The terminal speed of a 3-mm diameter spherical raindrop in standard air is relatively moderate but can vary depending on the specific conditions and characteristics of the raindrop and surrounding environment.
The terminal speed of a 3-mm diameter spherical raindrop in standard air depends on several factors such as the viscosity and density of the air, as well as the shape and size of the raindrop.
However, according to the Stoke's Law, which states that the terminal velocity of a small, dense, spherical particle moving through a viscous fluid is proportional to its radius squared, the terminal speed of a 3-mm diameter spherical raindrop in standard air would be approximately 7.7 meters per second.
Compared to smaller raindrops, larger raindrops have a higher terminal velocity due to their greater mass and surface area. Similarly, raindrops with irregular shapes or with surface imperfections may also experience higher terminal velocities due to turbulence and drag.
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Question # 6
Multiple Choice
Which of the following explains why James, who operates an apple orchard that sells a very rare type of gourmet apple, would probably
choose NOT to participate in contract production?
O Because he independently grows a unique product, he is already locked in to the best price of the market.
He operates as a price-taker, that so there is no need to contract.
His rare commodity offers an increased cash flow and an expansion of operation.
As a seller of a rare commodity he is in a position to negotiate higher prices than commodity food producers.
The statement that explains why James, who operates an apple orchard that sells a very rare type of gourmet apple, would probably choose not to participate in contract production is because he independently grows a unique product, he is already locked in to the best price of the market (option A).
What is contract manufacturing?Contract manufacturing or production occurs when a small business hires another company to produce its products.
This enables small business individuals to begin selling their products without obtaining the large amount of capital necessary to build and run a factory.
However, according to this question, James is a business individual who operates an apple orchard that sells a very rare type of gourmet apple.
Therefore, James would not need to participate in contract production because he independently grows a unique product, he is already locked in to the best price of the market.
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A 16.0 kg crate rests on a shelf 1.80 m above the floor in a warehouse. A forklift is used to raise the crate to a shelf 3.30 m above the warehouse floor. What is the increase in potential energy of the crate?
Group of answer choices
a. 240 J
b. 250 J
c. 230 J
d. 260 J
A 16.0 kg crate increases in height from 1.80 m to 3.30 m above the floor. The increase in potential energy is 240 J (a).
What is potential energy?It is the energy due to the position.
A 16.0 kg (m) crate rests on a shelf 1.80 m (h₁) above the floor in a warehouse. The potential energy is:
U₁ = m × g × h₁ = 16.0 kg × (9.81 m/s²) × 1.80 m = 283 J
A forklift is used to raise the crate to a shelf 3.30 m (h₂) above the warehouse floor. The potential energy is:
U₂ = m × g × h₂ = 16.0 kg × (9.81 m/s²) × 3.30 m = 518 J
The increase in the potential energy is:
518 J - 283 J = 235 J ≈ 240 J
A 16.0 kg crate increases in height from 1.80 m to 3.30 m above the floor. The increase in potential energy is 240 J (a).
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An inductance L and a resistance R are connected in series to an ideal battery. A switch in the circuit is closed at time t
Maximum energy stored at the time t = (L/R) ln 2 after the switch is closed
The magnetic field stops expanding when the current in a practical inductor achieves its steady-state value of Im = E/R. The power p = vi is also 0 because the voltage across the inductor has fallen to zero. As a result, the inductor's ability to store energy grows only as the current approaches its steady-state value.
The magnetic field's maximum stored energy is constant when the current is stable. The inductance of the practical inductor does not store any extra energy, but the inductor's resistance continuously loses energy. The magnetic field must continue to exist. current.
The area under the power curve represents the maximum energy stored by the inductance and is equal to the product of the average power and the elapsed time.
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Cytosine is methylated resulting in 5-methylcytosine. What is the most likely outcome?.
Answer: Cytosine is methylated resulting in 5-methylcytosine. Then the gene expression will decrease.
Explanation: To find the answer, we need to know more about the methylation of cytosine.
What is methylation of cytosine?Methylation means the addition of a methyl group on a substrate of an atom.It's a form of alkylation, here a methyl group replaces a hydrogen atom.Methylation of cytosine occurs at CpG palindrome in DNA.When cytosine is methylated to produce 5- methyl cytosine, which results in a decrease in gene expression.Thus, we can conclude that, Cytosine is methylated resulting in 5-methylcytosine. Then the gene expression will decrease.
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Tuning forks with a frequency of 500 to 1000 hz are most commonly used to measure:________
Tuning forks with a frequency of 500 to 1000 hz are most commonly used to measure: hearing loss
A person is said to have hearing loss if they are not able to hear as well as someone with normal hearing, meaning hearing thresholds of 20 dB or better in both ears. It can be mild, moderate, moderately severe, severe or profound, and can affect one or both ears.
High-pitched tuning fork with frequency of 500 to 1000 hertz (Hz) should be used to estimate hearing loss in range of normal speech (300 to 3000 Hz).
The 512-Hz Rinne tuning fork test could be very effective at detecting conductive hearing losses when performed by an experienced tester and when masking was used . Tuning forks are used to carry Rinne and Weber tests. These tests provide a quick easy method of determining whether a hearing loss is situated in the middle ear or inner ear
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he most accurate place to conduct a weight check is: Select one: At the surface, at the beginning of the dive. At the deepest point reached during the dive. At safety-stop depth, at the end of the dive. None of the above.
The most accurate place to conduct a weight check is at safety-stop death, at the end of the dive.
Why is a weight check important in diving?
A weight check before diving helps an individual decide on the right amount of weight needed for each scuba dive.
To do a weight check one must float upright on the surface, head placed above water. The individual then needs to release some air from their Buoyancy compensator as they take a deep breath from their regulator.
Now if the individual sinks rapidly below the surface, they are overweight and if their head stays above the water surface, then they are underweight. Thus, when an individual sinks up to the mask level, then the weight is just right.
Therefore, the most accurate place to conduct a weight check is at safety-stop depth, at the end of the dive.
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In addition to ozone, what four other greenhouse gases or groups of greenhouse gases are included in nearly all the climate models?
In addition to ozone, the four other greenhouse gases or groups of greenhouse gases are included in nearly all the climate models are Carbon dioxide, water vapor, and methane, nitrous oxide.
Carbon dioxide, absorbs energy at a variety of wavelengths, a range that overlaps with that of infrared energy. As CO2 soaks up this infrared energy, it vibrates and re-emits the infrared energy back in all directions. About half of that energy goes out into space, and about half of it returns to Earth as heat, contributing to the ‘greenhouse effect.’
As methane is emitted into the air, it reacts in several ways. It reacts and after oxidization methane forms water vapor and carbon dioxide. So, not only does methane contribute to global warming directly but also, indirectly through the release of carbon dioxide.
Nitrous oxide enhances the greenhouse effect by capturing reradiated infrared radiation from the Earth’s surface and subsequently warming the troposphere . It is chemically inert in the troposphere and stays in the troposphere for about 120 years before moving into the stratosphere where it ultimately leads to destruction of stratospheric ozone.
Water vapor does absorb longwave radiation and radiates it back to the surface, thus contributing to warming.
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A generator coil is rotated one quarter of a full revolution, from θ = 0° to θ = 90°,
in 13.2 ms. The coil has 353 loops, and it is a square 4.62 cm on a side. If the coil
is in a uniform magnetic field of 0.991 T, what is the maximum electromotive force
induced in the coil by the generator?
The maximum electromotive force induced in the coil by the generator is 56.45 V.
Maximum electromotive force induced in the coil
emf(max) = NAB/t
where;
N is number of turnsA is areaB is magnetic fieldt is timeSubstitute the given parameter and solve for maximum electromotive force induced in the coil.
Area of the loop = 0.0462 m x 0.0462 m = 0.00213 m²
emf(max) = (353 x 0.00213 x 0.991) / (13.2 x 10⁻³)
emf(max) = 56.45 V
Thus, the maximum electromotive force induced in the coil by the generator is 56.45 V.
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An RL series circuit is connected to an ac generator with a maximum emf of 20 V. If the maximum potential difference across the resistor is 16 V, then the maximum potential difference across the inductor is:
If the maximum emf of the ac generator is 20 V and the maximum potential difference across the resistor is 16 V Then the maximum potential difference across the inductor is 4 V.
Calculation:
Step-1:
It is given that the RL circuit is connected to a 20 V ac generator. The maximum potential difference across the resistor is 16 V. It is required to find the maximum potential drop across the inductor.
Step-2:
The maximum emf of the generator is equal to the sum of the maximum potential difference across the resistor and the maximum potential difference across the inductor.
Therefore,
The maximum potential difference across the inductor + Maximum maximum potential difference across the resistor = Maximum emf of the generator
Thus,
Maximum maximum potential difference across the inductor + 16 V = 20 V
Therefore,
Maximum maximum potential difference across the inductor = 20 V - 16 V = 4 V
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(a) Circular metal wires in electrical circuits may have different cross-sectional areas (different diameters) and different lengths. For a given applied voltage, how would the joule heat vary with these parameters
For the different wires the values given are
For Wire A, Area=[tex]A_{A}[/tex], Resistivity=[tex]ρ_{A}[/tex], Length= [tex]L_{A}[/tex], Heat=[tex]H_{A}[/tex], Voltage= V, Time= t, Wire B, Area=[tex]A_{B}[/tex], Resistivity=[tex]ρ_{B}[/tex], Length= [tex]L_{B}[/tex], Heat=[tex]H_{B}[/tex]
So, [tex]H_{A}[/tex]/ [tex]H_{A}[/tex]=[tex]\frac{V^{2} *t}{\frac{ρ(1)*L_{A} }{A_{A} } }[/tex]/[tex]\frac{V^{2} *t}{\frac{ρ(2)*L_{B} }{A_{B} } }[/tex]
Therefore [tex]H_{A}[/tex]/ [tex]H_{A}[/tex]= [tex]\frac{A_{A}*ρ_{B} *L_{B}}{A_{B}ρ_{A} L_{A} }[/tex]
HeatThe type of energy that moves between two materials with varying temperatures is referred to by scientists as heat. Because the average translational kinetic energy per molecule in the two materials varies, an energy transfer takes place. Up until thermal equilibrium is attained, heat is transferred from the substance with the higher temperature to the material with the lower temperature. The joule, with 1 joule equalling 1 newton meter, is the SI unit of heat. Imagine the following situation to better comprehend what happens when this energy transfer takes place: Tiny rubber balls are bouncing all over two distinct containers that are full with them. The difference between the average ball speed in one container and the second container is substantial.
(a) Circular metal wires in electrical circuits may have different cross-sectional areas (different diameters) and different lengths. For a given applied voltage, how would the joule heat vary with these parameters
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Which mineral property is the least useful for identifying minerals, and why?
Use Hooke's Law to determine the variable force in the spring problem. A force of 7 pounds compresses a 15-inch spring a total of 3 inches. How much work is done in compressing the spring 7 inches
Work done in compressing spring = 40.833
It simply needs a three-inch compression by applying a compressive force to a 15-inch long spring. we know that F(x)=kx. To act in displacement X and the poles' values cannot be substituted. Consequently, there will be 4. The spring constant K is therefore equal to 5, so. Three fit within this slot. We consequently derive the compressing spring constant K from this. , which is 5, 3. Now change this formula to include the value of the compressing spring constant. Four f will therefore equal 5.3 x and vice versa. Integration of four factors equals W.
In order to ensure the limit and further all of this, we currently have the range 0–7. Thus, this compressing spring task is completed. W is equal to 40.833
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These clouds are shaped like a column. they can start low and can stretch high in the sky. which forms of precipitation may occur from this type of clouds?
The form of precipitation which may occur from this type of clouds is cumulus clouds.
What is precipitation cloud?Precipitation cloud is the cloud from which rain falls or looks likely to fall.
Below are some types of precipitation:
Hail precipitationSnow precipitationSnow grains precipitationIce crystal precipitationRain precipitationDrizzlePrecipitation refers to any or all of the forms of water particles, whether liquid or solid, that fall from the atmosphere such as; rain, hail, snow or sleet).
It is a major class of hydrometeor, but it is distinguished from cloud, fog, dew, rime, frost, etc., in that it must fall. It is distinguished from cloud and virga in that it must reach the ground.
Cloud refers to visible mass of water droplets suspended in the air.
In conclusion, the form of precipitation which may occur from this type of clouds is cumulus clouds
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How does head to tail rule helps us to find the resultant of forces ?? Explain with the help of a diagram.
Head to tail rule helps us to find the resultant of forces because in this rule we join many vectors with each other forming resultant vector.
What is head to tail rule?
The joining of tail of the first vector with the head of the second vector represents the resultant vector whereas the direction of the resultant vector is from the tail of the first vector towards the head of the second.
So we can conclude that Head to tail rule helps us to find the resultant of forces because in this rule we join many vectors with each other forming resultant vector.
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And instead of tolling the bell, for church, our little sexton – sings. what is the most likely reason for the poet to oppose the phrases "tolling the bell" and "sings" in these lines? the poet is expressing her belief that the second, more natural option is far more desirable than the first option. the poet is hinting that religious worship should be considered a gloomy and serious activity. the poet is suggesting that those who worship in nature are more formal than those who worship in church. the poet is contrasting her attitude about religion with her feelings about the natural world, which remains largely unappreciated.
The poet is expressing her belief that the second, more natural option is far more desirable than the first option.
What is the summary of some keep the sabbath going to church?Some hold the Sabbath going to Church is set faith and meditation.
The poem explores the idea of spiritual practices in Christianity.
It additionally illustrates the speaker's angle in the direction of those practices.
According to this, it's far obligatory to put on a surplice even as attending church services.
While she wears her casual get dressed and prays to God, Some hold the Sabbath going to Church –' is one in every of Emily Dickinson's best-recognized poems.
It functions her aim to are seeking for salvation without resorting to the traditional means.
hence,
The most likely reason for the poet to oppose the phrases "tolling the bell" and "sings" in these lines is the poet is expressing her belief that the second, more natural option is far more desirable than the first option.
Thus, option "A" is correct.
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Answer:
(A)The poet is expressing her belief that the second, more natural option is far more desirable than the first option.
If m=2000 p=2. 25 and y=6000 what is velocity
The velocity of the money at the given price, and amount of money in the time frame is 6.75.
What is Velocity of money?The velocity of money is a measurement of the rate at which money is exchanged in an economy.
It is the number of times that money moves from one entity to another.
It also refers to how much a unit of currency is used in a given period of time.
MV = PY
V = PY/M
where;
P is priceY is transaction in time frameM is amount of moneySubstitute the given parameters and solve for velocity;
V = (2.25 x 6000) / 2000
V = 6.75
Thus, the velocity of the money at the given price, and amount of money in the time frame is 6.75.
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Chicago, il is currently in the e climate zone.
a) true
b) false
Answer:
false
Explanation:
A mass m is attached to an ideal massless spring. When this system is set in motion with amplitude a, it has a period t. What is the period if the amplitude of the motion is increased to 2a?.
The period remains the same if the amplitude of the motion is increased to 2a
What is Time period?
The time period is the time taken by a complete cycle of the wave to pass a point.
The equation of the period for spring is:
[tex]T = 2\pi \sqrt{\frac{m}{k} }[/tex]
Where,
Time period = T
mass of system = M
k is the spring constant
Amplitude of the motion is a
From the equation we can say that,
The period of a spring-mass system is proportional to the square root of the mass and inversely proportional to the square root of the spring constant.
Now if we increase the amplitude of the motion to 2a, the period of time remains the same.
Because the time period is not dependent on amplitude, it is independent of a.
Hence,
The period remains the same if the amplitude of the motion is increased to 2a.
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Three charges, qA is +6.0 μC, qB is –5.0 μC, and qc is +6.0 μC, are located at the corners of a square with each side length at 5.0 cm as shown in the diagram. Calculate the electric field at point D.
The net electric field at point D is determined as 3.95 x 10⁷ N/C.
Electric field at D due to charge A
E = kq/r²
where;
r is the distance between A and Dq is charge AE(AD) = (9 x 10⁹ x 6 x 10⁻⁶)/(0.05²)
E(AD) = 2.16 x 10⁷ i N/C
Electric field at D due to charge B
E = kq/r²
where;
r is the distance between A and Bq is charge Br² = 5² + 5²
r² = 50
r = √50
r = 7.07 cm
E(BD) = (9 x 10⁹ x 5 x 10⁻⁶)/(0.0707²)
E(BD) = 9 x 10⁶ N/C
in x - direction = 9 x 10⁶ N/C x cos(45) = 6.36 x 10⁶ i N/C
in y - direction = 9 x 10⁶ N/C x sin(45) = 6.36 x 10⁶j N/C
Electric field at D due to charge CE = kq/r²
where;
r is the distance between C and Dq is charge CE(CD) = (9 x 10⁹ x 6 x 10⁻⁶)/(0.05²)
E(CD) = 2.16 x 10⁷ j N/C
Net electric field in x directionEi = 2.16 x 10⁷ i N/C + 6.36 x 10⁶ i N/C
Ei = 2.796 x 10⁷ i N/C
Net electric field in y directionEj = 2.16 x 10⁷ j N/C + 6.36 x 10⁶j N/C
Ej = 2.796 x 10⁷ j N/C
Resultant electric field at DE = √Ei² + Ej²
E = √[(2.796 x 10⁷)² + (2.796 x 10⁷)²]
E = 3.95 x 10⁷ N/C
Thus, the net electric field at point D is determined as 3.95 x 10⁷ N/C.
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what was kobes passion for sports
What happens when the
atoms in a magnetic material
are lined up?
A. It is magnetic.
B. It is not magnetic.
C. The arrangement of the atoms does not
affect the magnetism of the material.
option (a)i.e, It is magnetic when the atoms in a magnetic material are lined up.
Magnetic fields can be represented visually using magnetic field lines. In each case, they specify the direction of the magnetic force acting on a north monopole. The lines' density reveals how large the field is. For example, the magnetic field is more intense and dense near a magnet's poles.
The spin and orbital momentum of an atom's electrons produce magnetism. The term "magnetic anisotropy" refers to how an atom's magnetic characteristics change depending on how the orbits of its electrons are oriented in relation to the composition of a substance. Additionally, it gives magnetization directionality and stability
Each atom creates a tiny magnetic field because the orbiting electrons are tiny moving charges. The direction or orientation of these magnetic fields is referred to as the atom's magnetic moment. In a nutshell, an object's atoms behave like a number of small magnets.
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State Newton's second law of motion and establish the relation F = m x a
F = ma is the formula of Newton's Second Law of Motion. Newton's Second Law of Motion is described as Force is equal to the rate of change of momentum. For a constant mass, force equals mass duration acceleration.
What is the significance of Newton's second law of motion explain?
Newton's Second Law of Motion F=ma is very significant because it indicates the relationship between forces and motion. It permits you to calculate the acceleration (and therefore velocity and position) of an object with known forces. This is extremely helpful for scientists, engineers, inventors, etc.
Force is directly proportional to Shift in momentum ÷ Time taken.Therefore : F is directly proportional to m×a. This relation F is directly proportional to m×a can be turned into an equation by placing in a constant k.
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A ball is thrown horizontally from the top of a building 0.10 km high. The ball strikes the ground at a point 78 m horizontally away from and below the point of release. What is the speed of the ball just before it strikes the ground
Answer:
Error
Explanation:
Speed= Distance / Time
Speed = 0.1
Basic elements for every contract include
1) an offer,
2) acceptance,
3) ___________,
4) with legal capacity, for a legal purpose
The basic elements for every contract include
1) an offer,
2) acceptance,
3) Awareness
4) with legal capacity, for a legal purpose
What is a contract?A contract is an agreement between two or more parties, to perform a specific job or duty. A contract is usually temporary or of fixed duration and usually governed by a written agreement.
The basic elements every contract should contain are as follows:
An offer, which encompasses the duties and responsibilities of each partyAcceptance; the offeree must decide whether to accept or reject the proposal/offer. Awareness; for a contract to be binding, the involved parties must first be aware that they are entering into an agreementLegal capacity; all contracts are subject to the laws of the jurisdiction in which they operateLearn more about contract at: https://brainly.com/question/2669219
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Calculate the wavelength of a photon of electromagnetic radiation with a frequency of 151.7 mhz
The wavelength of a photon of electromagnetic radiation with a frequency of 151.7 Mhz is 1.978 meter
According to the question
The frequency of a photon of electromagnetic radiation = 151.7 Mhz
By using the Formula of wavelength and frequency
λ = C/f
Where,
λ (Lambda) = Wavelength in meters
C = Speed of Light (c = 3x10⁸ m/s)
f = Frequency
Now, the wavelength of a photon of electromagnetic radiation with a frequency of 151.7 Mhz is
1 Mhz = 1000000 Hz
151.7 Mhz = 151.7 * 10⁶ Hz
λ = C/f
Substituting the value of C and f
λ = [tex]\frac{3*10^{8} }{151.7 * 10^{6} }[/tex]
λ = 1.978 meter
Hence, the wavelength of a photon of electromagnetic radiation with a frequency of 151.7 Mhz is 1.978 meter
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The coils in a motor have a resistance of 0.14 Ω and are driven by an EMF of 62 V.
The back EMF induced in the motor is 37 V. Calculate the difference in power
required by the motor at start up and at operating speed
The difference in the power required by the motor at start up and at operating speed is 9778.57
What is power?This is defined as the rate in which energy is consumed. Electrical power is expressed mathematically as:
Power (P) = voltage (V) × current (I)
P = IV
Power = square voltage (V²) / resistance ®
P = V² / R
How to determine the power by the EMFVoltage (V) = 37 VResistance (R) = 0.14 Ω Power by EMF (P₁) =?P = V² / R
P₁ = 62² / 0.14
P₁ = 27457.14 watts
How to determine the power by the back EMFVoltage (V) = 62 VResistance (R) = 0.14 Ω Power by back EMF (P₂) =?P = V² / R
P₂ = 37² / 0.14
P₂ = 9778.57 watts
How to determine the power differencePower by EMF (P₁) = 27457.14 wattsPower by back EMF (P₂) = 9778.57 wattsDifference in power =?Difference = P₁ - P₂
Difference in power = 27457.14 - 9778.57
Difference in power = 17678.57 watts
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Water falls without splashing at a rate of 0.400 L/s from a height of 2.20 m into a 0.720-kg bucket on a scale. If the bucket is originally empty, what does the scale read 3.60 s after water starts to accumulate in it
The reading of the scale after 3.6 seconds is 23.79 N.
Velocity of the water
v = √2gh
v = √(2 x 9.8 x 2.2)
v = 6.57 m/s
Rate of change of momentum of the water after impactmv/t = F = 0.4 x 6.57 = 2.628 N
Weight of the bucketWb = 0.72 x 9.8
Wb = 7.056 N
Weight of the accumulated waterWa = (RT)g
Wa = (0.4 x 3.6) x 9.8
Wa = 14.11 N
Reading of the scaleR = Wa + Wb + F
R = 14.11 N + 7.056 N + 2.628 N
R = 23.79 N
Thus, the reading of the scale after 3.6 seconds is 23.79 N.
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The speed of water flowing through a hose increases from 2.05 m/s to 31.4 m/s as it goes through the nozzle. What is the pressure in the hose, assuming the absolute pressure in the nozzle is atmospheric pressure
The pressure in the hose as the speed of water changes from 2.05 m/s to 31.4 m/s as it goes through the nozzle is 5.92 × 10⁵ N/m².
Given:
The flow of water through the hose initially, v₁ = 2.05 m/s
The flow of water through the hose initially, v₂ = 31.4 m/s
Calculation:
From Bernoulli's equation we have:
P₁ + 1/2 ρv₁² + ρgh₁ = P₂ + 1/2 ρv₂² + ρgh₂
where P₁ is atmospheric pressure
P₂ is the pressure in the hose
ρ is the density of the fluid
h₁ is the initial height
h₂ is the final height
v₁ is the initial velocity of the fluid
v₂ is the final velocity of the fluid and
g is the acceleration due to gravity
Re-arranging the above equation we get:
P₂ = P₁ + 1/2 ρ(v₁²-v₂²) + ρg (h₁-h₂)
Applying values in the above equation we get:
P₂ = P₁ + 1/2 ρ(v₁²-v₂²) + ρg (0)
= (1.01 × 10⁵ Pa)+ 1/2 (10³ g/m³) [(31.4m/s)²-(2.05 m/s)²]
= (1.01 × 10⁵ Pa)+ 1/2 (10³ g/m³) [981.7575]
= (1.01 × 10⁵ Pa)+ (4.91 × 10⁵ Pa)
= 5.92 × 10⁵ Pa
= 5.92 × 10⁵ N/m²
Therefore, the pressure in the hose is 5.92 × 10⁵ N/m².
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mechanical equivalent of heat Do the data for the second part of the experiment support or refute the second hypothesis
When we state something about the results on the basis whether the observed data supports the original hypothesis, we say that we are concluding the results.
What is the relationship between force and acceleration based on Newton's 2nd law?
Newton's second law of motion can be formally stated as follows: The acceleration of an object as produced by a net force is directly proportional to the magnitude of the net force, in the same direction as the net force, and inversely proportional to the mass of the object.
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A carnival ferris wheel has a 15-m radius and completes five turns about its horizontal axis every minute. What is the acceleration of a passenger at his lowest point during the ride?.
The acceleration of the person is 4.108 m/s^2.
What is acceleration?
The acceleration is the rate of change in the velocity in a unit of time.
Angular velocity: The change in angular displacement in a unit of time is called angular velocity.
Tangential velocity: The tangential velocity can be defined as the velocity of an object which is perpendicular to the radius in the rotational motion.
The relation between angular velocity ω, tangential velocity v, and radius r from the axis when the radius is perpendicular to the tangential velocity is,
v=ω*r
Given r=15 m, and ω=5 turns/minutes, substitute these values in the above formula.
Note: 1 turn/minute = 2π/60 rad/s.
v=(5 turns/minutes)*15 m
v=(5*2π/60 rad/s)* 15 m
v=7.85 m/s
Since the motion is circular, and the person is at the lowest point of the wheel, so the acceleration due to gravity will have no effect as it is perpendicular to tangential velocity here. The acceleration a for rotational motion is given by,
a=v^2/r
Substitute v=7.85 m/s, and r=15 m in this equation and solve it.
a=(2.094)^2/(15)
a=4.108 m/s^2
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