a novelty clock has a 0.014-kg mass object bouncing on a spring that has a force constant of 1.6 n/m. (a) what is the maximum velocity of the object if the object bounces 3.45 cm above and below its equilibrium position?

The vertical component of force is 10.78N

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Answer: True

Explanation:

A) Moment of inertia about an axis passing through the point where the two segments meet : [tex]$I_A=\frac{1}{12} M L^2$[/tex]

B) Moment of inertia passing through the point where the midpoint of the line connects to its two ends: [tex]$I x=\frac{1}{3} M L^2$[/tex]

What is Moment of inertia?

The term "moment of inertia" refers to a physical quantity that quantifies a body's resistance to having its speed of rotation along an axis changed by the application of a torque (turning force). The axis might be internal or exterior, fixed or not.

A) The moment of inertia about an axis passing through the point where the two segments meet is [tex]$I_A=\frac{1}{12} M L^2$[/tex]given that the rod is bent at the center and distance from all the points to the axis remains the same, the moment of inertia about the center will remain the same.

B) Determine the moment of inertia about an axis passing through the point midpoint of the line which connects the two ends

First step: determine the distance between the ends ( d )

After applying Pythagoras theorem[tex]$\mathrm{d}=\frac{\sqrt{2}}{2} L$[/tex]

Next step : determine distance between the two axis [tex]$(\mathrm{x})$[/tex]

After applying Pythagoras theorem

[tex]\mathrm{x}=\frac{\sqrt{2}}{4} L$$[/tex]

Final step : Calculate the value of [tex]$\mathrm{I}_{\mathrm{x}}$[/tex]

applying Parallel Axis Theorem

[tex]$$I_x=I_8+M x^2$$[/tex]

[tex]$$\begin{aligned}& =\frac{1}{12} M L^2+\frac{1}{4} M L^2 \\& \therefore \quad I x=\frac{1}{3} M L^2 \\&\end{aligned}$$[/tex]

Hence we can conclude that Moment of inertia about an axis passing through the point where the two segments meet: [tex]$I_A=\frac{1}{12} M L^2$[/tex], Moment of inertia passing through the point where the midpoint of the line connects its two ends: [tex]$I x=\frac{1}{3} M L^2$[/tex]

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Mutual inductance is the property by which one coil affects the current and voltage of the other coil.

Magnetic flux us the total magnetic field around both the coils.

EMF are invisible energy around the coils, which are mainly referred to as radiation.

How to find mutual inductance, magnetic flux and EMF around two coils?

We know

N = 30 turns

N¹= 310 turns

Inner solenoid length L¹= 20 CM= 0.2m long

Diameter d¹= 2.5 CM= 0.025m

Current i¹= 0.150 A

Rate of increase in current = di¹/dt= 1700A/s

Part A : magnetic flux = ∅¹= B¹A¹

B¹= ûⁿ × n¹ × i¹ = 2.92× 10↑-4T

Thus, ∅= 2.92×10↑-4× π/4×0.025²

= 1.432×10↑-7 Wb

Part B

Magnetic flux in one coil× number of turns in second coil = mutual inductance× current in the first coil

∅¹ × N² = Mi¹

= 1.432×10^-7 ×30

M × 0.150=1.432×10^-7×30

M=2.86×10^-5H

Part C

E = M di¹/dt

= 2.86×10^-5×1700 V

= 0.048 V

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In view of both the given query The inner solenoid's mean flux density per rotation is 1.43 * 10⁻⁷ Wb, or the two solenoids' mutual coupling is 2.86 x 10⁻⁴ H. The induced emf in the exterior loop is 4.86 * 10⁻¹ V.

A solenoid operates by creating an electromagnetic field surrounding an armature, which is a moving core. The electromagnetic field causes the armature to move, and when it does, it opens and closing valves or switches, converting mechanical energy into electrical movements and force.

Given:

N1 = 310 revolutions in the inner solenoid.

N2 = 30 is the number of revolutions in the outer solenoid.

The inner solenoid's length is 20 cm, or 0.2 meters.

Inner solenoid radius = r = diameter/2 = 2.50/2 = 1.25 cm = 0.0125 m

The inner solenoid's current I is equal to 0.150 A.

1700 A/s is the current growth rate, di/dt.

A). Average magnetic flux across the inner solenoid's turns is equal to BA.

Include the values:

Average magnetic flux via the inner solenoid's turns:

= [4π x 10⁻⁷][310/0.2][0.150]π(0.0125)²

= 1.43 * 10⁻⁷ Wb

B). The two solenoids' mutual inductance is given by M = N2 x (average flux) / current.

= (30 x 1.43 * 10⁻⁷) / 0.150

= 2.86 x 10⁻⁴ H

C). The change in current there in inner solenoid causes an induced emf in the outer magnet that is equal to M*di/dt.

= 2.86 x 10⁻⁴ * 1700

= 4.86 * 10⁻¹ V

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This set of angles would be the angles at which destructive interference occurs, which is 180° apart from the angles at which constructive interference occurs.

What is Intensity?

The power transmitted per unit area is known as the intensity as well as flux of radiant energy.

Uses of Intensity

Intensity is most frequently used to describe the average power transfer above one period of the wave. Other situations where energy is transmitted can also be described in terms of intensity.

Hence, The set of angles given by the equation in Part III is the set of angles at which the maximum intensity of light is produced.

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This set of angles would be the angles at which destructive interference occurs, which is 180° apart from the angles at which constructive interference occurs.

What is Intensity?

The power transmitted per unit area is known as the intensity as well as flux of radiant energy.

Uses of Intensity

Intensity is most frequently used to describe the average power transfer above one period of the wave. Other situations where energy is transmitted can also be described in terms of intensity.

Hence, The set of angles given by the equation in Part III is the set of angles at which the maximum intensity of light is produced.

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At a point, Y refraction is observed and the light ray is moving away from the normal means going from the denser to the rarer medium, at point Z, the light ray is moving towards the normal, which means travelling in the denser medium.

The redirection of a wave as it travels through one medium and into another is called refraction. The wave's altered speed or a shift in the medium might both result in a redirection. Refraction of light is governed by Snell's rule, which states that for a given set of media, the ratio of the sines of the angle of incidence and angle of refraction is equal to the phase velocities (v1/v2) or, alternatively, the refractive indices (n2/n1) of the two media.

A medium is said to be optically denser if the speed of light is lower in it. In terms of optical density, glass is a denser medium than air.

Hence, at a point, Y refraction is observed and the light ray is moving away from the normal means going from the denser to the rarer medium, at point Z, the light ray is moving towards the normal, which means travelling in the denser medium.

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The ball goes up to 35.83 ft high. The result is obtained by using the formula of motion with constant acceleration.

A motion along a straight line with a constant acceleration is a motion which the initial and final velocity change. There are 3 important formulas in this case for vertical motion.

v₁ = v₀ + gt

v₁² = v₀² + 2gh

h = v₀t + 1/2 gt²

Where

Note: If the object goes up, the value of g is (-).

A ball moves from the ground straight up with a velocity of 48 ft/sec. Find the height of the ball!

First, we change the unit of initial velocity.

v₀ = 48 ft/sec

v₀ = 48 × 0.3048 m/s

v₀ = 14.63 m/s

The ball will go up to a certain height. At the maximum height, the velocity of the ball is 0. Thus, we can use the following formula to find h.

v₁² = v₀² - 2gh

0 = (14.63)² - 2(9.8)h

214.04 = 19.6h

h = 10.92 m

h = 10.92/0.3048 ft

h = 35.83 ft

Hence, the ball will go straight up to a height of 35.83 ft.

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A diverging lens has a focal length of magnitude 21.8 cm and the images are located behind the lens.

(a) u = -10.9 cm

1/v= 1/10.9 - 1/21.9

v= 21.8cm

Behind the lens.

(b) 1. Virtual

    2. Virtual

    3. Real

(c) m = v/u

 1. Erect/ Upright

2. Upright

3. Inverted

(d) m = v/u

1. m = -43.6/-43.6 = 1.  Magnification = 1.

2. infinity.

 3. m = 21.8 / -10.9 = -2. Magnification = -2.

Therefore, these are the answers for above given question.

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The tension in string 1 is lesser than to the tension in string 2.

What is meant by tension in a string?

It is possible to refer to tension as the action-reaction pair of forces acting at each end of the aforementioned elements. Tension is defined as the pulling force transmitted axially by a string, rope, chain, or other similar object, or by each end of a rod, truss member, or other comparable three-dimensional object.

The tension in the string has a square root relationship with wave speed, while the linear density of the wire has a square root relationship with wave speed. v=sqrt(T/u)

A larger thickness suggests a higher linear density (mass per length. Thus, the speed would be slower. The wave in string 1 moves slower than the wave in string 2, and vice versa.

According to a thick string, there is a lot of mass per length and the wave speed is slow.

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Answer:

the answer is resistance

if the moon rises around 3 a.m., its phase must be  Waning crescent .

The moon will look as a half moon, or third quarter moon, when the light level drops. The shadow cast by a third quarter moon will increase until it resembles a crescent form, which is known as a fading crescent.

A fading crescent moon has an illuminated area of less than 50% but is still growing.

You'll notice that the energy is waning as the moon begins to move back into the new phase, allowing you to calm down and devote more attention to your inner thoughts.

When the moon is transitioning from a full moon to a new moon, it is said to be in its declining phase. The declining moon, keep in mind sympathetic magick, is wonderful for banishing work, or cutting ,

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The mechanical advantage can also be represented as the ratio of output work divided by input work. This ratio is usually greater than one, indicating that the machine is doing more work than the input force is providing.

What is mechanical advantage?
The force amplified by using a device, mechanical device, or machine system is known as mechanical advantage. To achieve the desired output force amplification, the device trades off input troops against movement. The law of the lever serves as a model for this. Mechanisms are machine parts made to control forces and motion in this way. An ideal transmission system does not increase or decrease power. Consequently, the ideal machine is devoid of a power source, frictionless, and built from rigid materials that do not flex or wear.

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The following relationship is true T1 < T2.

An ideal gas is defined as a gas in which all collisions between atoms or molecules are perfectly elastic and no intermolecular attractive forces occur. It can be thought of as a collection of perfectly rigid spheres that collide but do not interact.

The volume of gas particles is negligible. Gas particles are the same size and have no intermolecular forces as other gas particles. Gas particles move randomly according to Newton's laws of motion. Gas particles undergo perfectly elastic collisions without losing energy. This is the relationship between four variables and describes the state of the gas.

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The sound power at the threshold of hearing is 5* 10⁻¹⁷ W.

The sound power at the threshold of hearing:

Given that,

Area of the eardrum =  5* 10⁻⁵ m²

We know that, I = power/area

Threshold of hearing I = 1* 10⁻¹² W/m²

Form the above formula, we can write

Power = I* area = 1* 10⁻¹² * 5* 10⁻⁵ = 5* 10⁻¹⁷ W

The sound power incident on an eardrum at the threshold of pain is

We know that, I = power/area

Threshold of pain = 1 W

Power = I* area = 1* 5* 10⁻⁵ W

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A 1500-kg car moving around 25 m/s collides with a horizontal spring that is initially uncompressed but has a spring stiffness of 2.0?106 n/m as well as a max compress of x = 0.68 meters.

Compress, constrict, contract, inflate, and shrink are a few words that frequently replace the word compress. While all of these phrases refer to "decreasing in bulk or area," compress indicates squeezing over resistance into a constricted area with a certain shape.

Considering that,

The automobile weighs 1500 kg.

Vehicle speed, v = 25 m/s

spring's spring constant, k=2×10⁶ N/m

Let x be the greatest distance the spring may compress before breaking,

1/2mv²=1/2kx²

1/2mv²=1/2kx²

x=[tex]\sqrt{mv^{2} /k}[/tex]

x=[tex]\sqrt{1500*25x^{2} /2*10^{6} }[/tex]

x = 0.68 meters

The spring is thereby compressed by 0.68 meters.

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In an explosion a 6 g piece comes out of the right end and a 4 g piece comes out of the left end at twice the speed of the 6 g piece and the third piece comes out of the right end.

Initially all three balls are at rest so u = 0

Given m1 = 6g and m2=4g where m is the mass of balls

Let v1 be the velocity of the first ball = v(i) (denoted as (i) since the right end points to the positive X axis)

Let velocity v2 of second ball = 2(v)(-i) (denoted as (-i) since left end points negative X axis)

Mass of the third ball m3 = m and its velocity v3 = v'

By applying conservation of momentum

m1(u1) + m2(u2) + m3(u3) = m1(v1) + m2(v2) + m3(v3)

Since all balls are initially at rest u1 = u2 = u3 = u = 0

0 = (6×10⁻³)(v)(i) + (4×10⁻³)(2v)(-i) + m(v')

m(v') = (2×10⁻³)(v)(i)

v’ = (2×10⁻³)(v)(i)/(m)

So positive (i) indicates right end

So the third ball comes from the right end.

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The value of the speed will be [tex]2.7\times 10^4rm[/tex]

We have,

Radius of particle = 3.1 cm

Acceleration of particle = 20000 g's

As we know,

The value of acceleration can be determined by using the formula:

[tex]a & =v^2 / r \\v & =\sqrt{a r}{ }^2=a r \\[/tex], where, v = velocity, a = acclreation, and r = radius of particle

So, putting the value of "a" and 'r" in the above formula:

[tex]$$\begin{aligned}& =\sqrt{(200000 \mathrm{~g})\left(3.1 \times 10^2 \mathrm{~m}\right)} \\v & =\sqrt{(200000)\left(9.8 \mathrm{~m} / \mathrm{s}^2\right)\left(3.1 \times 10^{-2} \mathrm{~m}\right)} \\v & =1.745 \times 10^2 \mathrm{~m} / \mathrm{s} \\& =\left(1.745 \times 10^2 \mathrm{~m} / \mathrm{s}\right) \frac{1 \mathrm{rev}}{(2 \pi)\left(6.2 \times 10^{-2} \mathrm{~m}\right)}\left(\frac{60 \mathrm{~m}}{1 \mathrm{~min}}\right) \\& =2.7 \times 10^4 \mathrm{rm}\end{aligned}$$[/tex]

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Answer:

24.5°C

Explanation:

Structural engineering is the other course that are increasingly becoming relevant to space science careers

Investigating how gravity affects the human body, building the telescopes of the future. providing accessible explanations of solar system discoveries. These are just a few examples of the projects that people involved in space exploration employment work on.

Learning how to repair space stations, aircraft, or even make space shuttles or items you'll need in space requires knowledge in civil engineering, which is the notion of designing large transportation projects.

Structural engineering is the other course that are increasingly becoming relevant to space science careers

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A 4 kg ball is launched vertically into the air. The net force exerted on the ball at its highest point is 39.24N.

Given data

Ball mass m=4 kilogram

Gravitational acceleration is [tex]9.81 m/sec^{2}[/tex] , or g.

The location of the ball has no bearing on the net force applied to it in vertical projectile motion. As a result, the ball experiences a net downward force throughout its travel, and the size of this force is equal to the mass times the acceleration caused by gravity.

[tex]F_{net} = mg\\F= 4*9.81\\F= 39.24 N[/tex]

Therefore, the ball is subject to a net force of 39.24 N.

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Average speed of blood flow is given by:

V = n*Re/(rho*d)

n = viscosity of blood = 2.084*10^-3 Pa.s

Re = max reynolds number for which flow remains laminar = 2000

rho = density of blood = 1025 kg/m^3

d = diameter of artery = 2*radius = 2*2.50 mm = 5.0*10^-3 m

So,

V = 2.084*10^-3*2000/(1025*5.0*10^-3)

V = 0.813 m/sec

If the coefficient of kinetic friction among the tires and the street is 0. 20, 312.5m far will the truck skid before stopping.

What is kinetic friction?

Kinetic friction is defined as a force that acts between moving surfaces. A body moving on the surface experiences a force in the opposite direction of its movement. The magnitude of the force will depend on the coefficient of kinetic friction between the two materials.

m =  the mass of the truck

N = normal reaction

g = 9.8 m/s²

μ = 0.2, the coefficient of kinetic friction

The resistive force on the truck is

F = μN = μmg = 0.2*(9.8)m = 1.96m N

The acceleration (actually deceleration) is

a = F/m = -1.96 m/s²

Let d =  distance for the truck to come to rest from an initial velocity of u = 35 m/s.

Then

u² + 2ad = 0

(35 m/s)² + 2(-1.96 m/s²)(d m) = 0

d = 35²/3.92 = 312.5 m

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All the terms are related to languages.

Morpheme - smallest units of sound that carry meaning on their own

Phoneme -smallest units of sound that make a difference in meaning

Grammar - a combined set of rules that govern the use of a particular language

Syntax - rules for forming speech sounds into phrases and sentences

The smallest linguistic unit capable of meaning modification is the phoneme.

Morphemes are divided into two distinct types, bases (or roots) and affixes.

Most people think of grammar as a set of rules that help us form sentences.It covers a variety of language-related topics, such as Parts of speech (verbs, adjectives, nouns, adverbs, prepositions, conjunctions, modifiers, etc.) Clauses (e.g. independent, dependent, compound) (e.g. independent, dependent, compound)

The sequence of grammatical elements like subjects, verbs, direct and indirect objects, etc. is determined by syntax in English.

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The distance of your friend from you is 15.7 m.

The time take for the ball to travel to you friend is calculated by applying the principle of relative velocity as shown below.

( Vt - Vb ) t = d

where;

( Vt - Vb ) t = d

(75 - 5) t = 220

70t = 220

t = 220 / 70

t = 3.14 s

The distance of your friend from you is calculated as;

d1 = 5 m/s x 3.14 s

d1 = 15.7 m

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A jumper will drift half a mile if they fall for one minute through winds that are blowing from the west at an average speed of 30 knots.

Distance is an object's overall movement, regardless of direction. Regardless of an object's starting or ending point, distance can be defined as the amount of ground it has travelled.

The distance between two objects, points, lines, etc., in any direction. the condition or occurrence of being away from another object or person in space; distance. an area that is linear: Seven miles is too far to go in an hour of walking.

The entire path an object has taken can be used to define the distance of an object. an illustration If a car drives 5 km east, then turns to head north for 8 km, the final distance driven by the car must be 13 km.

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A watt is equivalent to an amp multiplied by a volt. All done! Therefore, watt = amp X volt. This equation is also sometimes written as W=A X V.

The power unit is the watt. It refers to the quantity of energy required for a given object to operate as well as the rate during which energy is used up. A joule of energy (or one watt) is equal to one joule of electricity flowing for one second.

Watts, which are determined by multiplying Amps by Volts, are used to measure energy. As the wattage rises, the appliance produces more power and output. This is the amount of water that the hosepipe example would emit.

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a. The period of the solar system's orbit, assuming the orbit is circular, is [tex]2.05X10^{8} years[/tex].

b. There have been 24.4 completed revolutions.

c. The star has a mass of [tex]1.87X10^{41}[/tex] kg.

d. There are [tex]9.45X10^{10}[/tex] stars in the galaxy's center.

a. Distance equals 25,000 light years.

[tex]3X10^{8}[/tex]m/s equals the speed of light (c)

230 m/s is the astronomers' speed.

Using the time period formula,

[tex]t=\frac{d}{v}[/tex]

[tex]t= \frac{2\pi r}{v}[/tex]

r = distance

t = time, and v = speed.

Fill out the formula with the value

[tex]t = \frac{2\pi * 25000 * 9.46 * 10^{15} }{230 * 10^{3} }[/tex]

[tex]t= 6.460*10^{15} sec[/tex]

Number of years

[tex]t= \frac{6.460*10^{15} }{3.15*10^{7} } \\t= 2.05*10^{8} years[/tex]

Consequently, the solar system's orbit lasts [tex]2.05*10^{8}[/tex].

b. The solar system's average age is Tn=5 billion years, or [tex]5* 10^{9}[/tex] years.

The number of completed revolutions can be computed as

[tex]N=\frac{T^{n} }{T} \\N= \frac{5*10^{9}years }{2.05*10^{8}years } \\N=24.4[/tex]

24.4 revolutions have been completed.

c. The solar system's radius, r=25000 light years

velocity = 230 km/s

We can determine the big star's mass as

[tex]M= \frac{v^2r}{G} \\[/tex]

By substituting values, we obtain

[tex]M= \frac{(230*10^{3})^2* (25000*3*10^{8}*365*24*60*60m) }{(6.67*10^{-11} N/kg^2.m^2)}[/tex]

[tex]M= 1.87*10^{41} kg[/tex]

The star has a mass of [tex]1.87*10^{41} kg[/tex].

d. The sun's mass, [tex]M_{s}[/tex], is [tex]1.99*10^{30} kg[/tex]

The star's number can be computed using

[tex]N=\frac{mass of glactic center}{mass of sun} \\N= \frac{1.88*10^{41} }{1.99*10^{30} } \\N= 9.45*10^{10}[/tex]

There are [tex]9.45*10^{10}[/tex] beginnings, or around 94.5 billion, each year.

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

Law of conservation of momentum states that total momentum of system remains conserved in the absence of external force.

As we know that know external no force is acting in the  on the system therefore momentum should be conserved according to the law of the conservation of momentum.

As we know that momentum is given by the formula

momentum = mass × velocity

initially momentum of the system is equal to zero because the velocity of the system is zero.

After fire ball move with high velocity means we have some momentum in the direction of the ball's motion but according to the law of the conservation there should be some momentum in the opposite direction which will cancel out the momentum of the ball therefore cannon will also move in opposite direction.

But as we know that momentum = mass × velocity

As the mass of the cannon is much higher than the mass of the ball therefore less velocity can generate the same amount of the momentum that is required to the cancel the momentum of the ball .

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1.47 MJ work does an elevator motor do to lift a 1500 kg elevator a height of 100 m.

In physics, the term "work" refers to the energy transfer that takes place when an item is displaced over a distance by such an external force, at least a portion of which is supplied in the displacement direction. Stimulates into an object to cause some displacement is what is referred to as work. The ability to perform tasks is referred to as energy. The work is consistently the same.

Work is simply the result of force multiplied by distance, so:

Work = Force * Distance

In this instance, force is simply equal to the elevator's weight, so:

Work = mass * gravity * distance

Work = 1500 kg * 9.8 m/s^2 * 100 m

Work = 1,470,000 J = 1.47 MJ

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The following characteristics of Earth's relationship to the Sun explain the existence of Earth's seasons is:

The tilt of the earth's axis creates the seasons. Throughout the year, different parts of the world receive the most direct sunlight. So when the North Pole tilts toward the Sun, it's summer in the Northern Hemisphere. And when the Antarctic tilts toward the Sun the northern hemisphere will be in winter.

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