I need help with this question Part a and Part b

(a) The ratio of the slit separation d, to the slit width D;

                               d/D = 0.0001

(b The ratio of the slit width to the wavelength of the light source λ;

                                d/λ = 51.25

(c) The wavelength, in nanometers, of the light source;

                                   λ = 331.7 nm

(d) The slit width, in micrometers;

                                   d = 20.5 µm

(a) We know that Fringe width is given by,

                                  \(\beta =\frac{D\lambda}{d}\)

Where,

           D = slit to screen distance

           λ = wavelength

           d = slit width

Given in the question,

           D = 2.05 m

           \(\beta =4 cm=0.04m\)

Now,

          \(\frac{d}{D} =\frac{\lambda}{\beta } =\frac{400*10^{-9} }{0.04}\)

                 d/D = 0.0001

Hence,

            The ratio of the slit separation d, to the slit width D;

                               d/D = 0.0001

(b) Ratio of d & λ,

                            \(\frac{d}{\lambda} =\frac{D}{\beta }\)

                            \(\frac{d}{\lambda}=\frac{2.05}{0.04}\)

                            \(\frac{d}{\lambda}=51.25\)

Hence,

           The ratio of the slit width to the wavelength of the light source λ;

                                d/λ = 51.25

(c)  The wavelength of the light source,  

                            \(\lambda=\frac{D\beta }{d}\)

                            \(\lambda=\frac{17*10^{-6} *0.04}{2.05}\)

                            \(\lambda=331.7nm\)

Hence,

            The wavelength, in nanometers, of the light source;

                             λ = 331.7 nm

(d) The slit width,

                           \(d =\frac{D\lambda}{\beta }\)

                           \(d=\frac{400*10^{-9} *2.05}{0.04}\)

                           \(d=20.5 \mu m\)

Hence,

           The slit width, in micrometers;

                                   d = 20.5 µm

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The unit of the potential energy is the same as the kinetic enrgy and it is kg·m²/s².

And the SI unit of the potential energy is Joule. It is represented by the symbol J.

Thus, Joules (J) is the SI unit of the measurement of the potential energy.

Main answer (final answer) – 1473515.58J

Supporting answer- Collision occurs when two objects come into contact with each other for a brief period of time. In other words, collision is a short-term reciprocal interaction between two masses in which the momentum and energy of the colliding masses change.

Body of the answer-

Final answer- therefore kinetic energy for the collision is 1473515.58J

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The mass of the planet is  5.98 × 10^24 kg.

To calculate the mass of the planet, we can use Kepler's Third Law of Planetary Motion. This law states that the square of the period of revolution of a planet around the sun is directly proportional to the cube of the semi-major axis of its orbit.

First, we need to convert the period of the satellite's orbit to seconds. We know that there are 60 minutes in an hour, so the period can be expressed as (6 × 60 + 12) minutes, which equals 372 minutes. Multiplying this by 60 seconds, we get a period of 22,320 seconds.

Next, we need to find the semi-major axis of the orbit. In a circular orbit, the semi-major axis is equal to the radius of the orbit. Therefore, the semi-major axis is 8.8 × 10^6 m.

Now, we can apply Kepler's Third Law to calculate the mass of the planet. The formula is T^2 = (4π^2/GM) × a^3, where T is the period of revolution, G is the gravitational constant, M is the mass of the planet, and a is the semi-major axis of the orbit.

Rearranging the formula, we can solve for the mass of the planet:
M = (4π^2/G) × a^3 / T^2

Plugging in the values, we get:
M = (4 × π^2 / 6.67430 × 10^-11) × (8.8 × 10^6)^3 / (22,320)^2

Evaluating this expression, we find that the mass of the planet is approximately 5.98 × 10^24 kg.

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An object with a velocity (v) of 9 m/s and a linear momentum (p) of 72 kg.m/s, has a mass (m) of 8 kg.

In Newtonian mechanics, linear momentum, or simply momentum, is the product of the mass and velocity of an object.

It is a vector quantity, possessing a magnitude and a direction.

The mathematical expression for momentum is:

p = m . v

where,

An object has a velocity (v) of 9 m/s and its linear momentum (p) is 72 kg.m/s. We will use the definition of linear momentum to calculate the mass of the object.

p = m . v

m = p / v

m = (72 kg.m/s) / (9 m/s) = 8 kg

An object with a velocity (v) of 9 m/s and a linear momentum (p) of 72 kg.m/s, has a mass (m) of 8 kg.

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The distance travelled by the vehicle around the circular track is 1,052.4 m.

The distance travelled by the vehicle in one complete cycle is calculated by using the following equation as show below.

d = 2πr

d = πd

Where;

In one complete cycle, the  vehicle will travel the circular track only once.

d = π(335 m)

d = 1,052.4 m

Thus, the distance travelled by the vehicle around the circular track is a function of the diameter of the circular track.

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The complete question is below:

A vehicle, starting from rest, accelerates on a circular track with a 335m diameter. What is the distance travelled by the vehicle when it makes one complete cycle?

Therefore, the magnitude of the velocity of the plane relative to the ground is approximately 150.2 mi/hr.

Velocity is a vector quantity that describes the rate of change of an object's position with respect to time. It is the displacement of an object divided by the time interval over which the displacement occurred. Velocity has both magnitude (speed) and direction, so it is a vector quantity.

Here,

To solve this problem, we need to use vector addition to find the velocity of the plane relative to the ground. We'll break down the given velocities into their x and y components and then add them up.

Let's define the following vectors:

Vp = velocity of the plane relative to the wind

Vw = velocity of the wind relative to the ground

Vg = velocity of the plane relative to the ground (what we're trying to find)

We're given that:

|Vp| = 142 mi/hr

The direction of Vp is N32.0°E, which means that the angle between Vp and the positive x-axis is 32.0° and the angle between Vp and the positive y-axis is 90° - 32.0° = 58.0°.

|Vw| = 32.0 mi/hr

The direction of Vw is E11.5°S, which means that the angle between Vw and the positive x-axis is -11.5° (because it's pointing to the south) and the angle between Vw and the positive y-axis is 90° - (-11.5°) = 101.5°.

To find the x and y components of Vp and Vw, we'll use trigonometry:

Vp,x = |Vp| cos(32.0°) ≈ 119.9 mi/hr

Vp,y = |Vp| sin(32.0°) ≈ 75.4 mi/hr

Vw,x = |Vw| cos(-11.5°) ≈ 31.4 mi/hr

Vw,y = |Vw| sin(-11.5°) ≈ -5.9 mi/hr

Note that we used -11.5° instead of 11.5° for the angle of Vw because it's pointing to the south (which is in the negative direction of the y-axis).

Now we can add up the x and y components of Vp and Vw to get the x and y components of Vg:

Vg,x = Vp,x + Vw,x ≈ 151.3 mi/hr

Vg,y = Vp,y + Vw,y ≈ 69.5 mi/hr

Finally, we can use the Pythagorean theorem to find the magnitude of Vg:

|Vg| = √(Vg,x² + Vg,y²) ≈ √(22554) ≈ 150.2 mi/hr

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The energy efficiency of the car is approximately 16.7%.

The energy efficiency of a car is the ratio of the useful work output (in this case, the kinetic energy of the car) to the total energy input (in this case, the energy released by burning the gasoline). The equation for energy efficiency is:

The useful work output can be calculated as the kinetic energy of the car using the equation:

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

Substituting the given values:

The total energy input is the energy released by burning 0.1 L of gasoline, which is:

Substituting these values into the equation for efficiency:

Therefore, the energy efficiency of the car is approximately 16.7%.

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(a) The inscriptions made in the design is possible due to friction when carving.

(b) The friction applied when you rub the crayons with the sandpaper is kinetic friction

Friction is a force that opposes two surfaces that are in contact. It limits the movement between these two surfaces.

The inscriptions made in the design is possible due to friction when carving.

There are two types of friction, static and kinetic friction. The friction applied when you rub the crayons with the sandpaper is kinetic friction because of there is movement between two surfaces.

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Most meteorites that enter the Earth's atmosphere burn up before they reach the Earth itself. When this happens, lots of energy is transferred from the meteorites' kinetic energy stores very quickly.

The kinetic energy storage of meteorites are communicated to the surrounding environment as heat, sound, and light energy.

A meteorite penetrates the atmosphere of the Earth. Friction acts on the meteorite when it reaches the Earth's atmosphere. When a meteorite enters the Earth's atmosphere, it gains kinetic energy. The meteorite catches fire due to friction. At this time, the meteorite's kinetic energy will be transformed into heat energy, sound energy, and light energy.

Hence kinetic word word completes the sentence.

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Answer:

219 m/s

Explanation:

Kinetic energy is calculated using the formula:

Given:

We can solve for the unknown variable v.

Substitute these known values into the formula.

The velocity of the car is around 219 m/s.

Answer:

you need to attach a picture so I can answer it

Answer:

Periodic.

Explanation:

Electromagnetic waves is a propagating medium used in all communications device to transmit data (messages) from the device of the sender to the device of the receiver.

Generally, the most commonly used electromagnetic wave technology in telecommunications is radio waves.

Radio waves can be defined as an electromagnetic wave that has its frequency ranging from 30 GHz to 300 GHz and its wavelength between 1mm and 3000m. Therefore, radio waves are a series of repetitive valleys and peaks that are typically characterized of having the longest wavelength in the electromagnetic spectrum.

Basically, as a result of radio waves having long wavelengths, they are mainly used in long-distance communications such as the carriage and transmission of data.

Generally, a fixed speed is used for the propagation of traveling waves and this speed is usually denoted with the variable "v" or sometimes "c."

Furthermore, if the waveform of a traveling wave is repeated every time at specific intervals T, it is referred to as periodic wave.

Mathematically, the period of a traveling wave is given by the formula;

\( Period = \frac {1}{T} \)

Where;

T is the time measured in seconds.

Therefore, the magnitude of the net force on the mower is 134.9 N.

Force is an influence that can cause an object to undergo a change in motion or acceleration. It is a vector quantity, which means it has both magnitude (size or strength) and direction. Force can be measured in units such as newtons (N) or pounds (lbs). It can result from a variety of sources, including gravity, electromagnetic fields, and contact between objects.

Here,

First, we need to resolve the pushing force into horizontal and vertical components.

F_horizontal = 264.8 N * cos(55.0°) = 152.9 N

F_vertical = 264.8 N * sin(55.0°) = 210.7 N

Since the net external force on the mower is horizontal to the right and the force of friction opposes the motion, we can write:

Net force = F_horizontal - f

where f is the force of friction.

Substituting the given values, we get:

Net force = 152.9 N - 18.0 N = 134.9 N

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Answer:

yess

Explanation:

Answer:

yes me

Answer:

frequency=velocity/wavelength

ie velocity=frequency×wavelength=33×4=134m/s

The speed of each ball  after the collision  is 1.69 m/s  and direction  is same of the tennis ball's initial motion.

According to the principle of momentum conservation, momentum is only modified by the action of forces as they are outlined by Newton's equations of motion; momentum is never created nor destroyed inside a problem domain.

According to principle of momentum conservation:

the velocity of the two ball  mass after the perfectly inelastic collision is

= (0.060 kg × 2.50 m/s + 0.090 kg × 1.15 m/s) ÷ ( 0.060 kg + 0.090 kg)

= 1.69 m/s

Hence, the speed of each ball is 1.69 m/s.

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Answer:

The range of the ball is 11.6 meters

Explanation:

Projectile Motion

It's the type of motion that experiences an object launched with an initial angle and moves along a curved path exclusively under the action of gravity.

Being vo the initial speed of the object, θ the initial launch angle, and g the acceleration of gravity, then the maximum horizontal distance traveled by the object (also called Range) is:

\(\displaystyle d={\frac {v_o^{2}\sin(2\theta )}{g}}\)

The football is kicked with an initial speed of vo=11 m/s at an angle of θ=35°.

Calculating the range:

\(\displaystyle d={\frac {11^{2}\sin(2\cdot 35^\circ)}{9.8}}\)

\(\displaystyle d={\frac {121\sin(70^\circ)}{9.8}}\)

d = 11.6 m

The range of the ball is 11.6 meters

Answer:

mass of an object = 4kg

acceleration due to gravity on earth = 9.8 m/s²

therefore , weight of an object on earth = Mass × gravity

=> weight = 4×9.8 => 39.2 N

since , weight is a force we measure it in newtons

The following statements accurately describe matter:

Matter is made up of tiny particles called atoms.

Atoms cannot be divided and still retain the properties of their original state.

What is Atom?

An atom is the basic unit of matter, consisting of a nucleus composed of protons and neutrons, surrounded by electrons in electron shells or energy levels. Atoms are the building blocks of all matter and are the smallest unit of an element that retains the chemical properties of that element.

The statement "Atoms cannot be divided and still retain the properties of their original state" refers to the concept of the indivisibility of atoms, as proposed by John Dalton in the early 19th century. According to Dalton's atomic theory, atoms are considered to be the smallest unit of matter that retains the properties of an element. In other words, atoms are considered to be indivisible and cannot be further broken down into smaller particles without losing their characteristic properties.

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The gravitational attraction force between the Earth and the Moon is approximately 1.982 × 10^20 Newtons.

The gravitational attraction force between the Earth and the Sun is approximately 3.52 × 10^22 Newtons.

The gravitational attraction between two objects can be calculated using Newton's law of universal gravitation, which states that the force of gravity between two objects is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers. The equation for the gravitational force (F) is given by:

F = (G * m1 * m2) / r^2

Where:

F is the gravitational force between the objects,

G is the gravitational constant (approximately 6.67430 × 10^-11 m^3 kg^-1 s^-2),

m1 and m2 are the masses of the two objects, and

r is the distance between the centers of the two objects.

Gravitational attraction between Earth and Moon:

The mass of the Earth is approximately 5.972 × 10^24 kg, and the mass of the Moon is approximately 7.342 × 10^22 kg. The average distance between the Earth and the Moon is about 384,400 kilometers (or 384,400,000 meters).

Plugging in these values into the equation, we can calculate the gravitational attraction force between the Earth and the Moon:

F = (G * m1 * m2) / r^2

= (6.67430 × 10^-11 * 5.972 × 10^24 * 7.342 × 10^22) / (384,400,000)^2

Calculating this, we find that the gravitational attraction force between the Earth and the Moon is approximately 1.982 × 10^20 Newtons.

Gravitational attraction between Earth and Sun:

The mass of the Sun is about 1.989 × 10^30 kg, and the average distance between the Earth and the Sun (known as an astronomical unit or AU) is about 149.6 million kilometers (or 149,600,000,000 meters).

Using the same equation as above:

F = (G * m1 * m2) / r^2

= (6.67430 × 10^-11 * 5.972 × 10^24 * 1.989 × 10^30) / (149,600,000,000)^2

Calculating this, we find that the gravitational attraction force between the Earth and the Sun is approximately 3.52 × 10^22 Newtons.

Answer:

49.05 N

Explanation:

5 × 9.81 = 49.05

Movements or forces of an object in the horizontal plane have no effect on movements or forces in the vertical dimension;

The movement of 0.2ms⁻¹ leftwards is irrelevant

The magnitude and direction of the resultant force can be determined by finding the vector sum of all the individual forces acting on an object using vector addition.

This is involves finding the components of the forces in x and y direction and using Pythagorean theorem to find the magnitude and using inverse tangent to find the direction.

A resultant force is the net force acting on an object, taking into account all the individual forces. The magnitude of the resultant force is the sum of the magnitudes of all the forces and the direction is the direction in which the net force is acting.

Vector addition is used to find the magnitude and direction of the resultant force, which can be determined by finding the components of the individual forces and finding the vector sum of the components. The vector sum can then be used to find the magnitude and direction of the resultant force.

For example, consider two forces F1 and F2 acting on an object. If F1 has a magnitude of 50 N and is acting at an angle of 30 degrees and F2 has a magnitude of 30 N and is acting at an angle of 60 degrees, the magnitude and direction of the resultant force can be determined using vector addition.

By finding the x and y components of each force and finding the vector sum, the magnitude and direction of the resultant force can be determined to be 50.6 N and 39.2 degrees, respectively.

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The displacement is defined as the shortest distance between the starting and ending point along with the direction. Thus, option D is correct.

The displacement is defined as the shortest distance between the starting and ending point. The displacement is the vector quantity. It is also defined as the distance traveled by the object along with a particular direction. The distance is the scalar quantity and the displacement is the vector quantity. The SI unit of distance is a meter. The rate of change of displacement gives rise to velocity and the rate of distance gives rise to distance.

From, the given displacement is defined as the shortest length and direction from a starting and ending point. Thus, the correct option is D.

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Answer:

While Jose is walking, his body is in motion, but when the bus stops, he continues to move forward due to inertia.

Explanation:

inertia

Answer:

Jose falls on the floor of the bus.

Explanation:

because his body is in motion

A light bulb uses electrical energy to generate light. It uses 3 V of an electric charge and 20 A of electric current.The light bulb's power is 60 Watt.

The term voltage is defined the pressure from an electrical circuit's power source that forces charged electrons through a conducting loop, enabling them to do work such as lighting a light. So, voltage = pressure, and it is measured in volts (V).

Power = Current × voltage

Given:

electric current = 20 A

voltage =  3 V

Power = ?

By substituting given values in equation and we get,

Power = 20 × 3

= 60 Watt

Thus, the light bulb's power is 60 Watt.

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$\sf\textbf{Tip\:speed\:of\: main\:rotor}\:\:=\:\pi \times$

$\sf\textbf{diameter\:of\:main\:rotor} \times {rotational\: speed\:of main\:rotor}$

$\implies\sf\textbf\:=\:\pi \times 7.59\:{ m} \times 448\:{\:rev/min}$

$\implies\sf\textbf\:=\:10,676.68\:{\:m/min}$

$\sf\textbf\:{Tip\:speed\:of\:tail\:rotor}\:=\:\pi \times$

$\sf\textbf\:{diameter\:of\:tail\:rotor} \times\:{rotational\:speed\:of\:tail\:rotor}$

$\implies\sf\textbf\:=\:\pi \times 1.00\:{ m} \times 4140\:{\:rev/min}$

$\implies\red\bigstar{\boxed{\textsf{\textbf{\:=\:13,015.93 \text{ m/min}}}}}$

\(\huge{\colorbox{black}{\textcolor{lime}{\textsf{\textbf{I\:hope\:this\:helps\:!}}}}}\)

\(\begin{align}\colorbox{black}{\textcolor{white}{\underline{\underline{\sf{Please\: mark\: as\: brillinest !}}}}}\end{align}\)

\(\textcolor{blue}{\small\textit{If you have any further questions, feel free to ask!}}\)

\({\bigstar{\underline{\boxed{\sf{\textbf{\color{red}{Sumit\:Roy}}}}}}}\\\)

The skater's final angular velocity is approximately 9.86 rad/s.

The skater's final angular velocity can be calculated using the principle of conservation of angular momentum. The equation for angular momentum is given by:

L = Iω

where L is the angular momentum, I is the moment of inertia, and ω is the angular velocity.

Initially, the skater has an angular momentum of:

L_initial = I_initial * ω_initial

Substituting the given values:

L_initial = 2.12 kg m² * 3.25 rad/s

The skater's final angular momentum remains the same, as angular momentum is conserved:

L_final = L_initial

The final moment of inertia is given as 0.699 kg m². Therefore, the final angular velocity can be calculated as:

L_final = I_final * ω_final

0.699 kg m² * ω_final = 2.12 kg m² * 3.25 rad/s

Solving for ω_final:

ω_final = (2.12 kg m² * 3.25 rad/s) / 0.699 kg m²

Hence, the skater's final angular velocity is approximately 9.86 rad/s.

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when Force (N) is 10.0 Length (m) is 0.60

when Force (N) is 8.0 Length (m) is 0.40

when Force (N) is 4.0 Length (m) is 0.20

when Force (N) is 4.0 Length (m) is 0.20

when Force (N) is 2.0 Length (m) is 0.10

chatgpt

49. To find the length of a pendulum that has a period of 2.3 seconds on the Moon, where the gravitational acceleration (g) is 1.6 N/kg, we can use the formula:

Period (T) = 2π√(Length (L) / g)

Substituting the given values:

2.3 = 2π√(L / 1.6)

To solve for L, we can rearrange the formula:

L = (2.3 / (2π))^2 * 1.6

L ≈ 0.781 meters (or 78.1 centimeters)

So, the pendulum must be approximately 0.781 meters (or 78.1 centimeters) long to have a period of 2.3 seconds on the Moon.

50. Ranking Task:

To rank the pendulums according to their periods, we need to consider both the length and mass of each pendulum.

Ranking from least to greatest period:

1. A: 10 cm long, mass = 0.25 kg

2. C: 20 cm long, mass = 0.25 kg

3. B: 10 cm long, mass = 0.35 kg

There is a tie between pendulums A and C, as they have the same length but different masses.