explain the relationship between diffraction angle and wavelength using the two dimensional diffraction relationship n

A. The acceleration of the bucket is 3.58 m/[tex]s^{2}[/tex].

B. bucket is moving with a velocity of 3.28 m/s.

What is acceleration?

If an object's velocity changes, it is said to have been accelerated. An object's velocity can alter depending on whether it moves faster or slower or in a different direction. A falling apple, the moon orbiting the earth, and a car stopped at a stop sign are a few instances of acceleration. Through these illustrations, we can see that acceleration happens whenever a moving object changes its direction or speed, or both.

What is Velocity?

The direction in which a body or an object is moving.

What are the calculations?

Given that the mass of bucket m = 22.0 kg

Weight of the box W = 375 N

Then the mass of box M = W / g

      = 375 / 9.8 m/[tex]s^{2}[/tex]

      = 38.27 N

Let T be the tension in the string

Let a be the acceleration of the bucket

Apply Newton's second law to the bucket

                    mg - T = ma

                            T = m (g - a)             ....... (1)

Apply Newton's second law to the box

                            T = Ma                     ....... (2)

From equations (1) and (2) we get

                         Ma = m (g-a)

              ( m+ M )a = m g

                            a = m g / (M + m)

= (22.0 kg) (9.8 m/[tex]s^{2}[/tex]) / (22.0 kg + 38.27 kg )

= 3.58 m/[tex]s^{2}[/tex]

Initial velocity of the bucket u = 0

Let  v be the final velocity of the bucket after displacement s = 1.5 m

From equation of motion

                  v2 - u2 = 2as

                  v2 - 0 = 2as

                       v  = √2as

                       v  = √2(3.58 m/[tex]s^{2}[/tex])(1.5 m)

                       v  = 3.28 m/s

Hence, the acceleration of the bucket is 3.58 m/[tex]s^{2}[/tex] and the bucket is moving with a velocity of 3.28 m/s.

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(D) Since both conservative and non-conservative forces are involved, so the sum of all of them will be conserved. The kinetic energy, potential energy and thermal energy all together is conserved in the system.

What is Kinetic energy?

A moving object or particle has kinetic energy, which depends on both its mass and its rate of motion. The type of motion can be vibration, rotation on an axis, translation (or travel along a path from one place to another), or any combination of these.

What is Thermal energy?

Heat is the transfer of thermal energy, whereas thermal energy is the entire internal energy of a system's temperature.

Hence, the kinetic energy, potential energy and thermal energy all together is conserved in the system.

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The potential energy of the spring when it is stretched 0.900 mm is 228 J. The potential energy when it is compressed is 2.88J.

Hooke's law states that the elongation of a material is proportional to the applied stress within the elastic limits of the material.

Using Hooke's law

F = kx

570 = k * 0.9

k = 712.5 N/m

(a) energy at x = 0.8 m

U = 0.5 k x^2 = 0.5* 712.8* 0.8^2

U = 228 J

(b) U = 0.5 * 712.8* 0.09^2

U = 2.887 J

Elastic potential energy is the potential energy released as a result of the deformation of an elastic body. B. Spring extension is stored. This is equal to the work done to stretch the spring, which depends on the spring constant k and the stretched distance. The force exerted by the spring is the restoring force that helps return the spring to its equilibrium length.

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Different torques can be generated by the same force. When the force and lever arm are both large, greater torques are generated.

A torque is a linear force's reciprocating rotating counterpart. Distance travelled over a predetermined period of time is referred to as speed. Torque and speed are related to one another inversely in proportion. Numerically describing the torque of a rotating object is done by dividing power by angular velocity.

Torque is the unit of measurement for the force that may rotate an item around an axis. The acceleration of an item in linear kinematics is caused by force. An angular acceleration is caused by torque in a manner similar to this. It follows that torque might be viewed as the rotational counterpart to force.

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Counterclockwise, Because north pole of magnet is moving towards loop and emf is induced in counterclockwise. b) Clockwise; Because north pole of magnet is moving away from the loop and flux is decreasing through loop so clockwise emf is induced.

Anything that creates a magnetic field is considered to be a magnet. The most noteworthy characteristic of a magnet—a force that pulls on other ferromagnetic elements like iron, steel, nickel, cobalt, etc.—is caused by this invisible magnetic field, which also attracts or repels other magnets.

A piece of equipment built from a substance that has been magnetized and produces a consistent magnetic field is called a permanent magnet. A typical illustration is a fridge magnet used to keep notes on the door of the refrigerator. Ferromagnetic materials are those that are both capable of magnetization and are attracted to magnets strongly (or ferrimagnetic).

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Answer: The maximum velocity of the object if the object bounces 3.45 cm above and below its equilibrium position is 4.62 m/s.

Reason:

The maximum velocity of the object is 4.62 m/s. This can be calculated by using the equation v = sqrt(2 * g * x), where g is the acceleration due to gravity (9.8 m/s2) and x is the displacement from the equilibrium position (3.45 cm), or 0.0345 m.

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The number of independent directions in which movement is possible  dimension in the context of relative motion.

To discuss relative motion in one or more dimensions, the idea of reference frames was initially developed. When we refer to an object's velocity, we are referring to it in relation to the so-called reference frame. When measuring an object's velocity in daily life, the ground or the earth is assumed to be the reference frame.

As an illustration, if you are travelling in a train that is moving at 100 km/h, then from the perspective of another passenger in the train, you are moving at a speed of zero. He says you're standing still. However, if a bystander sees you standing on the ground outside the train, he claims that you are going with the train.

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The total internal reflection is the complete reflection of a ray of light within a medium such as water or glass from the surrounding surfaces back into the medium. The phenomenon occurs if the angle of incidence is greater than a certain limiting angle, called the critical angle.

This is an internal total reflection exercise, the equation that describes this process is

        sin θ = n₂ / n₁

where n₂ is the index of the incident medium and n₁ the other medium must be met n₁> n₂

       θ = sin⁻¹ n₂ / n₁

let's calculate

      30⁰ = sin⁻¹ (n₂ / n₁)

Therefore, if the angle is greater then the totally internal reflection also increases.

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The turntable's angular velocity, in rpm, just after this event is 39,72 rad/m

We can use the law of conservation of angular momentum.

Its a law that states the amount of momentum before and after producing is equal or constant collision.

The equation:

L₁ = L₂

I₁ x ω₁ = I₂ x ω₂

We have,

Mass of the table = 2.0 kg ⇒ m₁

Diameter of the table = 20 cm = 0.2 m ⇒ d, so R = 0.1

Angular speed = 140 rpm = 14.65 rad/s ⇒ ω₁

Mass of the blocks = 520 g = 0.52 kg ⇒ m₂

So,

I₁ x ω₁ = I₂ x ω₂

(½ mR²) ω₁ = (½ mR² + m₁R² + m₂R²)  ω₂

(½ (2.0) (0.1)² (14.65) = (½ (2.0) (0.1)² + (2.0) (0.1)² + (0.52) (0.1)²  ω₂

0.1465 = (0.01 + 0.02 + 0.02 + 0.0052) ω₂

ω₂ = 4.16 rad/s ⇒ 39,72 rad/m

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The maximum speed of the object is 1.28 m/s.

What is Speed?

Speed is described as the rate at which an object's position changes in any direction. Speed is defined as the distance traveled divided by the travel time. Speed is a scalar quantity because it only has a direction and no magnitude.

One meter per second is the speed of an object, for instance, if it starts at the origin and moves three meters in three seconds. Simple math can be used to calculate speed. time-distance ratio.

According to the given information:

Force constant K:78.5 n/m

Mass: 0.185 kg

The maximum speed of the object is,

[tex]$$\begin{aligned}v_{\mathbf{n} E} & =A \omega \\& =A \sqrt{\frac{k}{m}}\end{aligned}$$[/tex]

Here A is the amplitude, k is force constant, m is mass.

[tex]$$\begin{aligned}v_{\mathrm{ne:}} & =\left(6.25 \times 10^{-2} \mathrm{~m}\right) \sqrt{\frac{78.5 \mathrm{~N} / \mathrm{m}}{0.185 \mathrm{~kg}}} \\& =1.28 \mathrm{~m} / \mathrm{s}\end{aligned}$$[/tex]

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Answer:

What is a Shepherd planet?

Image result for What is shepherding? (it involves space)

An international team of astronomers exploring the disk of gas and dust around a nearby star have uncovered a compact cloud of poisonous gas formed by ongoing rapid-fire collisions among a swarm of icy, comet-like bodies.

Explanation:

According to the principle of continuity, the velocity of a fluid multiplied by the cross-section through which it flows at one point will equal the product of velocity and cross-section at another point.

The principle of continuity, also known as the continuity equation, is the fluid mechanic's principle. Simply put, what flows into a defined volume over a specified period of time minus what flows out of that volume over that specified period of time must accumulate in that volume. The substance in that volume is depleted if the accumulation's sign is negative.

This is so that our eyes, once they start to follow anything, will keep moving in that direction until they come across another thing or object. A line with an arrow at the end of it, for instance, is a great illustration of the continuity concept.

Note that three conditions must be met for a function to be continuous at a point: At that time, the limit must exist.

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The average speed is 228.75 km/h.

Speed is the time rate at which an object is travelling along a route. To put it another way, velocity is a vector, whereas speed is a scalar value.

What is the speed-distance formula?

Speed is equal to distance traveled and time spent.

Distance is determined by multiplying the time and the speed.

Time is determined by speed and distance.

Given:

Distance = 30.5 kilometers

Time= 8 minutes

= 8/60 hour = 2/15 hour

Now, average speed equals distance / time.

= 30.5 x 15/2

= 228.75 Km/ h

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The period of the vibration is 3.9ms

The period (T) of a vibration is the time to complete one oscillation or revolution and is measured in seconds. The period of vibration is given as

T= 1/F

For example, if the period of a vibration is 0.1 second (one vibration takes 0.1 second), then the frequency of the vibration is 1/0.1=10 vibrations per second or 10 hertz.

Similarly if the frequency of a vibration is 256hz, the period T= 1/F= 1/256=0.0039s

1second= 1×10³ms

therefore 0.0039s = 0.0039×10³= 3.9ms

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The direction of the magnetic field depends on the direction of the current in the wire.

What is magnetic field?
A magnetic field is indeed a vector field which explains the magnetic influence on moving electrical charges, electric currents, as well as magnetic materials. A force perpendicular to the charge's own motion and the magnetic field acts on it when the charge is moving through a magnetic field. The magnetic field of a permanent magnet pulls on magnetic material like iron and attracts as well as repels other magnets. The three other magnetic effects of paramagnetism, diamagnetism, as well as antiferromagnetism also exert minute forces on "nonmagnetic" materials in a nonuniform magnetic field, though these forces are typically so minute that they can only be discovered by laboratory equipment. Electric currents, like those used in electromagnets, as well as electric fields that change over time produce magnetic fields that surround magnetised materials.

The magnitude of the magnetic field at P can be determined using the equation B = μ0I/2πr, where μ0 is the permeability of free space, I is the current, and r is the distance from the wire. Thus, the magnetic field at P is:
B = (4π x 10-7 T•m/A) x (3.10 A) / (2π x 0.239 m) = 0.817 T
The direction of the magnetic field depends on the direction of the current in the wire. If the current is flowing in the clockwise direction, then the magnetic field will be directed out of the plane of the paper at P. If the current is flowing in the counterclockwise direction, then the magnetic field will be directed into the plane of the paper at P.

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There are many different sizes and shapes of galaxies. Low-angular-momentum protogalactic clouds may have generated spheroidal star systems, whereas clouds with larger angular

The characteristic of just about any rotating object determined by the product of the moment of inertia and the angular velocity is known as angular momentum. It is a characteristic of rotating bodies determined by the sum of their moment of inertia + angular velocity.

The rotational equivalent of linear momentum in physics is called angular momentum, also known as moment of momentum , rotational momentum. Because this is a constant number total angular momentum of such a closed environment stays constant—it is a significant physical quantity.

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Answer: Endothermic and Exothermic reactions

The solar seems to be 1/39th, or zero.026 times as large as visible from Earth. when considered from the floor of Pluto.

Pluto is so far away from the sun (common distance to her is three,670,050,000 miles) that the solar seems much darker and smaller than it does from Earth.

From Pluto, the solar seems as a very brilliant star, illuminating Pluto at some point of the day approximately as a great deal as the whole Moon illuminates the Earth at night.

Nearest (perihelion) 2.seventy six billion miles from our megastar. at the furthest point (Aphelion) it's miles four.58 billion miles away. that is approximately zero.000456308 light years from sun.

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38 Bright fringes will be seen in the central diffraction maximum when a two-slit Fraunhofer interference-diffraction pattern is observed.

Diffraction is when waves such as light or sound spread as they travel around an object or through a slit.

In case of diffraction , angular width of central maxima = 2 λ/d

λ is wave length of light  = 660 nm

d is slit width = 0.01 mm

In case of interference , angular width of each fringe = λ /D

D is distance between two slits = 0.19 mm

Number of interference fringe in central diffraction fringe can be calculated by the formula

=2 λ/d x D/λ

= 2 x D /d = 2 x .19/0.01

= 38

38 bright fringes will be seen in the central diffraction maximum.

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Velocities V1 and V2 will exchange in general. Velocity may increase or decrease. If V1 decreases, then V2 increases. The angle between velocities also gets changed.

For a head-on elastic collision for two equal masses, the velocities gets exchanged. For a non-head-on elastic collision for two equal masses, the angle between the velocities is always 90 degrees.

Where the projectile is much heavier than the target, the velocity of the given target particle changes to about twice that of the projectile after the collision. And the projectile velocity will remain unchanged. In this case, the angle between the projectile and the target remains less than 90 degrees.

In the case of a head-on elastic collision, when there is a small projectile and a much more heavy target, the projectile will bounce back with the same speed, and the massive target will gain a very small velocity. In this case, the angle of the path of the projectile will be more than 90 degrees.

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The wavelength of light will be  5.17 x10⁻⁷ m

Since we are given the angle of  15.0, and transmission grating having 5000 slits/cm, for a normal incidence

since we know the diffraction of first-order formula is :

d sineθ =nλ ,and the separation os the slits are : d= 1/N

=>d=1/ 5000  = 2x 10^-6 m

Now subsituing the value of d in the main formula of diffraction, where we get the wavelength of :

λ = dsine θ/ n

since here n is 1

λ=  2x 10 *sine 15.0/ 1

λ = 2x 10^-6 *0.2588   = 5.17 x10⁻⁷ m

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The small rubber ball was moving quickly as well as a huge metal ball is now at rest. The massive metal ball starts to roll more slowly once they meet, slowing the small rubber ball's speed.

Momentum is characterized as the intensity of a body's motion. As momentum depends on both velocity as well as the direction of a body's motion, it is quantified by "mass velocity". Because velocity is just a vector and mass is a scalar, momentum is a vector.

Momentum can be viewed as a body's "power" while it is moving, or the amount of force it can exert on another body.

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13.7 × [tex]10^{8}[/tex], the approximate number of capillaries in the human body, that are carrying blood from the aorta.

What is Aorta?

A huge, cane-shaped blood channel called the aorta carries oxygen-rich blood to your body. It travels across the chest and belly after beginning in the lower left corner of the heart. Blood arteries leave the aorta along the way and extend to the organs and supporting tissue.

What are the Calculations?

The speed of the blood in the aorta is  v = 35cm/s

the radius of the aorta is r = 1.1 cm

the area of the cross-section of the aorta is A =π[tex](1.1cm^{2} )[/tex]

the speed of the blood in  the capillary v ' = 0.078 cm/s

radius of the capillary is r = 6.3 × [tex]10^{-4}[/tex]cm

Now area of cross-section of capillary is A' = Π[tex](6.3 * 10^{-4}) ^{2}[/tex]

Let  there be N number of capillaries

The volume rate of flow in the aorta is the total sum of the volume rate of flows in the capillaries.

Then  Av  = N*A' *v'

    Π(1.1cm)² (35 cm/s)   = N * (Π[tex](6.3 * 10^{-4}) ^{2}[/tex])* 0.078 cm/s

N = 13.7 × [tex]10^{8}[/tex]

Hence, 13.7 × [tex]10^{8}[/tex], the approximate number of capillaries in the human body, that are carrying blood from the aorta.

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Answer: 39.75 kg

Explanation:

p = mv where,

p = momentum

m = mass

v = velocity

Given p=318 kg*m/s

v=8 m/s

therefore, 318=8*m

or, m= 318/8= 39.75

According to the special theory of relativity, all laws of nature are the same in all uniformly moving reference frames. Option B.

Einstein's Special Theory of Relativity states that the same laws of physics apply to all inertial frames of reference and that the speed of light is the same for all observers. The basic laws of physics are the same for all inertial frames of reference.

Because otherwise, we wouldn't call it a fundamental law. Call them contingency laws and look for deeper fundamental laws that are invariant under a larger set of symmetries. Describes the propagation of matter and light at high speed. It is based on the constancy of the speed of light and the relativity principle in all inertial frames of reference.

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Answer:

Explanation:

Given:

Q = 2277 J

A = 508 J

__________

ΔU - ?

ΔU = Q - A

ΔU = 2277 - 208 = 2069 J

If the pebble on the board do not want to lose contact with one another, so the maximum acceleration would be equal, rather would be equal to four pies square times the frequency squared times the amplitude and this has to be less than G.

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The distance that the canoe moves in this process is 1.29 meters.

We first have to find the center of mass

X = MsXs + McXc/ Mw+Mc

Where

Ms = Woman's mass = 45

Mc = Canoe's mass = 60kg

Xs = position from left= 1 cm

Xc = position from left end of canoe's mass = 2.5cm

When we put these values into the equation we have:

X= 1.857

The center of gravity lies at the center of this boat. Therefore,

3.14 metres

To get the distance that is moved by this canoe distance = 3.143-1.857

= 1.286

≈ 1.29 meters

Thus, The distance that the canoe moves in this process is 1.29 meters.

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The strength of gravitational or electrostatic fields is frequently determined using the inverse square law as an illustration, the Earth's surface has a gravitational field strength of about 9.8 N/kg.

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The approximate distance to this new cluster is 1 billion light-years.

What is a Galaxy Cluster?

A galaxy cluster, also known as a cluster of galaxies, is a formation made up of a large number of gravitationally connected galaxies, typically with masses between 1014 and 1015 solar masses. Before superclusters were found in the 1980s, they were thought to be the largest known structures in the universe and are now the second-largest known gravitationally bound structures in the cosmos after galaxy filaments.

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The approximate distance to this new cluster is 1 billion light-years.

What is a Galaxy Cluster?

A galaxy cluster, also known as a cluster of galaxies, is a formation made up of a large number of gravitationally connected galaxies, typically with masses between 1014 and 1015 solar masses. Before superclusters were found in the 1980s, they were thought to be the largest known structures in the universe and are now the second-largest known gravitationally bound structures in the cosmos after galaxy filaments.

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