The total torque required to accelerate the wheel is 0.054 Nm.
What is the moment of inertia of the uniform cylinder?
The moment of inertia of the uniform cylinder is calculated by applying the following formula.
I = ¹/₂MR²
where;
M is the mass of the grinding wheel or uniform cylinder R is the radius of the grinding wheel or uniform cylinderI = ¹/₂(0.38)(0.085)²
I = 1.37 x 10⁻³ kgm²
The angular acceleration of the grinding wheel or uniform cylinder is calculated as follows;
α = ω/t
where;
ω is the angular speedω = 1750 rev/min x 2π rad/rev x 1 min / 60 s = 183.26 rad/s
α = (183.26 rad/s) / (5s)
α = 36.65 rad/s²
The torque required to accelerate;
τ = Iα
τ = (1.37 x 10⁻³ kgm²) x (36.65 rad/s²)
τ = 0.05 Nm
The frictional torque that is slowing down the wheel;
ω = 1500 rev/min x 2π rad/rev x 1 min / 60 s = 157.1 rad/s
α = (157.1 rad/s) / (55 s)
α = 2.86 rad/s²
τ = Iα
τ = (1.37 x 10⁻³ kgm²) x (2.86 rad/s²)
τ = 0.004 Nm
The total torque required to accelerate the wheel is calculated as;
τ(total) = 0.05 Nm + 0.004 Nm
τ(total) = 0.054 Nm
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light of wavelength 500 nm falls normally on 50 slits that are 2.5 x 10−3 mm wide and spaced 5.0 x 10−3 mm apart. how many interference fringes lie in the central peak of the diffraction pattern?
The interference fringes lie in the central peak of the diffraction pattern is 3.
How are interference fringes calculated?Two-Slit Diffraction Pattern: In other words, just as when the slits were seen as point sources, the positions of the interference fringes are determined by the equation d sin = m d sin = m, but now the intensities of the fringes are diminished by diffraction effects, as shown by Equation 4.4.Diffraction and interference effects usually result in minima at several angles and operate concurrently. If the maximum of the interference is in the same direction as the minimum of the diffraction, this results in a complicated pattern on the screen where some of the maxima of interference from the two slits are missing. Such a missing peak is referred to as a missing order.Find the attachment answer
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how many orbiting satellites at any given moment are there keeping a watchful eye on our planet? what altitudes do these satellites operate? group of answer choices 120; few hundred miles up to 25,000 miles 120; 500 miles above earth 25; few hundred miles up to a few thousand miles 600; mostly at 25,000 miles above earth
The source of the answers may be higher than us. 120 satellites are in orbit over our heads, keeping watch. Most work at altitudes between a few hundred miles and 25,000 miles above the surface of the globe.
Why is altitude important?The distance below sea level is known as altitude, just like elevation. If an area extends at than 2,400 meters (8,000 feet) into atmosphere, it is frequently referred to as being "high-altitude." Mount Everest, which is located in the Himalayan region on the border between Nepal and Tibet in China, is the highest point on Earth.
Is height the same as altitude?By drawing a right angle from a triangle's vertex toward its opposite side, one can calculate the triangle's altitude.. The altitude, sometimes referred to as the triangle's height, forms a rectangle with the base.
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the cosmic microwave background tells us a lot about our universe, including what shape it is, geometrically! what shape do we believe the universe is, and based on which property of the cmb?
Based on the crucial Cosmic Microwave Background density, we think that the form of the universe is geometrically flat.
The CMB is a faint glow of light that permeates the entire cosmos and falls on Earth with roughly uniform intensity from all directions.
Scientists can learn more about the early universe's formation thanks to the CMB. Only slight temperature variations that can be seen with accurate telescopes are present. With accurate telescopes, only minute temperature variations are discernible. Cosmologists can measure the fundamental components of the Big Bang theory and learn more about the history of galaxies and their large-scale structures by investigating these oscillations.
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in what ways is the electricity generation from a solar panel different from producing electricity with a turbine generator that works on wind, water, natural gas, coal, etc?
The electricity produced by a solar panel differs from the power produced by the a centrifugal compressor that runs on wind, liquid, oil and gas, coal, etc. by using solar and wind energy.
What are the 4 types of electricity?These days, it even fuels a lot of our automobiles. You may go to the most remote regions of the planet and still discover it in the stormy clouds above you. Different sources of electricity exist, including coal, freshwater, solar, wind, nuclear, hydro, and solar.
What is electricity made of?Based on the U.S. Energy Information Administration, lignite, nuclear power, and natural gas made up the majority of the country's electrical generation in 2020. Renewable energy sources like wind, hydro, solar power, biomass, and wind are also used to produce electricity.
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x-rays are scattered from a target at an angle of 60.9° with respect to the direction of the incident beam. what is the wavelength shift (in m) of the scattered x-rays?
The wavelength shift of the scattered x-rays is [tex]1.25 * 10^-^1^2 m[/tex]
What is wavelength shift?
A moving object produces light with a different wavelength. This effect is called Doppler shift.
The light is shifted toward shorter wavelengths, or blue shifted, if the object is moving in your direction. When an object is moving away from you, the light is red-shifted, or shifted toward longer wavelengths.
The expression for wavelength shift is:
Δλ = [tex]\frac{h}{mc}[/tex] (1 - cosθ)
where,
m = mass of electron ([tex]9.11 * 10^-^3^1 kg[/tex])
h = planks constant ([tex]6.63 * 10^-^3^4 Js[/tex])
c = speed of light ([tex]3 * 10^8 m/s[/tex])
θ = scattering angle (here, 60.9°)
Subsituting values in equation,
Δλ = [tex]\frac{h}{mc}[/tex] (1 - cosθ)
Δλ = [tex]\frac{6.63 * 10^-^3^4 Js}{(9.11 * 10^-^3^1)(3 * 10^8)}[/tex] [tex](1 - cos 60.9)[/tex]
Δλ = [tex]1.25 * 10^-^1^2 m[/tex]
The wavelength shift of the scattered x-rays is
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what is the kinetic energy of the object on the spring when the spring is compressed 3.2 cm from its equilibrium position? express your answer in joules using three significant figures.
The kinetic energy of the object on spring is 2.56 Joule.
The spring compressed at 3.2 cm from equilibrium position.
When you compress or stretch a spring, you can measure the amount of potential and kinetic energy it stores. The force, F, multiplied by the distance, s:, results in what is known as elastic potential energy.
W = Fs.
The force varies as you stretch or compress a spring, but it does so linearly (according to Hooke's law, force is proportional to displacement)
Applying force requires work, and once the work is finished, energy is transferred to the object, causing it to move with a constant speed.
When an object is set in motion, its mass and speed determine the amount of energy that is transferred, which is known as kinetic energy.
K=0.5
[tex]dK=\frac{Sy^2}{2} \\\\dK=kinetic \\S=constant\\y=compression[/tex]
[tex]dK=0.5 [3.2^2]/2\\\\dK=2.56Joule[/tex]
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although we know less about dark matter in elliptical galaxies than we do in spiral galaxies, what does current evidence suggest?
Elliptical galaxies probably contain about the same proportion of their mass in the form of dark matter as do spiral galaxies.
How do we know elliptical galaxies have dark matter?
The standard hypothesis is that elliptical galaxies originate from mergers of disks10 and should therefore be embedded in similar dark-matter haloes. There is evidence for dark matter in giant ellipticals, from X-rays11 and gravitational lensing12.
The stellar mass distribution does not account for the rotation curve of galaxies. If a spiral galaxy didn't contain any dark matter at all, its rotation curve would be decreasing with distance beyond the center of the galaxy.
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what is the work requird to lift a 215 kg mass a distance of 5.65 m using a machine that is 72.5% efficient?
The maximum work required by the machine is 16420 J.
What is work?Work is energy transferred to or from an object via the application of the force along with the displacement. Work is the standard mechanical quantity. In its simple form, for a constant force aligned with it direction of motions the work equals the product of the forced by the strength and to the distance traveled.
Here mass M is 215 kg
And the height lifted H is 5.65
The energy or workdone needed to lift is W= MgH = 215(9.8)(5.65)= 11904.5 J
The minimum efficiency of to the machine is 72.5 %
So we can write that
The workdone by machine is
11904.5(100/72.5) = 16420 J ( approx)
So the workdone by machine is 16420 J
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A person can see clearly up close but cannot focus on objects beyond 80.0 cm. She opts for contact lenses to correct her vision. (a) Is she nearsighted or farsighted? (b) What type of lens (converging or diverging) is needed to correct her vision? (c) What focal length contact lens is needed, and what is its power in diopters?
A person who can see clearly up close but cannot focus on objects beyond 80.0 cm is nearsighted and she is needed diverging type of lens to correct her vision. 1.25focal length contact lens is needed, and −1.25 D is its power in diopters.
What is nearsightedness?Myopia or nearsightedness , a disease that affects many people, causes near objects to appear clear while far distant objects to appear blurry.
According to given data :
The distance she can she is 80 cm=0.8 m
She needs to correct it to the distinct vision=infinity.
To find the power of the lens
Use the following formula
⇒ 1/-0.8-1/∞=1/d
⇒ 1/d=-1.25
⇒ P = 1/d
⇒ P=−1.25 D
Now to find the focal length we know that P=1/f
Hence,
⇒ f=1/P
⇒ f=1/-1.25
⇒ f=1.25
Hence 1.25focal length contact lens is needed, and −1.25 D is its power in diopters.
Hence, a person who can see clearly up close but cannot focus on objects beyond 80.0 cm is nearsighted (Myopia) and she is needed diverging type of lens to correct her vision. 1.25focal length contact lens is needed, and −1.25 D is its power in diopters.
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two slits are illuminated with green light with a wavelength of 540 nm. the slits are 0.05 mm apart and the distance to the screen is 1.5 m. at what distance (in mm) from the central maximum on the screen is the average intensity 50% of the intensity of the central maximum?
The distance (in mm) from the central maximum on the screen is the average intensity 50% of the intensity of the central maximum is 0.21486 mm
What is the central maximum?
The brightest central area of a diffraction pattern on the screen is called the central maximum. Of all the other diffraction fringes, the central maximum is the widest and has the highest intensity.
The formula for maximum intensity is :
I = I_o•cos²(Φ/2)
Φ not given but it can be expressed as :
Φ = πdy/(λL)
Where;
y - distance from the central maximum
d - distance between the slits
λ - wavelength
L - distance to the screen
Hence, the answer is The distance (in mm) from the central maximum on the screen is the average intensity 50% of the intensity of the central maximum is 0.21486 mm.
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a child is on a playground they start to slide down a large slide. at what point is the child in dynamic equilibrium with the slide?(1 point)
On the slide when the child is in motion as they are sliding down comes to dynamic equilibrium.
When a child reaches the bottom he has both kinetic and thermal energy. Energy is converted into heat by friction on the slide.Gravity pulls items down the slide and friction exist. Friction works against gravity and slows you down the slide.Charge electron transfer between the child clothing and the slide. At one point on a slide it comes to dynamic equilibrium.Therefore, as a child is in motion as they are sliding down and comes to dynamic equilibrium.
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the magnet in a large mri unit may have a 0.7-t magnetic field occupying a field of 1.3 m^3. how much magnetic field energy is in that volume
397887.358 is the volume in which the magnetic field energy is said to be present.
What is magnetic field and its unit?The magnetism is a field that is produced in the vicinity of a magnetic dipole or a moving charge. Tesla is the SI unit of field strength for magnetic fields (T). The region surrounding a magnet where electromotive flux is felt is known as the magnetic field.
What materials make up a magnetic field?Electric fields in motion create magnetic properties. Everything is constructed of molecules, and each atom contains a nucleus that is composed of protons and neutrons, with electron cloud. Each atom creates a tiny magnetic field because the circling electrons have tiny moving charges.
Briefing:Required Energy = (B²/2μ)*Volume
= 1²/(2 * 4* π *10⁻⁷)
= 397887.358
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if quasars are at the distances most astronomers believe they are, then (for the most luminous ones) their luminosities must be:
Like the combined luminosity of a hundred trillion (1014) Suns.
What is the luminosity of the most powerful quasars?A new quasar with a 12 billion solar mass central black hole and 430 trillion solar luminosity was found by the Peking University Department of Astronomy at a distance of 12.8 billion light years from the Earth. This quasar, driven by the most massive black hole then known to exist, is the most brilliant one to be found in the early Universe. The finding of this quasar, designated SDSS J0100+2802, represents a significant advancement in our understanding of the evolution of quasars, the most potent cosmic phenomena, from their inception nine hundred million years after the Big Bang. On February 26, 2015, the leading scientific publication Nature reported on this discovery.To learn more about quasars, refer to
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a 64 kg person rides in an elevator. if the elevator has a downward acceleration of 3.0 , what is the magnitude of the force of the person on the elevator floor?
The magnitude of the force if the of the person in the elevator is 448N
What is the apparent weight of a body in elevator?A body in an elevator will experience apparent weight. The motion of the elevator will decide if the actual weight of the body will increase or decrease.
When a body is moving upward with acceleration a, the apparent weight of the body will be R= m(a+g)
Also when the body is moving downward with acceleration a, the apparent weight will be R = m(a-g)
The apparent weight of the body will be actual weight when the elevator is at rest or at uniform velocity i.e a=0 and R= mg
Therefore,
For a body in a elevator with downward acceleration, it's apparent weight/force on the person is R= m(g-a)
R= 64(10-3)
R= 64×7= 448N
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50.0-kg skater is traveling due east at a speed of 3.00 m/s. a 70.0-kg skater is moving due south at a speed of 7.00 m/s. they collide and hold on to each other after the collision, managing to move off at an angle θ south of east, with a speed of vf. find (a)the angle θ and (b)the speed vf, assuming that friction can be ignored.
The angle θ is 72.97 and the speed vf is 4.27 m/s.
Net X momentum:
mv + 0 = (total mass)V.
50.0(3) = (50.0 + 70.0)V
V=1.25 m/s.
Net Y momentum
MV + 0 = (total mass)V.
70.0(-7.0) = (50.0 + 70)V.
V=4.0833 m/s
(a)According to conservation of momentum we have along x-direction:
m1 u1 = M Vfcosθ
Along the vertical direction
m2 u2 = M Vfsinθ
==> m2 u2 / m1 u1 = tanθ
==> tanθ = 7 * 7 / 5 * 3
= 3.2666
==> θ = 72.97
(b) Therefore
Vf = m 1 u1/ M cosθ
= 5 * 3 / 12 * cos72.97
= 4.27 m/s
What is speed?
Velocity is the distance traveled per unit time. It's how fast an object is moving. Velocity is a scalar quantity that is the magnitude of the velocity vector. No direction. Faster speed means the object is moving faster. Slow speed means slow movement. If you don't move at all, you have no speed.
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which sentence describes newton's second law
A box with a weight of 50 newtons rests at the bottom of a ramp and is pushed to the end of the ramp with a force of 20 newtons. This ramp is an inclined plane that is 10 meters long. What is the maximum height of the ramp?.
Height of the ramp is equal to the length of the ramp that is 10 m.
What is ramp ?A ramp is also called as an inclined plane. It is a flat supporting surface tilted at an angle, with one end higher than other and also used as an aid for raising or lowering a load.
Given, height of the ramp is 10 meters ;
We know, component of the weight acting on the incline is :
w = m g sin(θ)
Potential energy of box = 10× sin(θ) ×50 = 500·sin(θ)
F × 10 = 500·sin(θ)
F = 50·sin(θ)
Work done by the net force = Potential energy gained by box
Work done by the net force = (20 - 50·sin(θ)) × 10 = 500·sin(θ)
sin(θ) = 1/5
θ = arcsine(1/5) = 11.53°,
Height of the ramp =Length of the ramp = 10 m
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consider the following three statements: for any electromagnetic radiation, the product of the wavelength and the frequency is a constant. if a source of light has a wavelength of 3.0 å , its frequency is 1.0×1018 hz . the speed of ultraviolet light is greater than the speed of microwave radiation. which of these three statements is or are true?
First assertion:
The relationship between electromagnetic radiation's wave, wavelength λ, and oscillation frequency is established by the speed of light. The formula is provided by:
c=vλ
Thus, the first claim is accurate.
Second assertion:
c=vλ
c= 3.0A×1.0×10¹⁸Hz
c= 3.0×10⁻¹⁰m×1.0×10¹⁸s⁻¹
c= 3×10⁸m/s
In a vacuum, c has a value of 3×10⁸m/s. So, the second assertion is accurate.
Third assertion:
No matter the type of electromagnetic radiation, the speed is always the same.
As a result, the third claim is untrue.
What is electromagnetic radiation?
The speed of light (2.998 x 108 m/s) is the rate at which an electric and magnetic disturbance called electromagnetic radiation travels through space. It moves in radiant energy packets known as photons or quanta and is neither massless nor electrically charged.
What are the 7 types of electromagnetic radiations?
The parts of the electromagnetic spectrum are referred to as gamma rays, X-rays, ultraviolet radiation, visible light, infrared radiation, and radio waves, from highest to lowest energy.
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A car accelerate from ret to 18. 14 meter per econd in 5. 70 econd. What i the car’ rate of acceleration in meter per econd quared?
3.18m/[tex]s^{2}[/tex] is the rate of acceleration when the car accelerates from rest to 18. 14 meter per second in 5. 70 second.
What is the rate of acceleration?It is the change in acceleration over time where as acceleration is the rate of change of velocity of an object with respect to time.
acceleration, a=[tex]\frac{v}{t}[/tex] .
Solution:Given
car velocity=18.14 m/s
time taken =5.70 second
To Find the rate of acceleration
a=[tex]\frac{v}{t}[/tex]
a=18.14/5.70
a=3.18m/[tex]s^{2}[/tex]
Hence, 3.18m/[tex]s^{2}[/tex] is the rate of acceleration when the car accelerates from rest to 18. 14 meter per second in 5. 70 second.
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a circular coil of radius 5.0 cm and resistance 0.20 ω is placed in a uniform magnetic field perpendicular to the plane of the coil. the magnitude of the field changes with time according to b=0.50e−tt . what is the magnitude of the current induced in the coil at the time t = 2.0 s?
The magnitude of the current induced in the coil at the time of 2 seconds is calculated to be 0.00263 A
The equation for induced emf can be given as;
ε = - d/dt (BA cos θ)
In this equation B represents the magnetic field, A illustrates the area, and θ represents the angle.
Rearranging the equation;
ε = - A cos θ d/dt B
ε = - (πr²) d/dt (0.50e^-0.20t)
ε = 0.1 (πr²) e^-0.20t
As t = 2 seconds;
ε = 0.1 × π × 0.05² × e^-0.20(2)
ε = 5.26 × 10^-4 V
Now using the formula for induced current;
I = ε / R = 5.26 × 10^-4 V / 0.20 = 0.00263 A
Hence 0.00263 A is the magnitude of the current induced in the coil.
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ssm a 140 kg hoop rolls along a horizontal floor so that the hoop’s center of mass has a speed of 0.150 m/s. how much work must be done on the hoop to stop it?
The work needed to stop the hoop is -3.15j.
What is hoop?
In rhythmic gymnastics, a hoop is indeed an apparatus that can be made of plastic as well as wood as long as it maintains its shape throughout the routine. The hoop's interior diameter ranges from 20 to 35 inches, and its weight must be at least 300 grammes (11 oz). The hoop could be a natural colour or partially or entirely covered in one or more colours. It may also be covered to adhesive tape that is either the same colour as the hoop or a different colour. Rotation all around hand or body, rolling, swings, circles, throws, as well as passes through and across the hoop are all fundamental components of a hoop routine.
The work needed to stop the hoop can be calculated as follows:
Work = Force x Distance
Force = Mass x Acceleration
Mass = 140kg
Acceleration = Velocity / Time
Velocity = 0.150 m/s
Distance = Velocity x Time
Time = Velocity / Acceleration = 0.150 m/s / 0.150 m/s = 1 second
Therefore,
Work = (140 kg x 0.150 m/s) x 0.150 m/s = 3.15j
The work needed to stop the hoop is -3.15j.
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a phone cord is 4.89 m long. the cord has a mass of 0.212 kg. a transverse wave pulse is produced by plucking one end of the taut cord. that pulse makes four round trips (down and back) along the cord in 0.636 s. what is the tension in the cord? hint: four round trips is a total distance of eight lengths of the cord.
The tension in the given phone cord is 174.3 N.
Speed of the wave
v = fλ
v = (n/t) x 2L
v = (4/0.617) x (2 x 4.89)
v = 63.4 m/s
Tension on the rope
v = √T/μ
μ = 0.212/4.89 = 0.0434 kg/m
v² = T/μ
T = v²μ
T = (63.4)² X 0.0434
T = 174.3 N
the tension in the given phone cord is 174.3 N.
When two opposing pressures pull on a rope, string, or wire, the force communicated through the object is known as tension. The energy is pulled equally on the bodies at the ends by the tension force, which is applied over the entire length of the wire. The International System of Units (SI) uses newtons as the unit of tension measurement for transmitted forces, action-reaction pairs of forces, and restoring forces (or pounds-force in Imperial units).
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find the moment of inertia of the system about an axis through the center of the square, perpendicular to its plane (an axis through point o in the figure).
As a result, the system has a moment of inertia of 0.0636 kg-m around an axis that passes through the center of square and is perpendicular to its plane.
What are the definition and measurement of the moment of inertia?Moment of inertia is the propensity of an object to continue rotating at a constant speed or in a condition of rest. More torque is needed to shift this state the higher the moment of inertia. Similar to how force affects linear motion, torque affects rotational motion. It has the SI unit kg. metre2.
What does moment of inertia mean in everyday terms?When a body resists angular acceleration, it has a certain amount of moment of inertia, which is calculated as the product of the mass of each particle times the square of the particle's distance from the rotational axis. A scalar quantity is the moment of inertia.
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The corrrect question is
Four small spheres, each of which you can regard as a point of mass 0.200 kg, are arranged in a square 0.400 m on a side and connected by light rods. Find the moment of inertia of the system about an axis through the center of the square, perpendicular to its plane.
the speed of sound in air is around 345 m/s. a tuning fork vibrates at 553 hz above the open end of the sound resonance tube. what is the wavelength (in cm) of the sound waves in the tube? never include units with a numerical answer.
Above the sound resonance tube's open end. The wavelength of sound waves inside the tube is 0.63 cm.
Resonance: What does that mean?Resonance is a phenomena when a vibrating system or external force causes another system nearby to vibrate more intensely at a specific operating frequency. It is a phenomena where a body's intrinsic frequency and the period of a periodic force applied externally match up.
What is resonance's primary function?Resonance is a term used in the valence bond theory to describe how certain molecules combine a number of contributing structure (or forms, commonly known as benzene rings or classic structures) into the a hybrid resonance.
Briefing:Speed of sound, v = 345 m/s
frequency = 553hz
Speed = wavelength * frequency
Wavelength = Speed/frequency
Wavelength = 345/0.542
Wavelength = 0. 63cm
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while dexter is on a camping trip with his boy scout troop,the scout leader hands each boy a compass and map. the directionson dexter's map read as follows: walk 500.0 m north 200.0m east and 300.0 m south, and 400.0 m west. if he follows themap, what is dexters displacement?
The same spot he started, his displacement is 0 meters.
What is displacement?
A displacement is indeed a vector in geometry as well as mechanics that has a length equal to the shortest distance between a point P's initial and final positions. It measures the length and angle of the net motion, or total motion, in a straight line from the starting point to the destination of the point trajectory. The translation that links the starting point and the ending point can be used to spot a displacement. The final position xf of the a point relative towards its initial position xi, or even a relative position (resulting from of the motion), is another way to describe a displacement. The difference between both the final and initial positions can be used to define the corresponding displacement vector.
Dexter's displacement is 0 meters.
This is because the total distance traveled (500.0 m north + 200.0 m east + 300.0 m south + 400.0 m west) is 1,200.0 meters,
But the total displacement is 0 meters because he is ending up in the same place he started.
Displacement is the total distance traveled in a straight line from the starting point to the ending point.
Since Dexter is ending up in the same spot he started, his displacement is 0 meters.
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the area of a typical eardrum is about 5.0 10-5 m2. (a) calculate the sound power (the energy per second) incident on an eardrum at the threshold of hearing
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
Therefore, the power incident on eardrum will be 5*10⁻⁵ W
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if a solid sphere, solid cylinder, and hollow cylinder, with masses 1kg, 2kg, and 3kg, respectively, are all sitting at the top of a 10m long flat ramp of a given height and then released simultaneously to race downhill, which one wins?
The solid sphere reaches the ground first followed by the solid cylinder and then hollow sphere.
The depends on the inertia or moment of inertia. Moment of inertia is defined as the quantity expressed by the body resisting angular acceleration which is the sum of the product of the mass of every particle with its square of a distance from the axis of rotation.
Thus, the moment of inertia of solid sphere is less than that of the hollow cylinder. The radius of gyration of solid sphere is less than radius of gyration of hollow sphere.
However, the acceleration of the solid sphere is more than that of the hollow cylinder.
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A block with mass 0.50 kg is forced against a horizontal spring of negligible mass, compressing the spring a distance of 0.20 m (the figure (Figure 1)). When released, the block moves on a horizontal tabletop for 1.00 m before coming to rest. The spring constant k is 100 N/m. What is the coefficient of kinetic friction mu _k between the block and the tabletop? Express your answer using two significant figures. mu _k = __________
The coefficient of Kinetic friction (μk) is 0.408.
What is Friction?
It is the resistance to the relative motion of sliding solid surfaces, fluid layers, and material components. Friction can take many different forms: A force called "dry friction" resists the relative lateral motion of two solid surfaces coming into contact.
What are the calculations?
ΔE = ΔU + ΔK = [tex]- f_{friction} * d[/tex]
= [tex]U_{f}[/tex] - [tex]U_{o}[/tex] + [tex]K_{f} - K_{o} = - f_{friction} * d[/tex] = [tex]- f_{friction} * d[/tex]
= [tex]0[/tex] - [tex]\frac{kx_{0} ^{2} }{2} = f_{friction} * d[/tex]---------(1)
the friction force is, f = μkN = μkmg--------(2)
by inserting equation (2) into (1),
and inserting given values in it, we will get:
μk = [tex]\frac{( 100 N/m ) (0.2m)^{2} }{2 ( 0.50 Kg ) (9.8 m/s^{2} ( 1m)}[/tex]
or, 0.408.
Hence, coefficient of Kinetic friction (μk) is 0.408.
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what is the magnitude of the cross product of a vector of magnitude 2.00 m pointing east and a vector of magnitude 4.00 m pointing 30.0° west of north?
The magnitude of the cross product of both the given vectors is 6.91.
Given that, the magnitude of first vector is 2m and is pointing east
a = 2 (cos 0° i + sin 0° j) = 2 i
The magnitude of second vector is 4m pointing 30° west of north.
b = 4 (-cos 30° i + sin 30° j) = -4* 0.866 i + 4* 0.5 j = -3.46 i + 2 j
The total angle between a and b is 120°. (as one vector is on the east and the other is 30° west of north.
The formula for the cross product of two vectors is given by,
a × b = |a| |b| sinθ
where, |a| is the determinant of a
|b| is the determinant of b
θ is the angle between a and b
|a| = √(2)² = 2
|b| = √(-3.46)² + (2)² = 3.99
a × b = |a| |b| sinθ = 2* 3.99* sin 120° = 7.98* sin 120° = 6.91
Thus, the magnitude of cross product is 6.91.
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bilingual children and adults outperform others on tests of inhibition, sustained and selective attention, flexible thinking, analytical reasoning, concept formation, and false-belief understanding. the benefits of sustained bilingual education have inspired u.s. educators to devise two-way programs. these programs are growing rapidly in u.s. public schools.
Literature suggests that bilingual immersion programs are beneficial for elementary school students. Because this program will help fill the grade gap for elementary school students improve their academic performance and embrace their culture and new ones.
Bilingual education means teaching subjects in two different languages. It can be easily applied to help students transition from their native language to the language of the country in which they currently live, but can also be used to teach academic content in two languages at the same time.
Students can connect effectively with people from different cultures and backgrounds improve their ability to empathize with others and develop emotional intelligence. Teachers and students can use her two languages. One is the target language to learn and the other is the native language to reach the target language English.
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