The resolution of radio telescopes suffers greatly from the large wavelengths of the light they are observing. What can be done to a radio telescope to improve its angular resolution?.

Answers

Answer 1

make its dish bigger to improve its angular resolution

Because the wavelengths of radio waves are so larger than the wavelengths of visible light, radio telescopes must be much larger than optical telescopes. The wavelengths of radio waves range from 3 km to 1 cm, while the wavelengths of visible light range from 4 x 10-7 m (ultraviolet) to 7 x 10-7 m. (red). The degree of detail that can be observed in an area of the sky is measured in terms of angular resolution. More detail can be seen at a given wavelength with a larger telescope. The wavelength of the light or radio waves being observed by the telescope (λ) and the telescope's diameter (D) can be used to compute the angular resolution (θ) of the telescope.

θ = 2.5 × 105 × λ/D

θ = 1.22 × λ/D

The ability of any image-forming tool, such as a optical or radio telescope, a microscope, a camera, or an eye, to differentiate minute features of an object is known as angular resolution, and as such, it is a key factor in determining picture resolution. It is utilized in the application of acoustics to sound waves, antenna theory to radio waves, and optics to light waves.

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Related Questions

You decide to start running to get ready for a cross country race. You run 8 miles north and stop to take a small break. You then run 3 miles west before finally running 7 miles south. What is the total distance that you traveled?

Answers

The total distance traveled will be 18 miles because distance and displacement are different.

While distance and displacement appear to have the same meaning, they actually have very different definitions and implications. Displacement is the measurement of "how far an object is out of place," whereas distance refers to "how much ground an object has covered during its motion."

Distance is the sum of an object's movements, regardless of direction. The distance can be defined as the amount of space an object has covered, regardless of its starting or ending position.

Δd = d1 + d2 + d3.....

The term "displacement" refers to a shift in an object's position. It is a vector quantity with a magnitude and direction. The symbol for it is an arrow pointing from the initial location to the ending place.

Displacement = Final position - Initial position

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Tech a says that electric power steering systems are much heavier than hydraulic pumps. tech b says that hydraulic pumps are more compact than electric pumps. who is correct?

Answers

Electric power steering system  are more compact than the hydraulic  pumps , both statement are wrong.

Since electro-hydraulic and electric power steering systems are lighter and more compact than conventional hydraulic power steering systems.The hydraulic power steering system is basically a closed loop system that uses pressurized hydraulic fluids for changing the wheel angle of the front wheels based on the steering angle. It consists of a hydraulic pump driven by  valves, belt, reservoir, cylinder, and a driver control mechanism, whereas Electric power steering is for highly automated  driving, it  has an electric motor that controls the vehicle  and provides enjoying  and  optimal steering feel, and electro-hydraulic power steering is  where an electric motor  drives the pump which  is controlled according to the needed assisting steering force, the delivery of the hydraulic pump is increase at very low  speed in order give a large amount of steering power.

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A penny is pushed off a desk 2m high. How long does it take the penny to hit the floor?

Answers

Explanation:

why do you think is important to study about that different forms of precolonial literature?

A carnot engine operates on steam between 65 c and 425 c. what is the ideal efficiency?

Answers

A Carnot engine operates on steam between [tex]65^0[/tex] and [tex]425^0[/tex]. The ideal efficiency of the Carnot engine will be -1.065.

How to calculate the efficiency of the Carnot engine?

To find efficiency of the Carnot engine, following formula is used:

[tex]\eta =1-\frac{T_2}{T_1}[/tex]

where, [tex]T_1, T_2[/tex] are the temperatures on which the engine operates. They are always in Kelvin.

Now, we will convert Celsius to Kelvin.

[tex]65^0=338.15K\\425^0=698.15K[/tex]

Substituting the values in the formula,

We get:

[tex]\eta = 1-\frac{698.15}{338.15} \\\eta = 1-2.065\\\eta = -1.065[/tex]

Hence, the ideal efficiency of the Carnot engine will be -1.065.

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How long does it take our solar system to complete one orbit around the milky way galaxy? a. 10 thousand years b. 230 thousand years c. 1 million years d. 100 million years e. 230 million years

Answers

It takes our Solar system 230 million years to complete one orbit around the milky way galaxy; option E.

What is the solar system?

The solar system refers to the system of the Sun and the planets that orbit it.

The Sun is the star of our solar system. The planets in our system include:

MercuryVenusEarthMars,JupiterSaturnUranusNeptune

Our solar system is a part of the Milky Way Galaxy.

It takes about 230 million years for our Solar system to complete one orbit around the Milky Way Galaxy.

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What is the core ram clock speed for ram with a ddr2 speed rating of ddr2-800 and a pc speed rating of pc2-6400?

Answers

Answer:

400 MHz

Explanation:

voodoo$ knows all

The density of water is 1.0g/cm*3. This is useful as it means we can measure the mass of water and easily work out its volume.

a. What is the mass of 1cm*3 of water?
b. What is the mass of 20cm*3 of water?
c. What is the volume of 10g of water?
d. What is the volume of 22.5g of water?

e. Milan is measuring the density of ethanol. He weighs a bottle three times: first, empty;
then filled with ethanol. Here are his results:
mass of empty bottle = 30.0g
mass of bottle filled with water = 90.0g
mass of bottle filled with ethanol = 78.0g
i. Calculate the volume of the bottle.
ii. Calculate the mass of the ethanol.
iii. Calculate the density of ethanol.

Answers

B , hope this helps!!!!!

consider an airplane flying at a pressure altitude of 33,500 ft and a density altitud of 32,000 ft. calculate the outside air temperature.

Answers

The outside air temperature is 1° C.

Pressure is defined as the force applied to an object per unit area. It's represented by the symbol 'P'. The SI unit of pressure is Pascal (Pa).

The pressure altitude at which the aeroplane is flying = 33500 ft

The density altitude at which the aeroplane is flying = 3200 ft

The outside air temperature is,

[tex]T= \frac{ P}{ pR}[/tex]

The pressure altitude in Pascal is,

33500 ft = 23.800 Pa

The density of the altitude in Pascal is,

3200 ft = 1.225 Pa

[tex]Temperature = \frac{Pressure } {Density \times Gas \: constant }[/tex]

[tex]T= \frac{ P}{p \times R}[/tex]

[tex]T = \frac{23.800}{1.225 \times 287.05} [/tex]

T = 1° C.

Therefore, the outside air temperature is 1° C.

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What depth of oil, specific gravity of 0.750, will produce a pressure of 26 psig?

Answers

The depth of oil, specific gravity of 0.750, will produce a pressure of 26 psig is =92.3 ft

PSIG refers to pounds per square inch Gauge (S.G.) oil = 0.750

P(ress )=30 psig = 30lb/in²

density of water ρ(w)= 62.4 pound/ft³

=62.4/(12)³  lb/in³

=0.03611  lb/in³

p(ress)=ρ H

30=(s.g) xρ H

30 = 0.750X 62.4/(12)³   H

H = 30x (12)3/0.750 x 62.4

H = 1107.69 in.

=92.3 ft

Relative gravity is another name for specific gravity. Since it lacks any dimensions, it must be a dimensionless quantity. The ratio of a substance's density to that of water at a specific temperature can be used to characterize it. It is significant to remember that temperature is a key factor in influencing any substance's specific gravity. As a result, a substance's specific gravity is a quality that depends on its temperature. Additionally, every substance's specific gravity is impacted by pressure.

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increases our ability to produce greater quantities of physical activity such as maximal force over a short period (lifting a weight) or more moderate levels of force over longer periods (hiking long distances or running marathons), or to move our bodies through larger ranges of motions. group of answer choices training

Answers

Training increases our ability to produce greater quantities of physical activity such as maximal force over a short period more moderate levels of force over longer periods.

What is Training?

Performance in middle and long-distance running is governed by a number of significant aerobic and anaerobic factors.

In the literature, there has been a lot of discussion on how effective strength training (ST) is for distance runners.

However, no comprehensive assessment of the findings from these investigations of physical activity has been published so far.

Although there is very strong evidence that any kind of Strength training enhances RE, TT, and the sprint performance, this conclusion was not shared by all of the assessed research.

The differences in methodology that are emphasized may help to explain the inconsistencies in findings and should be taken into account in future research in this area.

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a student is calculating the gravitational force between the earth and the sun. she knows that mass of the earth is 5.972 x 10245.972 x 1024 kg, the mass of the sun is 1.989 x 10301.989 x 1030 kg, and the distance between the earth and the sun is 1.496 x 10121.496 x 1012 meters. what piece of information is she missing to be able to find the gravitational force?

Answers

The gravitational force is 3.54 x 10²⁰ N

We need to know about gravitational force to solve this problem. The gravitational force is the force caused by two masses objects. The magnitude of gravitational force can be determined as

F = G.m1.m2 / R²

where F is the gravitational force, G is the gravitational constant (6.674 × 10¯¹¹ Nm²/kg²), m1 and m2 are the mass of the object and R is the radius.

From the question above, we know that

m1 = 5.972 x 10²⁴ kg

m2 = 1.989 x 10³⁰ kg

R = 1.496 x 10¹² m

By substituting the following parameters, we get

F = G.m1.m2 / R²

F = 6.674 × 10¯¹¹  . 5.972 x 10²⁴ . 1.989 x 10³⁰ / (1.496 x 10¹²)²

F = 3.54 x 10²⁰ N

Hence, the gravitational force is 3.54 x 10²⁰ N

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A 0.1 g plastic bead is charged by the addition of 1*10^10 excess electrons. what electric field (strength and direction) will cause the bead to hang suspended in the air?

Answers

The electric field that cause the bead to hang suspended in the air is calculated as E = -612292.045 N/C

To find the electric field, the given values are:

Mass = 0.1g

Charged excess electrons = 1×10¹⁰

What is the Electric field?

The Electric field can be defined as the ratio of the electric force per unit charge.

So, the working equation for this is,

E = F/Q,

where E is the strength of electric field, F is the force and Q is the charge.

The force is equal to:

F = mg = (0.1/1000 kg)(9.81 m/s²) = 0.981 ×10⁻³ N

The charge of the excess electrons is equal to:

Q = (-1.6021766208×10⁻¹⁹ C/electron)(1×10¹⁰ electrons)

Q = -1.6021766208×10⁻⁹ C

E = 0.981 ×10⁻³ N/-1.6021766208×10⁻⁹ C

E = -612292.045 N/C

Thus, the electric field that cause the bead to hang suspended in the air is calculated as E = -612292.045 N/C

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6) How much time will it take for a bug to travel 6.5 meters across the floor if it is travelling at 1.25 m/s?

Answers

Answer: 4.8 seconds

Explanation:

d=r*t

6.5=1.25*t

6.5/1.25= 4.8

Hope this helps! :)

which of the following astronomers introduced the most widely accepted hypothesis regarding the origin of the solar system?

Answers

The astronomers introduced the most widely accepted hypothesis regarding the origin of the solar system is Immanuel Kant in 1755.

Newton's equations of gravity and rotatory motion served as the foundation for most of Kant's theories. He believed that primaeval matter, which he believed to have been generated supernaturally, was dispersed throughout the cosmos. Small, chilly, hard particles made up this substance.

Due to the gravitational pull of one another, these particles were drawn to one another.

In his 1755  "The Universal Natural History and Views of the Heavens," Kant discusses astronomy as well as two significant cosmological theories. The first is his "Nebular Hypothesis" on the formation of stars and planets, in which he proposed that faint, thin clouds of dust and gas far out in space would collapse in on themselves under the influence of gravity, forcing them to spin to form a disc. The development of stars and planets from this rotating disc would account for the rotation of Earth and the other planets.

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if the total magnification using a microscope is 800x and the objective magnifies the object 40x, what would the magnification be from the lens in the ocular?

Answers

The ocular microscope magnification is 20x.

We need to know about microscope magnification to solve this problem. Microscope is a device utilized for seeing a small object. The microscope has two lenses which are objective and ocular. The total magnification of the microscope lens is

M = Moc x Mobj

where M is total magnification, Moc is ocular magnification and Mobj is objective magnification.

From the question above, we know that

M = 800x

Mobj = 40x

By substituting the following parameter, we get

M = Moc x Mobj

800 = Moc x 40

Moc = 800 / 40

Moc = 20x

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When equal mass of hot water and oil at the same temperature are allowed to cool water cools slower than the oil why?​

Answers

It is because water has a higher heat capacity as compared to the heat capacity of oil.

The amount of heat that must be applied to an object in order to cause a unit change in temperature is known as the heat capacity or thermal capacity of that object. Heat capacity is measured in joules per kelvin (J/K), the SI unit.

Heat capacity is an example of extensive property. A physical quantity which is an extensive property has a value that is proportional to the size of the system it describes or the amount of matter present in the system. C stands for the heat capacity of an object.

Because water has a higher specific capacity than oil and must expend more energy to cool down, it does so more slowly when two equal masses of hot water and oil are allowed to cool.

Therefore, When the equal mass of hot water and oil at the same temperature is allowed to cool water cools slower than the oil.

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Which of the following is the source of wealth for a nation in a mercantilism system?
a. religion
B. population
c. natural resources
D. land​

Answers

Answer:

c. natural resources

Explanation:

mercantilism is an economic practice by which governments use their economies

so economies in this mean their natural resources

if am ryt

Answer:

C. natural resources

Explanation:

Mercantilism is based on the concept of a nation's power being directly related to its wealth. A nation's goal under mercantilism was to obtain as much gold and silver as possible and to export more goods than it imported from other nations. Gold and Silver are natural resources.

What is the formula for calculating resistance?
Volts / ohms
Volts x ohms
Volts / Current
Current / volts

Answers

The formula for calculating resistance is Volts / Current (option C). Details about resistance can be found below.

What is resistance?

Resistance is a force that tends to oppose motion. It is measured in a unit called ohms (Ω).

The electrical resistance of a circuit component or device is the ratio of the voltage applied to the electric current which flows through it.

The resistance of an object can be calculated by dividing the voltage (V) by its current (I) as follows:

R = V/I

Therefore, the formula for calculating resistance is Volts / Current.

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*need help ASAP *
Select the correct answer.
Read lines 44-45 from The Winter's Tale.
PAULINA: Tis time; descend; be stone no more; approach;
Strike all that look upon with marvel.
Which detail from "Pygmalion and Galatea" provided the source material for these lines from Shakespeare's play?

A.Pygmalion falling in love with his statue
B.Venus watching over the sleep of Adonis
C. Pygmalion adorning his statue with jewels
D. Venus giving life to Pygmalion's statue

Answers

Answer: D. Venus giving life to Pygmalion's statue

Explanation: Hi! I got it right on Edmentum. Hope this helps! <3

liquid helium has a very low boiling point, 4.2 k, as well as a very low latent heat of vaporization, 2.00 104 j/kg. if energy is transferred to a container of liquid helium at the boiling point from an immersed electric heater at a rate of 30.0 w, how long does it take to boil away 2.40 kg of the liquid?

Answers

[tex]4.80 \times 10^3 \text { seconds }[/tex]  long does it take to boil away 2.40 kg of the liquid.

Boiling point of He is [tex]$T=4.2 \mathrm{k}$[/tex]

Latent heat of vapourization [tex]$L=2.00 \times 10^4 \mathrm{~J} / \mathrm{kg}$[/tex]

Power of electrical heater [tex]$P=30 \mathrm{w}$[/tex]

mass of liquid is [tex]$m=2.40 \mathrm{~kg}$[/tex]

amount of heat required to boil

[tex]$$\begin{aligned}&Q=m L \\&Q=2.40 \times 2 \times 10^4 \mathrm{~J} \\&Q=4.80 \times 10^4 \mathrm{~J}\end{aligned}$$[/tex]

Power [tex]$p=\frac{\text { work }}{\text { time }}=\frac{\text { Energy }}{\text { Time }}$[/tex]

[tex]$$\begin{aligned}P &=\frac{Q}{t} \\\text { tine } t &=\frac{Q}{P}=\frac{4.80 \times 10^4 \mathrm{~J}}{10} \\t &=4.80 \times 10^3 \text { seconds }\end{aligned}$$[/tex]

The heat or energy that is absorbed or released during a substance's phase shift is known as latent heat. It could go from a solid to a liquid or from a liquid to a gas, or vice versa. Enthalpy, a characteristic of heat, is connected to latent heat.

The heat that is used or lost as matter melts and transitions from a solid to a fluid form at a constant temperature is known as the latent heat of fusion.

Due to the fact that during softening the heat energy anticipated to transform the substance from solid to fluid at air pressure is the latent heat of fusion and that the temperature remains constant during the process, the "enthalpy" of fusion is a latent heat. The enthalpy change of any quantity of material during dissolution is known as the latent heat of fusion.

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Find the speed of the waves on an 800.0 mg violin string 21.1-cm long if the fundamental frequency is 922.0 hz.

Answers

By using the lowest resonant frequency, the wave speed is 389.084 m/s.

We need to know about the fundamental resonant frequency to solve this problem. When the string is vibrating at its lowest resonant frequency, it should follow the rule

λ = 2L

where λ is wavelength and L is length of string

From the question above, we know that

f = 922 Hz

L = 21.1 cm

By substituting to the following equation, we can calculate the wavelength

λ = 2L

λ = 2 . 21.1

λ = 42.2 cm

λ = 0.422 m

Find the speed of wave

v = λ . f

v = 0.422 . 922

v = 389.084 m/s

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Zsm-5, a catalyst material, has a surface area of 425 m^2/g. what is the surface area of this material in cm^2/mg?

Answers

The surface area of the material in cm²/mg is 4250 cm²/mg

How to convert 425 m²/g to cm²/g

We'll begin by converting 425 m²/g to cm²/g. This can be obtained as follow:

1 m²/g = 10000 cm²/g

Therefore,

425 m²/g = (425 m²/g × 10000 cm²/g) / 1 m²/g

425 m²/g = 4250000 cm²/g

How to convert 4250000 cm²/g to cm²/mg

We can convert 4250000 cm²/g to cm²/mg as follow:

1000 cm²/g = 1 cm²/mg

Therefore,

4250000 cm²/g = (4250000 cm²/g × 1 cm²/mg) / 1000 cm²/g

4250000 cm²/g = 4250 cm²/mg

Thus, we can conclude that the surface area in cm²/mg is 4250 cm²/mg

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Be sure to answer all parts. chlorine has two naturally occurring isotopes, 35cl and 37cl. what is the mass number of each? how many protons, neutrons, and electrons are present in each?

Answers

Chlorine has two naturally occurring isotopes, [tex]^{35}Cl[/tex] and [tex]^{37}Cl[/tex].

What is the mass number,  number of  protons, neutrons, and electrons are present in [tex]^{35}Cl[/tex]?

The mass number of [tex]^{35}Cl[/tex] is 35.

The number of protons present in [tex]^{35}Cl[/tex] is 17.

The number of neutrons present in [tex]^{35}Cl[/tex] is 18.

The number of electrons present in [tex]^{35}Cl[/tex] is 17.

What is the mass number,  number of  protons, neutrons, and electrons are present in [tex]^{37}Cl[/tex]?

The mass number of [tex]^{37}Cl[/tex] is 37.

The number of protons present in [tex]^{37}Cl[/tex] is 17.

The number of neutrons present in [tex]^{37}Cl[/tex] is 20.

The number of electrons present in [tex]^{37}Cl[/tex] is 17.

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A 100g sample of radioactive material has decayed to 25g in 12 hours what is the half-life?

Answers

Answer:

24 hrs

Explanation:

12 hrs =25 g

24hrs = 50g

Protons that occupy identical electronic environments are called chemically equivalent, and they will produce only ____________ signal.

Answers

Chemically similar particles are those whose electrical surroundings are the same. If two protons can switch places by rotating or reflecting one another, they are chemically identical.

Protons that are chemically equivalent only generate one signal.

What are protons that are chemically equivalent?

All three Ha protons and all three Hb protons are chemically equal to one another, according to NMR nomenclature. However, the Ha protons and the Hb protons are not chemically similar.

The resonance frequency of the Ha protons differs from that of the Hb protons as a result.

Some examples to illustrate what equivalent and non-equivalent protons are.

A molecule with equivalent protons emits a single signal. The corresponding protons of ethane are four in ethylene, two in acetylene, and six in benzene.

A molecule, each of which results in an absorption and the absorptions are widely separated in the spectrum are called nonequivalent proton.

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an object is in a circular motion. the radius of the circle is 2 meters and it takes 6.28 seconds to complete the circle. what is its centripetal acceleration?

Answers

The centripetal acceleration of the object will be 2 m/s^2.

An object moving in a circular motion has a centripetal force(F)

F = mv^2/R

Its centripetal acceleration is given by the following equation,

ma = mv^2/R

a = v^2/R

We know that in the case of circular motion, v = wr

Here, W is the angular frequency which is equal to 2pi/Time Period(T).

Hence its centripetal acceleration is

a = w^2(R)

Putting w = 2pi/T= 2pi/6.28 and R= 2 meters in the above equation

a = (2pi/6.28)(2)

a = 2 m/s^2.

Hence, the centripetal acceleration of the object will be 2 m/s^2.

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The centripetal acceleration of the object will be 2 m/s^2.

An object moving in a circular motion has a centripetal force(F)

F = mv^2/R

Its centripetal acceleration is given by the following equation,

ma = mv^2/R

a = v^2/R

We know that in the case of circular motion, v = wr

Here, W is the angular frequency which is equal to 2pi/Time Period(T).

Hence its centripetal acceleration is

a = w^2(R)

Putting w = 2pi/T= 2pi/6.28 and R= 2 meters in the above equation

a = (2pi/6.28)(2)

a = 2 m/s^2.

Hence, the centripetal acceleration of the object will be 2 m/s^2.

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An electromagnetic wave with frequency f = 10 mhz is propagating in a material with parameters h = 3 h0, p = p0 (h0 = 8.85 x 10-12 f/m; p0 = 1.257 x 10-6 h/m), and v = 10-7 s/m. find:__________

Answers

When An electromagnetic wave with frequency f = 10 mhz is propagating in a material with parameters h = 3 h0, p = p0 (h0 = 8.85 x 10-12 f/m; p0 = 1.257 x 10-6 h/m), and v = 10-7 s/m. Then wavelength of electromagnetic wave is 410 nm.

What is electromagnetic wave?

When a magnetic field and an electric field interact, electromagnetic waves are created. An electromagnetic wave has an electric field and a magnetic field that are perpendicular to one another.

The parts of the electromagnetic spectrum are designated as follows, from highest to lowest energy: gamma rays, X-rays, ultraviolet radiation, visible light, infrared radiation, and radio waves. The radio wave region of the electromagnetic spectrum includes microwaves (such as those found in microwave ovens).

An electromagnetic wave first encounters the atoms of a physical substance, which absorb the radiation. Vibrations. The electrons inside of this atom begin vibrating as a result of the absorption of this electromagnetic energy.

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A motorcycle, starting from rest, has an acceleration of +2.6 m/s². After the motorcycle has traveled a distance of 120 m, it slows down with an acceleration of -1.5 m/s² until its velocity is +12 m/s. a. Calculate the final velocity of the motorcycle after the first 120 m interval.

Answers

The velocity of the motorcycle after the first 120 m is 24.97 m/s and the total displacement of the motorcycle is 280 m.

The acceleration of the motorcycle starting from rest is 2.6 m/s².

The acceleration of the motorcycle after traveling a distance of 120 m id -1.5 m/s² and the velocity is 12 m/s.

The initial velocity of the motorcycle, u = 0 m/s

The acceleration of the motorcycle, a = 2.6 m/s²

Therefore, the final velocity of the motorcycle after d = 120m is:

v² - u² = 2as

v² = u² + 2as

v² = (0)² + 2 × 2.6 × 120

v² =  624

v = √624

v = 24.97 m/s

Now, the motorcycle slows down to -1.5 m/s² and a velocity of 12 m/s.

So, the initial velocity is u = √624 m/s and final velocity is v = - 12 m/s.

So,

v² - u² = 2as

( - 12)² - (√624)² = 2 × -1.5 × d

144 - 624 = - 3 × d

- 480 = - 3d

d = 480 / 3 = 160 m

Therefore, the total displacement of the motorcycle is 120 m + 160 m = 280 m.

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a metal ball hangs from the ceiling by an insulating thread. the ball is attracted to a positively charged rod held near the ball. the charge of the ball must be

Answers

A metal ball is hanging from the ceiling through an insulating thread. This ball is attracted to a positively charged rod that is held near the ball and thus the charge of the ball must be Negative or Neutral.

Study and theory applied

Whether any object is made up of conductive or nonconductive material, it affects how it behaves once it has been charged.

Electrons can move freely between particles when they are in conductors, which are substances. Charge can be transported across the whole surface of an object constructed of a conducting substance.

Charge is swiftly dispersed all across the full surface of the object if it is applied to it at a specific point. The motion of the electrons causes the distribution of charge.

A charged conductor can even transfer its charge to any another object if it comes into contact with that other object. When one object is constructed of a conducting substance, the charge can be transferred from one object to another more easily.

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the g string on a guitar is a 0.44-mm-diameter steel string with a linear density of 1.1 g/m . when the string is properly tuned to 196 hz, the wave speed on the string is 250 m/s. tuning is done by turning the tuning screw, which slowly tightens-and stretches-the string.

Answers

The G string on a guitar stretches by 1.696 mm when it is first tuned by using the formula of young's modulus.

Expression for the velocity of the waves on the stretched string

ν = √T/μ

Where, T = tension on the string

250 =√T/ 1.1 × 10⁻³

T = 68.75 N

The young modulus of the steel is given by

Y = 200 × 10⁹ Pa

Y = (T/A)/(Δl/l)

Δl = Tl/AY

By putting the values, we get,

Δl = 68.75 × 0.75/ 200 × 10⁹ × π × (0.22 × 10⁻³)²

Δl = 1.696 × 10⁻³m

Or, Δl = 1.696 mm

Hence, by 1.696 mm, the G string stretch when it is first tuned.

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