Grandma Dynamite accelerates her bus from a dead start to 90 m/sec in just 12 seconds. What is her acceleration?

A roadway for stunt drivers is designed for race cars moving at a speed of 40 m/s. A curved section of the roadway is a circular arc of 230 m radius. Approximately 1° is the angle of banking.

Given data

Friction force between the road and car = 0

Because the car is moving in circular motion, the force on the car should be inwards towards the center of the circular motion. To balance this force, there is a requirement of a centripetal force in the opposite direction. It's the resultant of two other forces, the horizontal component of the normal force and the force of gravity. When the horizontal component of the normal force equals the force of gravity, there is no friction force present.θ is the angle at which the roadway should be banked.

Hence, we need to find the angle θ using given data.

The angle of banking is given by:

tan θ = v2 / rgwherev = speedr = radius of curvatureg = acceleration due to gravity

tan θ = v²/rg = (40)²/ (230 × 9.8) = 0.76°

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The movement of the school bus that is powered by petroleum as chemical potential energy is an example of Kinetic energy. This is because the chemical potential energy from the petroleum is transferred through the engine, converting it into kinetic energy which then moves the bus.

Kinetic energy refers to the energy of an object in motion. It is defined as the work required to bring a body of a given mass from a state of rest to a state of motion. It is measured as the amount of work needed to accelerate a body of a given mass to a given speed. Kinetic energy is proportional to the square of the object's speed, which means that as the object's speed increases, so does its kinetic energy. Therefore, the movement of the bus, which is an object in motion, is an example of kinetic energy.

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Answer:

Gases don't have a fixed shape or a fixed volume. The particles move around all the time and spread out. This is why a gas fills its container and takes it shape and volume

Explanation:

Because the particles of gasses can move about each other rather freely, a gas has no definite shape so it takes the shape dictated by its container.

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The work done on the block by the spring during the motion of the block from its initial position to where the spring has returned to its uncompressed length is 8.325 J.

When a horizontal spring having a force constant of k=185 N/m is compressed by 0.045m and released, it propels a block of ice of mass m=4.00kg along a horizontal surface. Neglecting the mass of the spring and friction, this problem asks us to find the work done by the spring in moving the block from its initial position to where the spring returns to its uncompressed length.

Work, which is a scalar quantity, can be calculated using the following formula: W = Fs

where s is the displacement of the object and F is the net force acting on it.

In this case, the work done on the block is equivalent to the elastic potential energy stored in the spring when it is compressed. We can find this elastic potential energy using the following formula: PE = 1/2 kx²

where x is the distance the spring is compressed from its equilibrium length.

We can now use these equations to determine the work done by the spring on the block. Here are the steps to follow:

1. Determine the displacement of the block: Since the block moves from its initial position to where the spring returns to its uncompressed length, the displacement of the block is equal to the compression of the spring, which is given as 0.045 m. Therefore, s = 0.045 m.

2. Find the elastic potential energy of the compressed spring: Using the formula for elastic potential energy, we get:

PE = 1/2 kx² = 1/2 x (185 N/m) (0.045 m)² = 0.0389 J3.

Calculate the work done by the spring: Using the formula for work, we get: W = Fs = (185 N/m) (0.045 m) = 8.325 J.

Therefore, the work done by the spring on the block during its motion is 8.325 J.

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We must compute the following in order to resolve this issue:The entire price of purchasing 100 N moon pebbles.the money earned from the sale of 35 kg of lunar pebbles on eBay.The money made from selling the last of Mars' moon rocks.The whole profit, which is the sum of the total costs minus the total revenues

Buzz has always been a made-up character, both in our reality and the universe of Toy Story, as MacLane's remarks have made clear. While Pixar fans would want to see Andy and his Buzz Lightyear action figure make another appearance, MacLane emphasised that Lightyear was created as a true independent movie.

The triotagonist in the story is Jessie the Cowgirl.Toy Story series. She is the love interest of Buzz Lightyear. She first appeared in Toy Story 2.

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In general, the most stable point in simulations involving energy, potential, or force usually refers to a point of equilibrium where the forces acting on the system are balanced, and there is no net movement or change in the system.

An experiment in science is a carefully designed and controlled procedure that is carried out to test a hypothesis or answer a research question. It is a systematic and empirical approach to investigating phenomena and understanding the natural world.

In an experiment, a researcher manipulates one or more variables and observes the effects of the manipulation on the dependent variable. The independent variable is the variable that is manipulated, while the dependent variable is the variable that is being measured or observed to see if it changes in response to the manipulation.

The goal of an experiment is to establish cause-and-effect relationships between variables by controlling for other factors that could influence the outcome. The experiment should be designed to minimize bias and confounding factors that could affect the results, and the results should be analyzed statistically to determine the significance of any observed effects.

Experiments are an essential part of the scientific method and are used in many scientific disciplines, including physics, chemistry, biology, psychology, and others. They allow researchers to test hypotheses, make predictions, and draw conclusions based on empirical evidence.

Here in the question,

The similarity of the most stable point in different trials will depend on the specifics of the simulation and the initial conditions set up for each trial. If the simulations involve similar systems and starting conditions, then the most stable point may be similar in terms of the position, potential energy, force, or other parameters being measured.

Therefore, Simulations involving energy, potential, or force usually refer to a point of equilibrium where the forces acting on the system are balanced.

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When placed near a negatively charged metal sphere.The electric field strength at this location is 1.25 × 10⁴ N/C directed toward the sphere .

Electric field strength = 6.00 ×10⁻² N -   4 .80 × 10⁶ C

                                                     =   1.25 × 10⁴N/C

The intensity of an electric field at a specific location is quantified by its electric field strength. The volt per meter (V/m or Vm-1) is the most common measurement. A potential difference of one V between two points separated by one meter is represented by a field strength of one V/m. The intensity of an electric field at a specific location is quantified by its electric field strength.

Where electric field lines are closer together, the field is stronger, and where they are further apart, the field is weaker. As you get further away from a point charge, the electric field gets weaker.

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The main advantage of using two sets of coils to generate the magnetic field in Helmholtz's experiment instead of using just one coil centered about the electron tube is that the magnetic field is more uniform.

Helmholtz's experiment was an experiment in which an electron beam was fired through a magnetic field created by two coils. It was discovered by Hermann von Helmholtz in 1851, and the experiment was designed to study the properties of magnetic fields.

The Helmholtz coil is an instrument that produces a uniform magnetic field in a specific region of space. It consists of two circular coils, each with a radius equal to the distance between the two coils. The current in each coil flows in the same direction and produces a magnetic field that is parallel to the axis of the coils.

The advantage of using Helmholtz's coil in this experiment is that it produces a magnetic field that is much more uniform than that produced by a single coil. The coils are placed parallel to each other and the electron beam is passed between them.

By controlling the current in the coils, the strength of the magnetic field can be varied. This allows the properties of the magnetic field to be studied. The main reason Helmholtz used two sets of coils is that it produces a magnetic field that is more uniform than that produced by a single coil.

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Instantaneous insolation at the top of the atmosphere increases with factors such as solar constant, solar altitude, and atmospheric transparency.

Instantaneous insolation, or the amount of solar energy received by the Earth at a given place and time per unit area and per unit time, is determined by several factors. The most significant of these is the angle at which the sun's rays strike the Earth's surface, which varies depending on the latitude, time of day, and time of year. Insolation is also influenced by the distance between the Earth and the sun, as well as any atmospheric interference or absorption that might occur. The amount of insolation at the top of the atmosphere increases with a decrease in latitude, an increase in altitude, and a reduction in atmospheric absorption, among other factors. These variables influence the amount of energy that reaches the Earth's surface and contribute to the variations in insolation experienced across different regions of the planet.

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The ball was moving at 5.2 m/s before something dropped (also known as its velocity because it has a course of action in a given time).

Considering the data provided,

The baseball weighs 0.15 kg in terms of bulk.

A baseball has a momentum of 0.78 kilogram per second.

The momentum of an item is often exactly related to its mass and speed for something like an object travelling in such a given direction during a given period of time.

∴ Mass times speed is how you calculate momentum.

mass/momentum formula for calculating velocity

speed = 0.78 kgm/s 0.15 kg

speed = 5.2 m/s

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The synchronous motor and generator need to have a speed ratio of 1.2 (60 Hz/50 Hz) in order to convert 60 Hz to 50 Hz power. Therefore, the number of poles in each machine must be such that their synchronous speeds are in the ratio of 1.2. So if the synchronous speed of the motor is Ns1, the synchronous speed of the generator must be Ns2 = 1.2 Ns1.

The synchronous speed of a machine is given by the formula: Ns = (120f)/P where f is the frequency and P is the number of poles.

For the motor, we get: Ns1 = (120*60)/P1

For the generator, we get: Ns2 = (120*50)/P2

Equating these, we get: P2 = 1.2 P1

So if the motor has P1 poles, the generator should have P2 = 1.2 P1 poles in order to convert 60 Hz to 50 Hz power.

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Therefore, option c) is the correct statement since the image produced by a convex mirror is always smaller than the object and hence larger than one produced by a plane mirror in its place.

A convex mirror is a spherical mirror with its reflective surface bulging outward, away from the incident light. It is also called a diverging mirror since it diverges the incoming light rays.

The image formed by a convex mirror is always virtual, meaning that it cannot be projected on a screen. It is formed by the apparent intersection of the reflected light rays, and it appears to be behind the mirror. Since the light rays are diverged by the convex mirror, the image produced is always smaller than the actual object. Hence, option e) is false.

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Option c.The statement that relates to Bernoulli's principle is Air traveling faster over the curved upper surface of an airfoil causes lower pressure on the top surface.

The statement that pertains to Bernoulli's principle air passing quicker across the curved upper surface of an airfoil creates lower pressure on the top surface. Bernoulli's principle is a concept of fluid dynamics that states that as the speed of a fluid (gas or liquid) increases, the pressure within the fluid decreases. It is the explanation for the phenomenon of lift that keeps airplanes flying.

So "air traveling faster over the curved upper surface of an airfoil causes lower pressure on the top surface" is correct.

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The work that must be done to compress the spring by 6 cm is 0.3528 J.

To determine the work that must be done to compress the spring by 6 cm:

[tex]U = (1/2)kx^{2}[/tex]

where U is the potential energy, k is the spring constant, and x is the displacement from the equilibrium position :

[tex]F = kx[/tex]

where F is the force exerted by the spring and x is the displacement from the equilibrium position:

[tex]F = mg = 2 kg * 9.8 m/s^{2} = 19.6 N[/tex]

[tex]k = F/x = 19.6 N / 0.1 m = 196 N/m[/tex]

Now, to find the work required to compress the spring by 6 cm (or 0.06 m), we can use the potential energy formula :

[tex]U = (1/2)kx^2 = (1/2)(196 N/m)(-0.06 m)^{2} = 0.3528 J[/tex]

Therefore, the work that must be done to compress the spring by 6 cm is 0.3528 J.

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To find the resistor with the largest resistance, let's use Ohm's law formula V = IR. where V is the voltage, I is the current, and R is the resistance. The resistor A has the largest resistance. The correct answer is resistor A.

We are given that two resistors, A and B, are connected in series to a 9 V battery. Also, the first resistor, A, has a voltage of 6 V across it. This means that the voltage across resistor B is 9 V - 6 V = 3 V.

Now, let's find the resistance of resistor A using Ohm's law:

R = V / I

where V = 6 V and I is the same as the current flowing through resistor B since they are connected in series. Let's assume the current is I.

Therefore,

Ra = 6 V / I

Now, let's find the resistance of resistor B using Ohm's law:

R = V / I

where V = 3 V and I is the current flowing through both resistors in series.

Therefore,

Rb = 3 V / I

We are to find which resistor has the largest resistance.

This means we should compare Ra and Rb.

Ra = 6 V / I

Rb = 3 V / I

To compare the two resistances, we can simplify them as follows:

Ra = 6 / I

Rb = 3 / I

We can see that Ra is twice the value of Rb.

Therefore, resistor A has the largest resistance. Answer: Resistor A

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Explanation:

The slope of a lens refers to the angle at which the lens surface is inclined relative to the optical axis of the lens. The significance of the slope of a lens depends on whether the lens is convex or concave.

In a convex lens, the slope of the lens surface is steeper at the center than at the edges. This slope is what causes the lens to converge light rays that pass through it, making it useful for applications such as focusing light in a camera or microscope. The steeper the slope, the greater the lens's refractive power, which determines how much the lens bends the light passing through it.

In a concave lens, the slope of the lens surface is steeper at the edges than at the center. This slope causes the lens to diverge light rays that pass through it, making it useful for applications such as correcting nearsightedness. The flatter the slope, the greater the lens's refractive power, which determines how much the lens bends the light passing through it.

In both convex and concave lenses, the slope of the lens surface is a crucial factor in determining the lens's optical properties. The curvature of the lens surface determines the amount of bending of light rays passing through it, and the slope determines the magnitude of that bending.

Answer:

Explanation:

The slope helps to converge and diverge the light rays making enlarged and small images

The galaxies which contain a mixture of old and young stars are ellipticals and spirals.

Galaxies can be classified into three basic types: elliptical, spiral, and irregular. The most frequently observed and most easily recognized of the three types is spiral galaxies. Spiral galaxies are a type of galaxy with a structure that resembles a disk. They have arms that spiral outwards, giving the galaxy the appearance of a pinwheel.

The galaxies that contain a mixture of old and young stars are ellipticals and spirals.

Elliptical galaxies, as opposed to spiral galaxies, have a smooth, oval form. Elliptical galaxies have no spiral arms and, unlike spiral galaxies, contain very little gas and dust, which implies that there are no new stars being formed in these galaxies.

Irregular galaxies are galaxies that do not fall into any of the other two groups. Irregular galaxies do not have the symmetry of spiral galaxies or the rounded shape of elliptical galaxies, and they lack the structure that is typical of other galaxies. Irregular galaxies are thought to be relatively rare.

Therefore, the correct answer is: ellipticals and spirals.

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The human auditory system evolved to be sensitive to sounds in the range of 20 to 20000 Hz because it encompasses frequencies relevant to communication and survival, and matches the resonant properties of the human ear.

The human auditory system evolved to be sensitive to sounds in the range of 20 to 20000 Hz because this range encompasses the frequencies that are most relevant for communication and survival in the natural environment. Frequencies below 20 Hz, such as those produced by earthquakes or very low-frequency sounds in the ocean, are not very useful for communication and survival in most terrestrial environments. Frequencies above 20000 Hz, on the other hand, are less important for communication in many species and also require more energy to produce and detect. The range of 20 to 20000 Hz is also well-matched to the resonant properties of the human ear, which amplifies sounds in this range. Therefore, the sensitivity of the human auditory system to this range of frequencies is likely a product of both the ecological demands and the physical properties of the ear.

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A wiggle in time is called a vibration, while a wiggle in space and time is called a wave.

A vibration is a back-and-forth or oscillating motion that occurs in a periodic manner. It can be related to the frequency, which measures the number of cycles of the vibration that occur within a specific time period, usually in one second. Frequency is measured in units called Hertz (Hz).

A wave, on the other hand, is a disturbance that travels through space and time, transferring energy from one point to another. Waves can be mechanical, such as sound waves, or electromagnetic, such as light waves. There are several key properties of waves, including wavelength, amplitude, and frequency.

In summary, a wiggle in time is known as a vibration, which is related to the frequency of the oscillation. A wiggle in space and time is called a wave, which involves the transfer of energy and has properties such as wavelength, amplitude, and frequency.

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A 1-mm diameter wire is made up of a 3-m steel wire connected end to end to a 2-m copper wire. If the tension in the wire is 100 N, The speed of a transverse wave on this wire is 202 m/s

The speed of a transverse wave on the wire can be found using the formula:

v = √(T/μ),

where v is the speed of the wave, T is the tension in the wire, and μ is the linear density of the wire.

The linear density of the wire can be found by adding the linear densities of the steel and copper wires:

μ = μsteel + μcopper = (3 m)(π/4)(0.001 m)²(7850 kg/m³) + (2 m)(π/4)(0.001 m)²(8900 kg/m³)

μ = 0.0188 kg/m

Plugging in the values for T and μ, we get:

v = √(100 N/0.0188 kg/m)

v ≈ 202 m/s

Therefore, the speed of a transverse wave on the wire is approximately 202 m/s.

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When the cat nears the right end, the plank just begins to tip. If the cat has a mass of 4.7 kg, Cat is close to the right end of the two-by-four can it walk before the board begins to tip is: 1.52m

The cat can walk up to 1.52 m from the right end of the two-by-four before it begins to tip. This is because the plank has a mass of 7.00 kg and the cat has a mass of 4.7 kg. The total mass is 11.7 kg, which is slightly larger than the 1.44 kg needed to tip the plank (7.00 kg multiplied by 0.44 m).

In other words, the cat's mass is greater than the additional weight needed to tip the plank. To determine how close the cat can walk to the right end before it tips, you must first determine the total weight of the plank and the cat. The total weight is the mass of the plank, 7.00 kg, plus the mass of the cat, 4.7 kg. This gives a total mass of 11.7 kg.

The distance from the left end to the center of the plank is 0.44 m. So, the additional weight needed to tip the plank is 7.00 kg multiplied by 0.44 m, which equals 1.44 kg. Since the total weight of 11.7 kg is slightly larger than 1.44 kg, the plank will just begin to tip when the cat is 1.52 m from the right end.

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The SI unit of k is, the y component of the force is given by and  the y component of the force on the particle is J/m,-ky/√(x² + y² + z²) and -0.429 J/m respectively.

(a) The potential energy function of a particle is given by U(r) = kr, where k is a constant. The units of k can be determined by considering the units of potential energy and distance. The SI unit of potential energy is joules (J), and the SI unit of distance is meters (m). Therefore, the SI unit of k is J/m.

(b) The force on a particle is given by the negative gradient of the potential energy function. That is,

F = - ∇U

where ∇ is the gradient operator. In Cartesian coordinates, the y component of the force is given by:

Fy = - ∂U/∂y

To find ∂U/∂y, we need to express U in terms of y. Using the equation for r given in the problem statement, we have:

r² = x² + y² + z²

Substituting this expression into the equation for U, we get:

U = kr = [tex]k(x^2 + y^2 + z^2)^{(1/2)}[/tex]

To find ∂U/∂y, we differentiate U with respect to y, treating x and z as constants:

∂U/∂y = ky/√(x² + y² + z²)

Therefore, the y component of the force is given by:

Fy = - ∂U/∂y = -ky/√(x² + y² + z²)

(c) Given that U = 3.00 J when the particle is 2.00 m from the origin, we can use the equation U = kr to find the value of k:

k = U/r = 3.00 J / 2.00 m = 1.50 J/m

To find the y component of the force on the particle at the point (-1.00 m, 2.00 m, 3.00 m), we need to calculate y and plug it into the expression we derived in part (b):

y = 2.00 m

Fy = -ky/√(x² + y² + z²) = -1.50 J/m × 2.00 m / √((-1.00 m)² + (2.00 m)² + (3.00 m)²) = -0.429 J/m

Therefore, the y component of the force on the particle is -0.429 J/m.

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If the motorcyclist applies the front brake too hard, the front wheel may lock and the motorcycle may flip over, causing a dangerous situation.

When a motorcyclist applies the front brake too hard, the front wheel may lock up due to a loss of traction, causing the motorcycle to flip over and resulting in a hazardous scenario. This is known as a front wheel lockup, and it can occur if the motorcyclist is going too fast or if there is insufficient weight on the front wheel

When the front wheel of a motorcycle stops spinning abruptly and the motorcycle flips forward, it is known as a front wheel lockup. This occurs because the motorcyclist applies the front brake too hard, causing the front wheel to lose traction and lock up. When a motorcyclist applies the front brake too hard, the motorcycle's weight shifts forward and places more weight on the front wheel, causing it to lose traction and lock up.

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Answer:

The accelerating voltage needed to produce electrons with wavelength 0.0600 nm is 590 V.

Explanation:

In an electron microscope, the accelerating voltage needed to produce electrons with wavelength 0.0600 nm is 590 V.

An electron microscope is a microscope that employs a beam of electrons as a source of illumination. Because of their short wavelengths, electrons can provide higher resolution images than light microscopes.

Theoretically, this would make it possible to distinguish between two points that are less than a single angstrom apart (0.1 nm).

In an electron microscope, the accelerating voltage needed to produce electrons with a wavelength of 0.0600 nm is given by the de Broglie wavelength equation.

The formula for de Broglie wavelength is: λ = h / p Where,λ is the wavelength of electrons. h is Planck's constant, 6.63 × 10−34 J·s. p is the momentum of electrons, m·v.

Now, the momentum of an electron is given by: m· v = √(2mkT) Here, m is the mass of electrons, k is Boltzmann's constant, and T is the temperature.

As the initial kinetic energy is negligible, we assume that the initial velocity of electrons is zero.

Therefore, the formula for momentum becomes: m· v = √(2mkT) = √(2m·0·kT) = 0 Also, we know that p = mv So, p = 0, which means λ = h / p = ∞This indicates that the de Broglie wavelength of the electrons is undefined, or infinite.

Therefore, we cannot use the de Broglie wavelength equation to find the accelerating voltage.

However, we can use the following formula to find the accelerating voltage: voltage = (h^2 / 2m) × (1 / λ^2)Substituting the given values, we get: voltage = (6.63 × 10^-34 J·s)^2 / (2 × 9.11 × 10^-31 kg) × (1 / (0.0600 × 10^-9 m)^2)

Therefore, the accelerating voltage needed to produce electrons with wavelength 0.0600 nm is 590 V.

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The time taken for the grinding wheel to slow down from 185 rad/s to 105 rad/s while it rotates through 16.0 revolutions is 4.62 s (to two decimal places). The appropriate unit for time is seconds (s).

We know that when a jeweler's grinding wheel slows down at a constant rate from 185 rad/s to 105 rad/s while it rotates through 16.0 revolutions, the time it takes for this to happen can be calculated as follows:Given,ω0 = 185 rad/sωf = 105 rad/sn = 16.0 revolutions = 16.0 × 2π radians = 100.5.

We know that the angular acceleration of the wheel is given by the formula:

α = (ωf - ω0)/t1

Here,α = (105 rad/s - 185 rad/s)/t1α = -80 rad/s²/t1. We also know that the total angle rotated by the wheel is given by:θ = n × 2π = 100.5 rad. Therefore, we have the formula for angular displacement as follows:θ = ω0t1 + 1/2αt12

Substituting the given values, we have:100.5 rad = 185 rad/s × t1 + 1/2 × -80 rad/s²/t1 × t1²Solving for t1, we have:

t1 = ( -185 + sqrt(185² + 4 × 1/2 × (-80) × 100.5)) / -80t1 = 4.62 s

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Answer:

a) The work function (in eV) can be calculated using the formula:

Φ = hν - EK

where h is the Planck constant (6.626 x 10^-34 J·s), ν is the frequency of the radiation, and EK is the maximum kinetic energy of the emitted photoelectrons.

First, we need to convert the minimum frequency of electromagnetic radiation to energy using the formula:

E = hν

E = (6.626 x 10^-34 J·s) x (8.9 x 10^14 s^-1) = 5.90 x 10^-19 J

Next, we can use the formula for work function:

Φ = E - EK

where E is the energy of the incident photon, which we have already calculated.

Φ = (5.90 x 10^-19 J)/(1.602 x 10^-19 J/eV) = 3.68 eV

b) i. To calculate the maximum kinetic energy of the emitted photoelectrons, we can use the formula:

EK = hc/λ - Φ

where h is the Planck constant, c is the speed of light (3.00 x 10^8 m/s), λ is the wavelength of the incident radiation, and Φ is the work function.

First, we need to convert the wavelength of the incident radiation to meters:

λ = 250 nm = 250 x 10^-9 m

Now we can calculate the maximum kinetic energy:

EK = [(6.626 x 10^-34 J·s) x (3.00 x 10^8 m/s)]/(250 x 10^-9 m) - 3.68 eV

EK = 2.49 eV

ii. To calculate the maximum velocity of the emitted photoelectrons, we can use the formula:

EK = 1/2 mv^2

where m is the mass of the electron and v is its velocity.

First, we need to convert the maximum kinetic energy to joules:

EK = 2.49 eV x 1.602 x 10^-19 J/eV = 3.98 x 10^-19 J

Now we can solve for the velocity:

v = √(2EK/m)

where m is the mass of an electron (9.11 x 10^-31 kg)

v = √[(2 x 3.98 x 10^-19 J)/(9.11 x 10^-31 kg)]

v = 1.61 x 10^6 m/s

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In the given process, work done by the friction is equal to the work done by the force applied. The work done by the force applied is equal to the product of force and distance, i.e. 25N x 18m = 450J.

The work done by friction will be equal to the change in kinetic energy of the box which is equal to 1/2 mv², where m is the mass of the box and v is the velocity of the box. Here, m = 4kg and v = 5m/s.

Therefore, work done by friction = 1/2 x 4x (5)² = 50J. Thus, the total work done by the friction in the given process is 50J.

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A disk and a hoop of the same mass and radius are released at the same time at the top of an inclined plane. If both are uniform, the one that reaches the bottom of the incline first if there is no slipping is the hoop.

A hoop is a type of toy that is in the shape of a circle, it is usually made of metal or plastic and is often used by children to play games. A hoop is a uniform body that has a radius r and mass m. The moment of inertia of a hoop is given by I=mr2. The kinetic energy of a rolling hoop is given by K=12mv2+(1/2)Iω2.

Therefore, for a rolling hoop, the energy is shared between the kinetic energy of the center of mass and the rotational energy. The net force acting on the hoop as it rolls down the inclined plane is F=mgSinθ−(1/2)ma.

The acceleration of the hoop is given by a=(2/3)(gSinθ).

The acceleration of the disk is given by a=(1/2)(gSinθ).

Thus, the hoop will reach the bottom of the incline faster than the disk.

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The top reaches an angular velocity of 28.28 rad/s when the string is fully unwound.

We can use the kinematic equation of rotational motion to solve this problem. The third kinematic equation relates the final angular velocity of a rotating object to its initial angular velocity, angular acceleration, and the angle through which it rotates:

[tex]\omega_f^2 = \omega_i^2 + 2\alpha\theta[/tex]

where θ is the angle through which the object rotates.

The number of turns the body turns to unwind the string is calculated as,

[tex]n=L/(2\pi r)[/tex]

[tex]n=80/(2\pi \times 2)[/tex]

[tex]n=6.366[/tex]

Therefore the angle turned by the body in unwinding the string is calculated as,

[tex]\theta = 2\pi \times 6.366 \ rad[/tex]

[tex]\theta = 39.99\  radians[/tex]

The initial angular velocity of the top is zero, the angular acceleration is [tex]10 \ rad/s^2[/tex], and we need to find the final angular velocity when the string is completely unwound.

Substituting the values given in the problem into the equation, we get:

[tex]\omega_f^2 = 0 + 2\times 10 \times 39.99[/tex]

Simplifying, we get:

[tex]\omega _f = 28.28 \ rad/s[/tex]

Therefore, the final angular velocity of the top when the string is completely unwound is 28.28 rad/s.

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