You are raising up a big bucket of water from a 22.5 m deep well. The combined mass of the water and the bucket is 11.3 kg. The bucket is attached to a heavy duty steel chain. The mass of the chain is 17.9 kg. How much work do you perform during the lifting process? Tries 0/12 If it takes 1.75 minutes for you to raise the bucket of water out of the well, then what was your average power?

Answers

Answer 1

The amount of work done during the lifting process is 4465.125 J and our average power will be 42.525 W.

Given:

Depth of the well, h = 22.5m

Mass of heavy-duty steel chain, M = 17.9 kg

The combined mass of the water and bucket, m = 11.3 kg

time taken to raise the bucket out of the water, T = 1.75 min = 105 s

Calculation:

Consider that the center of mass of the steel chain is at the midpoint of the depth of the well.

Now, the work done during the lifting process can be calculated as:

W.D = (Work done in lifting bucket filled with water) + (work done to lift    

                                                                                              the steel chain)

W.D = mgh + Mg (h/2)      -( 1 )

where g is the acceleration due to gravity

Applying values in the above equation we get:

W.D = mgh + Mg (h/2)

       = (11.3 kg)(9.8 m/s²)(22.5 m) + (17.9 kg)(9.8 m/s²)(22.5 m / 2)

       = 2491.65 + 1973.475

       = 4465.125 J

We know that the average power is given as:

P_avg = W.D / T     - ( 2 )

where W.D is the work done during the lifting process

            T is the time taken to raise the bucket out of the well

Applying values in the above equation, we get:

P_avg = W.D / T

           = (4465.125 J)/(105 s)

           = 42.525 W

Therefore, the amount of work done during the lifting process is 4465.125 J and our average power will be 42.525 W.  

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Related Questions

What does a dielectric do to a capacitor?

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A dielectric fabric is used to split the conductive plates of a capacitor. This insulating cloth significantly determines the properties of a component. The dielectric constant of fabric determines the amount of strength that a capacitor can keep while voltage is applied.

A capacitor is an electrical component that attracts energy from a battery and stores the power. Internal, the terminals connect with metal plates separated by way of a non-engaging in substance. While activated, a capacitor quickly releases electricity in a tiny fraction of a 2d.

Capacitor, a tool for storing electric electricity, together with two conductors in near proximity and insulated from each different. A simple example of this sort of garage tool is the parallel-plate capacitor.

A capacitor is a tool that shops electric power in an electric-powered area. it is a passive digital thing with terminals. The effect of a capacitor is called capacitance.

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Upon inspiration, what is the name of the air in the conducting zone that is not available for gas exchange?.

Answers

Dead space is the name of the air in the conducting zone that is not available for gas exchange.

What is conducting zone?

The conducting zone consists of all of the structures that provide passageways for air to travel into and out of the lungs.

The conducting zone is part of the respiratory system. It serves as a route for incoming and outgoing air and filtering debris and pathogens from the incoming air.In order to compensate for the reduction in gas exchange in the respiratory system, ventilation will increase

The volume of air that is inhaled that does not take part in the gas exchange is dead space. Because it either remains in the conducting airways or reaches alveoli that are not perfused or poorly perfused.

Dead space volume is air in the conducting airways that does not participate in gas exchange between the alveoli and blood.

Hence,

Dead space is the name of the air in the conducting zone that is not available for gas exchange.

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Question 5 of 32
According to the periodic table below, which element has the largest average
atomic mass?
OA. Helium (He)
OB. Oxygen (0)
OC. Nitrogen (N)
OD. Neon (Ne)

Answers

The answer is D
Neon has 20.0026 element more then the other

Normal human body temperature is 98.6°F. What is this temperature expressed in Celsius (°C) and in Kelvin (K)?

Answers

Answer: 37 Celsius and 310.15 K

Explanation:

C/5 = (F-32)/9 = (98.6-32)/9 = 66.6/9 = 7.4

C = 7.4 * 5 = 37 so the temperature is 37 Celsius

K = C + 273.15 = 37 + 273.15 = 310.15 K

Normally, whem I shut my door, it takes quite a bit of effort to shut it, but when my window is open, even if I just pull it slightly then let go, it slams automatically. It isn't an issue, I just want to know the physics behind it. Is it something to do with difference in pressure?​

Answers

Answer:

gravity

Explanation:

gravity pulls anything with with weight towards the earth.

Answer

The reason why this occurs is because if there is any apparent wind being pushed towards the direction of the door, there will be an attempt of equalizing pressure and thus it will slam, or close very loudly when you even just push it shut with some effort.

Explanation

This has happened to me a variety of times, I would have the garage open, and it would be a little bit windy, and when I tried to close it, it would slam shut.

Airflow is a significant factor in the pressure appliance.

Your question at the end is correct (Differences in air pressure.)

Apologies for the late response, but I was interested in this as well.

A person riding a Ferris wheel moves through positions at (1) the top, (2) the bottom, and (3) mid-
height. If the wheel rotates at a constant rate, rank these three positions according to

(a)the magnitude of the person’s centripetal acceleration,
(b) the magnitude of the net centripetal force on the person, and
(c) the magnitude of the normal force on the person from the bottom, and
(d) the weight the person feels, greatest first.​

Answers

A person riding a Ferris wheel moves through positions at

(1) the top,

(2) the bottom, and

(3) mid-height. If the wheel rotates at a constant rate, rank these three positions according to

(a)the magnitude of the person’s centripetal acceleration, is same in all cases.

(b) the magnitude of the net centripetal force on the person, is same in all three cases.

(c) the magnitude of the normal force on the person from the bottom,

2<3<1

(d) the weight the person feels, greatest first is at the bottom.

What is the relation between force and acceleration?The centripetal acceleration [tex]a_{c}[/tex] exists provided by : a= [tex]v^{2} /r[/tex] , therefore the magnitude depends upon the speed and the radius. This represents that in the case of the Ferris wheel the centripetal acceleration includes a constant magnitude so its value exists the same in all cases.From Newton's second law the force is provided by F=ma and since a exists constant in magnitude , F is also constant in magnitude. and its value exists the same in all three cases.At the top [tex]a_{c}[/tex] stands directed downward so the normal force exist given by [tex]F_{N}[/tex]=[tex]mg[/tex]- [tex]ma_{c}[/tex]While at the bottom [tex]a_{c}[/tex] exist directed upward and the normal force is provided by [tex]F_{N}[/tex]=mg +m[tex]a_{c}[/tex]Meanwhile,at mid -height [tex]a_{c}[/tex] stands directed horizontally to the inside so it doesn't have a vertical component so its normal force is provided by [tex]F_{N}[/tex]=mgThe normal force exists greatest at the bottom than at mid-height than at the top.

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When recording physical findings, which data are recorded first for all systems?

Answers

When recording physical findings, which data are recorded first for all systems: Inspection.

The definition of physical is things that are of nature or of the body. An example of physical is plantlife growing in the ground. An example of physical is someone confined to a wheelchair because of disabilities. physical indicates connected with, pertaining to, the animal or human body as a material organism.

Physical health is defined as the condition of your body, taking into consideration everything from the absence of disease to fitness level.

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An object falls from the top of a building that is 25 m high. Air resistance is negligible.
What is the speed of the object when it hits the ground?

Answers

The velocity of the object s calculated as 22.1 m/s.

What is the speed of the object?

Given that we can write that;

v^2 = u^2 + 2gh

Now u = 0 m/s because the object was dropped from a height

v^2 = 2gh

v = √2 * 9.8 * 25

v = 22.1 m/s

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A peregrine falcon in a tight, circular turn can attain a centripetal acceleration 1.5 times the free-fall acceleration.

Answers

The acceleration of a body traveling in a circular route is known as centripetal acceleration. The radius of the turn if the falcon will be 19.7 m.

What is Centripetal acceleration?

The acceleration of a body traveling in a circular route is known as centripetal acceleration. Because velocity is a vector quantity. It has both a magnitude and a direction.

Given:

a is the centripetal acceleration = 1.5g

v is the velocity = 17 m/sec

To Find:

r is the radius of circular turn = ?

Mathematically centripetal acceleration is given as

a = v^2/r

r = v^2/a. = (17)^2/1.5 x 9.81

r = 19.7 m

Hence the radius of the turn if the falcon will be 19.7 m.

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Why would we prefer to use the 0. 01uf capacitor in the feedback loop even though the circuit does not integrate quite as well over as large a range?

Answers

At 0 frequency (0Hz) or DC, the capacitor acts like an open circuit due to its reactance for this reason blocking off any output voltage feedback. As a result, little or no negative feedback is furnished from the output again to the input of the amplifier.

Therefore at low frequencies, the LPF has finite output and at high frequencies the output is nil, that's identical to an integrator circuit. for this reason, a low skip filter can be said to be worked as an integrator. Then the voltage variant in C may be very small.

A common op-amp circuit uses a remarks capacitor to limit the bandwidth. proscribing op-amp bandwidth will reduce noise, so a remarks capacitor is not an unusual way to reduce noise. To apprehend how the comments capacitor works, remember that a capacitor acts as a brief to “high frequency” AC indicators.

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The coefficients of static and kinetic frictions for plastic on wood are 0.50 and 0.40,respectively. How much horizontal force would you need to apply to a 3.0 N plastic calculatorto start it moving from rest?

Answers

The horizontal force needed to start the calculator moving from rest is 1.5 N

What is Kinetic friction?

It is defined as a force that acts between moving surfaces.

The magnitude of the force will depend on the coefficient of kinetic friction between the two materials.

Here,

weight of calculator, N = 3 N

The coefficients of static frictions, µ (static) = 0.50

The coefficients of kinetic frictions, µ (kinetic) = 0.40

Now,

The horizontal force required = The static friction force

F = µ (static) * weight of calculator

F = 0.50 * 3.0

F = 1.5 N

Hence,

The horizontal force needed to start the calculator moving from rest is 1.5 N

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Interstellar dust is effective at blocking visible light because Choose one: A. the dust is so dense. B. dust grains are so small. C. dust grains are so large. D. dust grains are so few.

Answers

Answer: Interstellar dust is effective at blocking visible light because dust grains are so small.

Explanation: To find the answer, we need to know more about the interstellar dust.

What is interstellar dust?Interstellar dust developed from dying stars as they burn out.This dust can block the visible light as well as UV emerging from the stars, because dust grains can block light at optical wavelengths.it absorbs and scatters blue light more than red. thus, red light can pass through it.If we place a star behind the dust, it will look more redder than its usual color. This is called interstellar reddening.Grains have a typical size of [tex]10^-6 m[/tex].

Thus, we can conclude that, Interstellar dust is effective at blocking visible light because dust grains are so small.

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Is it possible to code the impact force using an accelerometer?

Answers

Yes, it possible to code the impact force using an accelerometer.

Accelerometers can be used to measure vibration on cars, machines, buildings, process control systems and safety installations

What is an Accelerometer ?

An accelerometer is a device that measures the vibration, or acceleration of motion of a structure.

The force caused by vibration or a change in motion (acceleration) causes the mass to "squeeze" the piezoelectric material which produces an electrical charge that is proportional to the force exerted upon it.

They can also be used to measure seismic activity, inclination, machine vibration, dynamic distance and speed with or without the influence of gravity.

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derric climbs onto his roof to hang Christmas light. If the roof is 4.3 meters from the ground and derrick gains 2730 J of potential energy while climbing, what is his mass​

Answers

Mass of Derrick at a height 4.3 m having 2730 joule of energy is 65 Kg.

What is the expression of gravitational potential energy near the earth surface?Mathematically, gravitational potential energy near the earth surface= m×g×hm= mass of Derrick, g= acceleration due to gravity, h= height at which Derrick present Then, mass (m) of Derrick = potential energy/ (g×h)

What is the mass of Derrick, if he gains 2730 joule of energy at 4.3m above the ground?

Mass of Derrick= 2730/(9.8×4.3)

= 65 kg

Thus, we can conclude that the mass of Derrick is 65 Kg.

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A bicyclist covers the first leg of a journey that is d1meters in t1seconds at a speed of v1m/s and the second leg of d2meters in t2seconds at a speed of v2m/sIf his average speed is equal to the average of v1 and v2
then which of the following is true?
1. t1=t2
2. t1≠t2
3. d1=d2
4. d1≠d2

Answers

According to motion in straight line  t1≠t2


A biker travels d1 meters in t1 seconds at v1 m/s for the first leg and d2 meters in t2 seconds at v2 m/s for the second leg. It's possible that t1t2 if his average speed is equal to the average of v1 and v2.
An object is said to be in motion if its position in relation to its surroundings changes over time. It is a shift in an object's position over time. The only type of motion that exists is motion in a straight line.


A reference system is constantly used to describe a particle's motion. An arbitrary origin point is used to create a reference system, and a coordinate system is imagined to be connected to it. The reference system for a specific problem is the coordinate system that has been selected for it. For the majority of the problems, we typically select an earth-based coordinate system as the reference system.


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A Carnot engine operates between a hot reservoir at 320 degrees Kelvin and a cold reservoir at 260 degrees Kelvin. If it absorbs 500 Joules of heat at the hot reservoir, how much work does it deliver

Answers

The work done delivered by the Carnot engine is 93.75 J.

What is Carnot Engine?Leonard Carnot proposed the Carnot engine, a hypothetical thermodynamic cycle. It calculates the highest feasible efficiency that a heat engine can have when converting heat into work and when operating between two reservoirs.Any system working between [tex]T_1[/tex] (hot reservoir) and [tex]T_2[/tex] (cold reservoir) will never have better efficiency than the Carnot engine running between the identical reservoirs.Additionally, the efficiency of this form of engine is only reliant on the temperature of the hot and cold reservoirs and is independent of the composition of the working substance.

Solution:

[tex]T_c = 260 K\\ T_h = 320K\\ Q_h = 500J[/tex]

As we know that Carnot engine is ideal, the efficiency depends only on the temperature of the reservoirs(in kelvin scale):

[tex]n = 1 - \frac{T_c}{T_h} \\n = 1 - \frac{260}{320}[/tex]

[tex]n = 1- 0.8125\\n = 0.1875[/tex]

Also, we know that the work done is equal to product of efficiency and heat at hot reservoir:

[tex]W = n\times Q_h\\W = 0.1875 \times 500\\W = 93.75 J[/tex]

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Arrange these objects according to size, largest to smallest. Group of answer choices traditional dwarf elliptical, ultra-compact dwarfs, globular clusters ultra-compact dwarfs, traditional dwarf galaxies, globular clusters globular clusters, traditional dwarf elliptical, ultra-compact dwarfs globular clusters, ultra-compact dwarfs, traditional dwarf elliptical

Answers

Among the given objects, the largest one is dwarf elliptical, then ultra-compact dwarf and then globular clusters. Thus, option a is correct.

To find the correct answer, we need to know about the galaxies.

Are galaxies bigger than globular clusters?Globular clusters are spherical groups of stars that are primarily located in the spiral galaxy' stellar halo. There are 150 or so globular clusters in our Milky Way galaxy, some of which house our galaxy's oldest stars.Globular clusters are much smaller than galaxies.a system of gas and dust, as well as millions or billions of stars, kept together by gravitational attraction is called galaxy.Ultracompact dwarfs are more extended and have higher surface brightness than typical dwarf nuclei.Dwarf elliptical galaxies are elliptical galaxies that are smaller than ordinary elliptical galaxies. They are quite common in galaxy groups and clusters and are usually companions to other galaxies.

Thus, we can conclude that, option a is correct.

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Which types of decay will cause the mass number a of a nucleus to change?.

Answers

Nuclear decay results in the change in the mass number of a nucleus. In precise it is alpha decay.

What is nuclear decay?

The process through which an unstable atomic nucleus loses energy through radiation is known as radioactive decay, also known as nuclear decay, radioactivity, radioactive disintegration, or nuclear disintegration.

What is alpha decay?A nuclear process known as "alpha decay" releases a particle made up of two protons and two neutrons when an unstable nucleus transforms to another element. The helium nucleus that is being ejected is known as an alpha particle. Positive charge and a sizable mass characterize alpha particles.

How is mass number of nucleus is changed by alpha decay?

When a nucleus emits an alpha particle, these changes happen:

the mass number decreases by 4. the atomic number decreases by 2.

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Potentiometric measurements are based on galvanic electrochemical cells. these types of cells consist of:_______

Answers

Two-electron or metallic conducting electrodes that are connected by an electrolyte solution that conducts ions.

What are potentiometric measurements?

An electrochemical measurement method is potentiometry. The phrase was first used in relation to possible electrochemical measurement chain determinations. Potentiometer is a tool that measures an electrochemical cell's potential without drawing current or changing the makeup of the cell.

Potentiometric measurement is done to detect the difference in potential between a working (an indicator) electrode and a counter (a reference), using a potentiometer. The working/indicator electrode is called the cathode (right half-cell) and the counter/reference electrode is called an anode(half of a left cell).

A basic galvanic cell may just have one electrolyte isolated from it by a semi-permeable membrane, but a more complex one has two independent half-cells linked together by a salt bridge. An inert electrolyte like potassium sulfate is included in the salt bridge, and its ions will diffuse into each of the individual half-cells to balance the charges that are building up at the electrodes.

I understand the question you are looking for is this:

Potentiometric measurements are based on galvanic electrochemical cells. These types of cells consist of:

two inert metal electrodes to which an electrical potential is applied.two-electron or metallic conducting electrodes that are connected by an electrolyte solution that conducts ions.a biological recognition element and a physicochemical transducer, often an electrochemical or optical device.a polarizable working electrode to which an external voltage is applied with the resulting cathodic or anodic current of the cell being monitored.

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If a car increases its velocity from +6 m/s to +30 m/s in 6 seconds, its acceleration in m/s2 is__________.

Answers

Answer:

4m/s^2

Explanation:

v = 30m/s, u = 6m/s, t = 6s

Change in velocity = v(final velocity) - u (initial velocity)

v-u = 30-6 = 24m/s

acceleration = (v-u)/t

(24m/s)/6s = 4m/s^2

The wavelength of an electromagnetic wave is 600 nm. what is its frequency? (c = 3.0 × 108 m/s)

Answers

Answer:

5.0×10^-9

Explanation:

velocity = frequency × wavelength

3.0×10^8=f600×10^-9

divide both sides by 600×10^-9

f=3.0×10^8/600×10-9

f=5.0×10^-9

The wavelength of an electromagnetic wave is 600 nm. The frequency of the electromagnetic wave is 5.0 × 10^14 Hz.

To find the frequency of an electromagnetic wave, we can use the equation:

Frequency (f) = Speed of light (c) / Wavelength (λ)

where:

c = speed of light in a vacuum = 3.0 × 10^8 m/s

λ = wavelength of the electromagnetic wave in meters

First, we need to convert the given wavelength from nanometers (nm) to meters (m). Since 1 nm = 1 × 10^-9 m, the wavelength is:

λ = 600 nm × (1 × 10^-9 m/nm) = 600 × 10^-9 m = 6.0 × 10^-7 m

Now, we can calculate the frequency using the equation:

f = c / λ

f = 3.0 × 10^8 m/s / (6.0 × 10^-7 m)

f = 5 × 10^14 Hz

So, the frequency of the electromagnetic wave is 5 × 10^14 Hz (hertz).

This means that the wave oscillates or completes 5 × 10^14 cycles per second. Higher frequencies correspond to shorter wavelengths and vice versa. Electromagnetic waves with higher frequencies are more energetic, such as X-rays and gamma rays, while waves with lower frequencies, like radio waves, have longer wavelengths and are less energetic.

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A mass m is attached to an ideal massless spring. When this system is set in motion, it has a period t. What is the period if the mass is doubled to 2m?.

Answers

If a mass m is attached to an ideal massless spring and has a period of t, then the period of the system when the mass is 2m is [tex]\sqrt{2}t[/tex].

Calculation:

Step-1:

It is given that a mass m is attached to an ideal massless spring and the period of the system is t. It is required to find the period when the mass is doubled.

The time it takes an object to complete one oscillation and return to its initial position is measured in terms of a period, or T.

It is known that the period is calculated as,

[tex]T=2 \pi \sqrt{\frac{m}{k}}[/tex]

Here m is the mass of the object, and k is the spring constant.

Step-2:

Thus the period of the system with the first mass is,

[tex]t=2 \pi \sqrt{\frac{m}{k}}[/tex]

The period of the system with the second mass is,

[tex]\begin{aligned}\\t^'&=2 \pi \sqrt{\frac{m}{k}}\\&=\sqrt{2}\times2 \pi \sqrt{\frac{2m}{k}}\\&=\sqrt{2}\times t\end{aligned}[/tex]

Then the period of the system with the second mass is [tex]\sqrt{2}[/tex] times more than the period of the system with the first mass.

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a skier’s most important piece of equipment

Answers

Answer: A skier’s most important piece of equipment is Ski boots.

Explanation: To find the answer, we need to know about the ski boots.

Why ski boots are the most important equipment for a skier?Skiing can be defined as the action of travelling over snow on skis.There are different equipment's we use during skiing, among them, the most important equipment's is ski boot.Ski boots are not meant for walking, but they provide the skis an extension for their legs.The other equipment's are ski goggles, ski helmets, ski jackets and so on.

Thus, we can conclude that, a skier's most important equipment is Ski boots.

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Ski boots are a skier's most essential piece of gear.

We must understand the ski boots in order to determine the solution.

Why are ski boots the most crucial piece of gear for a skier?Skiing is the activity of moving over snow on a pair of skis.While we utilize a variety of equipment when skiing, the ski boot is by far the most crucial piece of gear.Although ski boots are not designed for walking, they provide the skis an extra leg.The other equipment includes ski coats, ski helmets, and ski goggles.

So, it stands to reason that ski boots are a skier's most essential piece of gear.

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What must the charge (sign and magnitude) of a 3.45 g particle be for it to remain stationary when placed in a downward-directed electric field of magnitude 590 N/C

Answers

     charge must be equal to 5.74 ×10⁻⁵

 In the question it is said that the particle remains stationary which means the the net force on the particle is zero. So, the counterbalancing forces must be equal which means weight is equal to upward electric force.

     →    Fnet =0

     →    mg =  qE

 substituting the values we get :

         0.00345 × 9.81 =  q × 590

   →       q = 5.74 ×10⁻⁵

    Hence the charge must be equal to   5.74 ×10⁻⁵.

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For vibrational motion, what term denotes the maximum displacement from the equilibrium position?.

Answers

For vibrational motion, the amplitude denotes the maximum displacement from the equilibrium position.

What is vibrational motion?

The motion in which there are some vibrations about the fixed position called mean position is termed vibrational motion. For example, the motion of a wave on the string has perpendicular vibration.

What is amplitude?

The amplitude is defined as the maximum displacement of the vibration from its mean position. For vibrational motion, the mean position is the equilibrium position. So amplitude is the term that denotes the maximum displacement from the equilibrium position. For example, the displacement of the string wave from its equilibrium position is the amplitude of the string wave.

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Which meteorological parameter is expressed as the ratio between the air’s actual water vapor content and the amount of water vapor required for saturation at that temperature?

Answers

Which meteorological parameter is expressed as the ratio between the air’s actual water vapour content and the amount of water vapour required for saturation at that temperature: relative humidity.

Water vapour is the primary form of atmospheric moisture. Although its storage in the atmosphere is comparatively small, water vapour is extremely important in forming the moisture supply for dew, frost, fog, clouds, and precipitation.

Water vapour is also the most important greenhouse gas in the atmosphere. Water vapour can be produced from the evaporation or boiling of liquid water or from the sublimation of ice.

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How much the aproximate number of atoms in bacteria.assume that average mass of an atom in bacteria is ten times the mass of hydrogen atom

Answers

The approximate number of atoms is 15 because I said and if it’s not that’s cool but that’s what I think it is 15 and the hydrogen is 11

Even though the Sun gets lower in the sky after solar noon, and the intensity of incident solar radiation is reduced, the air temperature continues to climb after solar noon because

Answers

Even though the Sun gets lower in the sky after solar noon, and the intensity of incident solar radiation is reduced, the air temperature continues to climb after solar noon because energy is still being absorbed by the ground faster than it is being lost

Solar radiation is a broad word for the electromagnetic radiation that the sun emits. It is also sometimes referred to as the solar resource or just sunshine. A multitude of devices can be used to catch solar radiation and transform it into useful forms of energy, such as heat and electricity.

The energy that the Sun emits into space in the form of electromagnetic waves is known as solar radiation. This energy, which is released by the Sun's surface, affects climatological and atmospheric processes. Visible light, ultraviolet light, infrared, radio waves, X-rays, and gamma rays are all types of solar radiation.

Cardiovascular disease can be caused by radiation by altering the cardiovascular system, harming the heart, hardening and narrowing arteries, and/or removing part of the cells from the blood vessel linings.

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In a series lrc circuit, the frequency at which the circuit is at resonance is f0. If you double the resistance, the inductance, the capacitance, and the voltage amplitude of the ac source, what is the new resonance frequency?.

Answers

When you double capacitance and inductance, the new resonance frequency becomes f/2.

Resonance frequency:

The resonance frequency of RLC series circuit, is the frequency at which the capacity reactance is equal to inductive reactance.

It can also be defined as the natural frequency of an object where it tends to vibrate at a higher amplitude.

Xc = Xl

which gives the value for resonance frequency:

[tex]f = \frac{1}{2\pi \sqrt{LC} }[/tex]

where;

f is the resonance frequency

L is the inductance

C is the capacitance

When you double capacitance and inductance, the new resonance frequency becomes;

[tex]f' = \frac{1}{2\pi \sqrt{2L2C} }[/tex]

[tex]f' = \frac{1}{2\pi \sqrt{4LC} }[/tex]

[tex]f' = \frac{1}{\pi \sqrt{LC} }\frac{1}{2}[/tex]

[tex]f' = \frac{1}{2} f[/tex]

Thus from above,

When you double capacitance and inductance, the new resonance frequency becomes f/2.

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Answer the following regarding Momentum Change and Force:

A) A top-class tennis player can serve the ball, of mass 57 g, at an initial horizontal speed of 50 m/s. The ball remains in contact with the racket for 0.05 s. Calculate the average force exerted on the ball during the serve.

B) A motor car of mass 3000 kg moving with 72 km h-1 made to reduce its speed to 18 km h^-1, in 40 s, by applying brakes. Find the resistive force.

Answers

A. The average force exerted on the ball during the serve is 57 N

B. The resistive force, given the data is -1125 N

A. How to determine the average forceMass (m) = 57 g = 57 / 1000 = 0.057 KgInitial velocity (u) = 50 m/sTime (t) = 0.05 sAcceleration (a) = u / t = 50 / 0.05 = 1000 m/s²Force (F) = ?

F = ma

F = 0.057 × 1000

F = 57 N

B. How to determine the resistive forceMass (m) = 3000 KgInitial velocity (u) = 72 Km/h = 72 / 3.6 = 20 m/sFinal velocity (v) = 18 Km/h = 18 / 3.6 = 5 m/sTime (t) = 40 sForce (F) = ?

F = m(v – u) / t

F = 3000(5 – 20) / 40

F = -1125 N

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