a) Calculate the ratios of longitudinal modulus of the composite to the matrix modulus for glass/epoxy and carbon /epoxy composites with 10% and 50% fibers by volume. Elastic modules of glass fibers, carbon fibers and epoxy resin are 70, 350, and 3.5 GPa, respectively.
b) Discuss what is the effect of the fibers in the elastic modulus of the composite in the longitudinal direction (2-3 phrases.)

The degeneracies of the first, fourth and fifth energy levels for the three dimensionsal cubical box are 1, 3 and 1.

Calculation :

Given Data

A three-dimensional cubic box with

lx=ly=lz=Li.

For a 3D cubic box, the energy of the particle in a box is having a formula given below,

E3D=h²8m(n²x/l²x+n²y/l²y+n²z/l²z)

Given,

lx=ly=lz=Li, put in the above equation, we get,

E3D=h²/8m(n²x/L²+n²y/L²+n²z/L²)

E3D=h²/8mL²(n²x+n²y+n²z)

Now, for the First energy level, the energy will be,

E3D=h²/8mL²(1²+1²+1²)

E3D=3h²/8mL²

The degeneracy is equal to 1 because nx=ny=nz=1.

Now, for the Fourth energy level, the energy will be,

E3D=h²/8mL²(1²+1²+3²)

E3D=h²/8mL²(1+1+9)

E3D=11h²8mL²

The degeneracy is equal to 3 because, nx=1,ny=1,nz=3,nx=1,ny=3,nz=1 and nx=3,ny=1,nz=1.

Now, for the Fifth energy level, the energy will be,

E3D=h²/8mL²(2²+2²+2²)

E3D=h²/8mL²(4+4+4)

E3D=12h²/8mL²

The degeneracy is equal to 1 because nx=2,ny=2,nz=2.

Therefore, the degeneracies of the first, fourth and fifth energy levels are 1, 3 and 1.

Energy levels are degenerate if they correspond to two or more different measurable states of a quantum system. Conversely, two or more distinct states of a quantum mechanical system are said to be degenerate if they have the same energy value when measured. The number of different states corresponding to a particular energy level is called the degeneracy of the level.

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The smooth plastic jar has five pennies placed inside of it. The normal reactions of the bottom coin on the container at locations a and b will be 0.0705 lb and 0.1175 lb respectively if each coin weighs 0.0235 lb.

A contact force, the normal force is often referred to as the normal reaction force. On two surfaces that are not attached to one another, a normal force cannot be applied.

The body's weight determines the usual deceleration force. A body's position relative to the ground tells us when it is about to fall. The normal force is the portion of a force that is perpendicular to any contact surface.

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1.25 cm is the height of the image. 160 cm separates a converging lens with such a 40 cm focal length from a diverging lens with the a -40 cm focal length. The converging lens is 60 cm away from a 2.5 cm tall item.

A lens that conforms a parallel source beam of light is known as a converging lens. One kind of converging lens is a double convex lens. Converging Lens A lens that separates a parallel light beam is known as a diverging lens. Diverging lenses include those that are double concave.

For the diverging lens, this image height corresponds to object height. We obtain h ′D=(20cm40cm)(5.0cm)=1.25cm again for diverging lens as a result.

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(a) The angular speed of the new system is 2.455 rad/s.

(b) The angular speed of the new system is 1.64 rad/s.

(a) The Angular Momentum Conservation Principle is observed since there are no outside forces acting on either disk.The fact that the axes of rotation of each disk coincide allows for the principle to be reduced to its scalar version. The ratio of the inertial moment to the angular speed determines the angular momentum's size. The moment of inertia doubles and the angular speed is cut in half as soon as both disks start to revolve.

It is given by, I ω₀ = 2* I * ωf

Where,

I - Moment of inertia of a disk, measured in kilogram-square meter

ω₀ - Initial angular speed, measured in radians per second

ωf - Final angular speed, measured in radians per second

The expression for relating final angular speed to initial angular speed is,

ωf = 1/2 * ω₀

Given that, ω₀ = 4.91 rad/s

The new system's angular speed is,

ωf = 1/2 * 4.91 = 2.455 rad/s

(b) If third such disk is dropped on the first two, the expression on angular velocity becomes,

I ω₀ = 3* I * ωf

ωf = 1/3* ω₀ = 1/3* 4.91 = 1.64 rad/s.

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Answer: m = 72 kg

Explanation:

The maximum torque on the wire is 392.3 µN·m and the range of potential energy is -392.3µN·m(minimum) to +392.3µN·m(maximum)

Torque: Torque is a measure of the force that can cause an object to rotate about an axis. It is a vector quantity.

Given that,

diameter D=20cm

Radius r =10cm

magnetic field B =2.5mT

current I=5A

Torque= n×B

           =nBsinФ

torque=nB= NIAB

                 = 1×5×π×[tex]10^{2}[/tex]×[tex]10^{-4}[/tex]×2.5×[tex]10^{-3}[/tex]

                 = 39.23×[tex]10^{-5}[/tex]

                 = 392.3µN·m

minimum potential energy= -nB= -392.3µN·m

maximum potential energy =+nB= +392.3µN·m

Therefore the maximum torque on the wire is 392.3 µN·m when is placed in an uniform magnetic field of 2.50mT and the range of potential energy is -392.3µN·m(minimum) to +392.3µN·m(maximum)

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Initial current via the inductor is lo = 0, and initial charge at the capacitor is Q-o = 3.2 C. The only two devices allowed by the loop rule.

Find the current (sign included) flowing through the inductor at the point t = 2.2 seconds using the loop rule and the differential equation derived for an LC circuit. Derive the differential equation for an LC circuit using the loop rule. To improve comprehension of complex concepts in electrical circuit analysis, such as inductance, capacitance, and reactance, By building up electric charges on two nearby surfaces, a capacitor is a device that stores electrical energy in an electric field. An RL circuit is one with resistance and self-inductance, and an RL circuit with a resistor.

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A basketball experiences four forces as it soars through the air. The ball is being pulled down to the Earth by gravity, being propelled upward by buoyancy, and slowed down due to the drag force created by the air it collides with.

A force is an influence that has the power to alter an object's motion. An object with mass can change its velocity, or accelerate, as a result of a force. An obvious way to describe force is as a push or a pull. A force is a vector quantity since it has both magnitude and direction.

For instance, a basketball will strike the ground hard when it is dribbled. The ground's force on the ball is balanced by this force of the ball on the ground. The ball is sent upwards by the second force since it acts in the opposite direction. There are numerous characteristics of motion that depend on this interaction.

Thus, A basketball experiences four forces as it soars through the air.

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A lens with an 11 cm focal length is 22 cm to the left of a 1.8 cm tall object. The image's height has decreased by 0.25 pixels when a second lens with a focal length of -5cm is placed 37cm to the right of the first lens.

Let's determine the distance at which the image is formed from the first lens since the image of the first lens serves as a virtual object for the second lens. Use the lens manufacturer's formula:

1/o + 1/i = 1/f, where I am the image distance and o is the object distance,

1/i = 1/f - 1/o = 1/(11cm) - 1/(22cm) = 0.045 1/cm, so

i = 22cm

the virtual object for the second lens is left at a distance of 37 cm - 22 cm, or 15 cm, from the second lens. Utilize the lens manufacturer's formula once more:

1/i = 1/f - 1/o (This time, the object distance is the separation between the second lens and the virtual object.)

1/i = 1/(-5cm) - 1/(15cm) = -0.26 1/cm, so

i = -15/4cm away from the second lens.

The sum of the two magnifications from the two lenses is the total magnification: m = m1m2, where m = -i/o, so

m = (-22 cm/22 cm)( 15/4cm/15cm) = -0.25, Consequently, the image's height is 0.25 pixels shorter than it was before.

It is the inverse of the system's optical power that determines how strongly an optical system diverges or converges light: the focal length. The convergence or divergence of light is indicated by a positive focal length, whilst the opposite is true for a negative focal length.

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Answer:

Newton's first law: An object at rest remains at rest, or if in motion, remains in motion at a constant velocity unless acted on by a net external force.

(A) With 268.94 N tension must she stretch it.

26% increase in tension is needed to increase the frequency from 65.4 Hz to 73.4 Hz, corresponding to a rise in pitch from C to D.

Part (A)

Fundamental frequency =f0= 65.4 Hz.

The length of the vibrating portion of the string = l = 0.615 m

Mass= m = 14.8 g

We know, [tex]f_0 = \frac{v}{2l}[/tex]

So, the value of v will be 65.4*2*0.615 = 80.442 m/s

As, We know,

[tex]T=\frac{v^2}{\frac{m}{l}}[/tex]

So, the value of tension will be: [tex]\frac{80.442^2}{\frac{14.8}{0.615}}=\frac{6470.91}{24.06}=268.94\:N[/tex]

Part (B)

Fundamental frequency =f0= 73.4 Hz.

The length of the vibrating portion of the string = l = 0.615 m

Mass= m = 14.8 g

We know, [tex]f_0 = \frac{v}{2l}[/tex]

So, the value of v will be 73.4*2*0.615 = 90.282 m/s

As, We know,

[tex]T=\frac{v^2}{\frac{m}{l}}[/tex]

So, the value of tension will be: [tex]\frac{90.282^2}{\frac{14.8}{0.615}}=\frac{8150.8395}{24.06}=338.77\:N[/tex]

So, the percentage increase in tension will be [tex]\frac{338.77-268.94}{268.94}\times 100\%=25.96\% \approx 26\%[/tex]

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The complete question should be:

a cellist tunes the c-string of her instrument to a fundamental frequency of 65.4 hz. the vibrating portion of the string is 0.615 m long and has a mass of 14.8 g .

Part A: With what tension must she stretch it?

Part B

What percent increase in tension is needed to increase the frequency from 65.4 Hz to 73.4 Hz, corresponding to a rise in pitch from C to D?

The value of 'x' such that the mass то exerts a force of mg on the inclined surface at P. (N=mg)​ is given by

x = N / (mg cos θ)

Generally, To determine the value of 'x', you need to know the angle of inclination of the surface and the mass of the object. The force of gravity (N) acting on the object is equal to the mass of the object (m) multiplied by the acceleration due to gravity (g). The force of gravity is also equal to the normal force (N) exerted by the surface on the object, which is perpendicular to the surface.

If the surface is inclined at an angle θ with respect to the horizontal, the normal force will be equal to the component of the force of gravity along the surface. This component can be calculated using the formula N = mg cos θ, where θ is the angle of inclination and m is the mass of the object.

Therefore, to determine the value of 'x', you need to solve the equation N = mg cos θ for 'x'. To do this, you can rearrange the equation to solve for x:

x = N / (mg cos θ)

Substituting the values of N, m, and θ into this equation will give you the value of 'x' that you are looking for.

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The spring and pan have very little mass. The mass executes a SHM when it is lightly squeezed and then released.

Forces, location, velocity, and energy—both kinetic and potential energy—are some examples of these quantities. Hoare's Rule. Energy conservation: When the compressed spring returns to its natural length, all of the energy that was stored in it is transformed into kinetic energy. The block is propelled along a horizontal surface as the spring is let go. Friction and the spring's bulk can be disregarded. Between two blocks with masses of 1 kg and 2 kg that are lying on a smooth horizontal surface is a compressed elastic spring. The block is freed from rest once the spring has been compressed by 2.0 cm.

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A roller coaster starts from rest at point  is option C) the kinetic energy of the coaster at C will be equal to its potential energy at A.

Since Two objects are sliding at the same speed across a wooden surface. The  distance traveled by the second object is option B) 2S

A person's weight measured in the elevator immediately after the elevator starts to fall is option E) zero A force F produces an acceleration a on an object of mass m.

The mass of the second object is option D) (3/8)m.

The amount of kinetic energy change and the amount of potential energy change are identical in all physical processes that take place in closed systems. When the kinetic energy rises, the potential energy falls, and vice versa.

Wave speed is the number of meters a wave travels in a second, or the distance a wave travels in a particular amount of time. Equation Speed = Wavelength x Frequency describes how wave speed relates to wave wavelength and wave frequency.

Therefore, When wavelength and frequency are known potential energy stored energy that depends on the relative positions of different components of a system may be utilized to compute wave speed—this equation can be used to determine wave speed. When stretched or squeezed, a spring has higher potential energy.

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There are two girders and 5 beams Each beam spans between two girders. The tributary area of rim  joist is  864ft²

Length of the rim joist = Y ft = 36ft

Length of each bay out of 4 = X/4 = 96/4 = 24ft

Tributary width of rim joist is half on each bay to its side

Tw = 24/2 + 24/2 = 24

Tributary area Ta = tw × length

Ta = 24 × 36 = 864ft²

The floor or roof area (in plan) that results in loading on a certain structural element is known as the tributary area. In each direction, name the adjacent column.

the distance between the two, measured.

multiplying by two the distance

From here, create a perpendicular line.

Repeat until a bounding polygon appears for each gridline that is close by.

A beam's tributary area is equal to its length times the addition of half its space to each adjacent girder.

The square footage of the deck surface area supported by one post is known as the tributary area. Depending on how the deck is set up, this can differ for each post.

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Note that for a severe supercell ts to form over the great plains, one would expect the 5,000 AGL wind to be 190/45kts (Option D)

A supercell thunderstorm is distinguished by the presence of a mesocyclone, which is a deep, continually revolving updraft. As a result, these storms are sometimes known as spinning thunderstorms.

Supercells are storms that have updrafts that spin along a vertical axis and are generally but not always thunderstorms. This rotation is caused by shear in the environmental wind field (a change in wind direction and/or speed with height) that surrounds the storm as it grows.

Supercell thunderstorms are intense, long-lived storms that are characterized by strong wind shear and rotational dynamics.

The wind shear, or the change in wind speed and direction with height, is a key factor in the development and maintenance of supercell thunderstorms.

Note that AGL means Above Ground Level; while

KTS means Knots. Knots are a unit measurement of speed. I nautical mile is usually equated to one knot.

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If A + B = 0, then the magnitude of B is equal to the magnitude of A. This is because the magnitude of a vector is simply its size or length, and if two vectors add up to zero, then their magnitudes must be equal.

As for the direction of B, it is the opposite of the direction of A. This is because if two vectors are equal in magnitude and opposite in direction, their sum will be zero. For example, if A is a vector pointing to the right and B is a vector pointing to the left, their sum will be zero. Similarly, if A is a vector pointing upwards and B is a vector pointing downwards, their sum will also be zero.

In summary, if A + B = 0, then the magnitude of B is equal to the magnitude of A, and the direction of B is opposite to the direction of A.

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Air resistance is hardly noticeable. true regarding the 0.09-kilogram component. This causes 0.01kg to land farther from the launch site than 0.09kg did.

0.09kg will move to the west due to momentum conservation (opposite of 0.01 kg). Additionally, since both are at the same height above the ground, it will take them equal amounts of time to descend to the ground.

Allowing v to be the speed of 0.01 kg, which means that the speed of 0.09kg will be smaller than 0.01 kg,

0.01v - (0.09)V = 0

V = 0.01 v/ 0.09 = 0.111v

The speed of 0.09 kg = 0.111v

The speed of 0.09 kg is less than 0.01kg.

Because of this, 0.01kg hits the ground farther from the launch point than 0.09kg did.

The amount of resistance in an electrical circuit represents the resistance to current flow. The Greek letter omega (), which represents resistance, represents ohms. German physicist Georg Simon Ohm (1784–1854), who investigated the connection between voltage, current, and resistance, is the name given to the unit of resistance known as an ohm.

Resistance measurements are typically performed in order to evaluate the health of a component or a circuit.

Current flow is inversely correlated with resistance. Conductor damage from corrosion or burning could be one of several potential causes if it is extremely high.

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Particles can exist in classically forbidden regions outside the finite square-well potential.

The correct option is D.

In the absence of quantum effects, everything would be continuous, smooth, and completely predictable in the Newtonian sense. However, we may not be here to get bored with this if Planck's constant were 0.

At the atomic scale, the behavior of both particles and waves is described by Planck's constant. One of the factors that led to the creation of quantum mechanics is Planck's constant. It was a surprise when those boundaries also turned to represent the limits where known rules of physics applied since the Planck scaled was developed as an universal set of units.

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4th paths out of 1 - 5 would the bowling ball most closely follow as it falls to the ground

The bowling ball moves due to the resultant force of the vertical and horizontal direction.

The overall force operating on the item or body as well as the direction in which the body is moving are referred to as the resultant force. When the object is stationary or moving at the same speed as it, there is no consequent force.

The outcome is what is produced when vectors are added together. The biggest (maximum) consequent when adding two vectors is equal to their sum when forces are acting in the same direction.

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(a) θ5 in the air is 56.9° and (b) θ4 in the bottom material 35.30°. Normally, a light beam that strikes an angle on a prism's refracting face emerges from the opposite face.

(a) Approximating n=1 for air, we have

n1. sinθ1 = (1)sinθ5 ⇒56.9°=θ5

​and with the more accurate value for n air in Table below, we obtain 56.80.(b) Equation n1 sinθ c =n2 sin 90° leads to,

n1 sinθ 1=n2 ​sinθ2​ =n3​ sinθ 3​ =n4 sinθ 4

​so that. θ4 =sin −1( n1/n4.sinθ 1 )=35.30° .

The angle of incidence is formed by a line drawn perpendicular to the reflecting barrier and the wave's direction of motion.

Refraction Depending on the Refractive Indices in the Two Media and the Angle of Incidence. Snell's law states that the angle of incidence, I and the proportion of the refractive indices of the two media that make up the interface determine the angle of refraction, r.

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The force necessary to lift an object is the same as the force necessary to fight gravity.

We may calculate the gravitational force acting on the object using Newton's second law if we assume that the acceleration caused by gravity is 9.8ms2. By exerting force that is produced by the person's muscles, the weights are raised. It is therefore a muscular force. Lift can be in any direction with respect to gravity, contrary to the popular understanding of the word, which defines it with respect to the direction of flow rather than the direction of gravity. If the force on an object's bottom is greater than the force of gravity coming from above, lift will result. Lift must equal gravity for a height to be sustained.

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This statement is False because Solid-state sensors are used in place of a water - absorbing element in electronic humidistats. A damper in the bypassed duct is closed during the summer period to stop airflow.

Hygroscopy - A material is said to be hygroscopic if it has the capacity to adsorb and retain water or water from its immediate surroundings. Examples include ethanol, glycerin, concentrated sulfuric acid, honey, silica gel, and methanol.

Around the soil particles, some water in the soil creates an incredibly thin, firmly held layer. It's referred to as hydroscopic water. A little amount of water in the soil is chemically linked to soil components in the soil. We refer to it as mixed water.

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Option B is Correct

The velocity of the center of mass remains constant before the collision, when they collide there is a slight decrease in kinetic energy of the system since the collision is inelastic, resulting in a slight decrease of velocity, afterwards the velocity is constant again.

Velocity is the directional velocity of a moving object, observed from a given frame of reference and indicating the rate of change of position measured at a given time reference (eg 60 km/h northward). Velocity is a fundamental concept in kinematics, a branch of classical mechanics that describes the motion of bodies.

Velocity is a physical vector quantity. Both magnitude and direction are required to define it. The scalar absolute value (magnitude) of velocity is called velocity, and its magnitude is a consistent derived unit measured in the SI (metric) system as meters per second (m/s or m⋅s−1). For example, " meters/second" is a scalar, but "5 meters/second east" is a vector. An object is said to be accelerating if its velocity, direction, or both change.

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The new rotational inertia or final moment of inertia of the girl is I₀ / 4.

option D is the correct answer.

Rotational inertia is a property of any object which can be rotated.

Rotational inertia or moment of inertia of an object is a measure of the resistance of an object to changes in its angular velocity.

Based on the law of conservation of angular momentum, the formula for her new rotational inertia is given as;

I₀ω₀ = I₁ω₁

where;

The given parameters include,

initial angular velocity = ω₀

final angular velocity = 4ω₀

initial moment of inertia = I₀

The final moment of inertia of the girl is calculated as

I₁ = ( I₀ω₀ ) / (ω₁)

I₁ = ( I₀ω₀ ) / (4ω₀)

I₁ = I₀ / 4

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Answer:

amplitude:1m

period:10s

Explanation:

The induced current in the loop of the copper wire is found to be 7.85 mA.

The single loop of the copper wire is lying in flat plane and the magnetic field is pointing perpendicular to the plane of the loop. The area of the loop is given to be 7.8cm²

The magnetic field initially has a magnitude of 0.500 Tesla and it finally increases manner to grow to a magnitude of 3.50 Tesla in a time 1.10 seconds.

The induced EMF in the circuit will be given by the relation,

E = A∆B/∆T

Where,

B is magnetic field,

A is the area and T is the time taken.

Putting all the values,

E = 0.00078×(3.5-0.5)/1.1

E = 21.2mV.

The resistance in the copper loop is given to be 2.7 ohm.

Now, the induced current in the circuit will be given by the relation,

I = E/R

Putting all the values

I = 21.2/2.7

I = 7.85 mA.

So, the induced current in the wire is 7.85 milliamps.

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When the gymnast starts to jump his potential energy starts to convert to kinetic energy. But when he reaches the maximum height and stop there for seconds, potential energy regains. Thus, option C is correct.

Potential energy of an object is the energy stored in it by virtue of its position. Potential energy increases with increases in mass and height which is clear from the equation for potential energy

p = mgh

Kinetic energy is generated by motion of the object. Thus, only a moving body attains a kinetic energy. Kinetic energy depends on the mass and velocity of the object.

Here, the gymnast gains a kinetic energy when he starts to jump from rest. But, when he reaches the maximum height where the speed slows down, his kinetic energy converts to potential energy. Thus, option C is correct.

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Your question is incomplete. But your complete question probably was:

A gymnast uses a flexible stick to jump over the bar. Which of the following

describes energy changes when he reaches the highest point of his jump?

A) kinetic- potential- potential

B) kinetic- potential- kinetic

C) potential - kinetic – potential

D) potential- potential- kinetic

The following vectors best describes the path of the airplane Aniseed of the as plan is 528 [tex]\mathrm{mi} / \mathrm{hr}[/tex]

What is airplane?

A fixed-wing aircraft that is pushed forward by the thrust of a jet engine, propeller, or rocket engine is known as an aeroplane or aeroplane. There are many different sizes, forms, and wing arrangements for airplanes.

[tex]\text { bearing } 25^{\circ} \text { west of north }[/tex]

[tex]\text { Since } \quad 90^{\circ}+25^{\circ}=115^{\circ}[/tex]

[tex]\text { so path of the airplane is }[/tex]

[tex]\left.v=528 \cos \left(i 15^{\circ}\right) i+528 \sin \left(115^{\circ}\right)\right][/tex]

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A cup anemometer, made up of three or four cups with a conical or hemispherical shape set symmetrically around a vertical spindle, is typically used to measure wind speed. The spindle turns because of the wind blowing into the cups.

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