 15 \; {\rm m\cdot s^{-1}}\). It would take another \((50\; {\rm m}) / (15\; {\rm m\cdot s^{-1}}) = (10/3)\; {\rm s}\) before the car catches up with the truck.

Hence, the car would catch up with the truck at \(t = (20 + (10/3))\; {\rm s} = (70 / 3)\; {\rm s}\).

Answer:

build the resilience of the society physically, socially and economically.

Explanation:

They actually build the resilience of the society , physically or socially or economically All three .

The refractive index for a transparent medium with a critical angle, c, for light travelling from the medium to air is \(\mu=\frac{1}{\sin \mathrm{iC}}\\\)  =  \(\sin ^{-1}\left(\frac{2}{3}\right) .\end{aligned}$$\)

Refractive index of a transparent medium decreases with increase in wavelength of the incident light used.

The critical angle definition explains a lot about the laws of refraction and how the angle of incidence can be adjusted to bring a 90-degree angle of refraction

Refractive index of glass with respect to air is given:

\($$\mu=\frac{\text { Speed of light in air }}{\text { speed of light in glass }}\\\\=\frac{3 \times 10^8 \mathrm{~m} / \mathrm{s}}{2 \times 10^3 \mathrm{~m} / \mathrm{s}}\\\\=1.5$$\)

Now,

\(\mu=\frac{1}{\sin \mathrm{iC}}\\\\\sin \mathrm{i}_{\mathrm{C}}=\frac{1}{\mu} \\\\& \mathrm{i}_{\mathrm{C}}=\sin ^{-1}\left(\frac{1}{\mu}\right)\\\\=\sin ^{-1}\left(\frac{1}{1.5}\right)\\\\= \sin ^{-1}\left(\frac{2}{3}\right) .\end{aligned}$$\)

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