assuming the merry-go-round is a uniform disk of radius 6.0 m and mass 3.20×104 kg , calculate the net torque required to accelerate it.

Answers

Answer 1

The net torque required to accelerate a uniform disk of radius 6.0 m and mass 3.20 X 104 kg is 1.22 × 10^6 N.m. Assuming the merry-go-round is a uniform disk of radius 6.0 m and mass 3.20×10^4 kg,

the moment of inertia (I) of the merry-go-round is given by the equation:

I = (1/2) mr² where m is the mass and r is the radius of the merry-go-round.

I = (1/2)(3.20 × 10^4 kg)(6.0 m)²I

= 3.84 × 10^5 kg.m²

The net torque required to accelerate a uniform disk is given by the equation:

τ = Iαwhere τ is the net torque, I is the moment of inertia, and α is the angular acceleration.

Since the merry-go-round is being accelerated from rest, the initial angular velocity (ω0) is zero. The final angular velocity (ω) is not given. Therefore, we can use the equation:ω² = ω0² + 2αθwhere θ is the angle through which the merry-go-round rotates and can be taken as 1 revolution or 2π radians. Substituting the given values, we get:ω² = 0 + 2α(2π)ω² = 4παThe final angular velocity (ω) can also be written in terms of linear velocity (v) using the equation: v = rωwhere r is the radius of the merry-go-round. Substituting the given values, we get: v = (6.0 m)ωWe can now use the equation: F = ma to calculate the net force required to accelerate the merry-go-round, where F is the net force, m is the mass of the merry-go-round, and a is the linear acceleration.

Since the linear acceleration is related to the angular acceleration by the equation:

a = rαwe can rewrite the equation as:

F = mr α Substituting the given values,

we get:  F = (3.20 × 10^4 kg)(2α)(6.0 m)F

= 3.84 × 10^5 α NN

is the net force required to accelerate the merry-go-round.

The net torque required to produce this force can be calculated using the equation:τ

= r F Substituting the given values,

we get:τ = (6.0 m)(3.84 × 10^5 α N)τ = 2.30 × 10^6 α N.m

Since τ = Iα, we can substitute this value to get:

2.30 × 10^6 α N.m = (3.84 × 10^5 kg.m²)α

Therefore,

α = 6 N.m/ (3.84 × 10^5 kg.m²)α

= 1.56 × 10^-5 rad/s²Substituting this value into the equation:τ

= 2.30 × 10^6 α N.mτ = (2.30 × 10^6 N.m) (1.56 × 10^-5)τ = 1.22 × 10^1 N.m

Therefore, the net torque required to accelerate the merry-go-round is 1.22 × 10^6 N.m.

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Related Questions

Calculate the molarity of the oxalic acid solution if 25 00 ml of 0. 2500 m naoh is required to trate 20. 00 ml of oxalic acid the reaction h₂c2o4 naoh -->

Answers

The molarity of the oxalic acid solution is 0.3125 M.

First, let's write the balanced equation for the reaction:

\(H_2C_2O_4 + 2NaOH\) ⇒ \(Na_2C_2O_4\) + \(2H_2O\)

From the equation, we can see that one mole of oxalic acid (\(H_2C_2O_4\)) reacts with two moles of NaOH.

Therefore, the number of moles of NaOH used can be calculated using the formula:

moles of NaOH = molarity of NaOH x volume of NaOH (in liters)

= 0.2500 mol/L x 0.02500 L

= 0.00625 mol

Since the stoichiometry of the reaction is 1:1 between \(H_2C_2O_4\) and NaOH, we can conclude that the number of moles of oxalic acid used is also 0.00625 mol.

molarity = moles of solute / volume of solution (in liters)

The volume of the oxalic acid solution is given as 20.00 mL, which is equal to 0.02000 L.

molarity = 0.00625 mol / 0.02000 L

= 0.3125 M

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Sodium chloride is NaCl, and zinc chloride ZnCl₂. Why are there more chloride ions in the zinc compound?

Answers

Answer:

Zinc chloride (ZnCl2) has more chloride ions compared to sodium chloride (NaCl) because the zinc ion has a +2 charge, while the sodium ion has a +1 charge.

Chlorine (Cl) is a halogen element with a -1 charge when it gains an electron to form an ion. To form a neutral compound, the number of positive and negative charges must be balanced.

In NaCl, the sodium ion has a +1 charge and can only bond with one negatively charged chloride ion, which has a -1 charge. Therefore, the formula for sodium chloride is NaCl, with one sodium ion and one chloride ion.

In ZnCl2, the zinc ion has a +2 charge, and it requires two negatively charged chloride ions, each with a -1 charge, to form a neutral compound. Therefore, the formula for zinc chloride is ZnCl2, with one zinc ion and two chloride ions.

Thus, the reason why there are more chloride ions in the zinc compound is because the zinc ion has a higher charge compared to the sodium ion, and it requires two chloride ions to balance its charge, whereas sodium ion requires only one chloride ion.

Weather conditions (high or low temperature) to the mineral wool.

Answers

Answer:

high temperature

Explanation:

What do you think is the primary reason why the Unionid mussel population declined whenever there is a dramatic increase in the Zebra mussel population?

Answers

Answer:

When the Zebra arrived they ate all the food so the Unionid mussels declined as they died from the lack of food. Causing the Zebra Zebra numbers to increase and Unionid numbers to decline.

How many grams of CO 2 are present in a container with a volume of 5.61 L if the gas exhibits a pressure of 5.66 atm at a temperature of 311 K?

Answers

Answer:

54.72 g

Explanation:

Mass = ?

Volume = 5.61 L

Pressure = 5.66 atm

Temperature = 311 K

The relationship between these equations is given by the ideal gas equation;

PV = nRT

where R = gas constant = 0.0821 atm L K-1 mol-1

n = PV / RT

n = 5.66 * 5.61 / (0.0821 * 311 )

n = 1.2436 mol

Number of moles = Mass / Molar mass

Mass = Number of moles * Molar mass = 1.2436 * 44 = 54.72 g

a cup of hot tea has blank energy

Answers

Answer: thermal energy

Explanation: Thermal energy is what we call energy that comes from heat.

which would most likely cause a rise in sea levels

which would most likely cause a rise in sea levels

Answers

Answer:

B. melting of ice caps

Explanation:

the melting of polar ice caps

What is the empirical formula of these molecules? Down below. Show your work.

What is the empirical formula of these molecules? Down below. Show your work.

Answers

censures hydrogen Oxygen

Answer:

v

- A beam of electrons has.....
(A) Wave properties.
(B) Particle properties.
(C) Both of these
(D) Neither of these​

Answers

Answer:

(C) Both of these

Explanation:

A beam of electrons has both of these Wave properties and Particle properties.

write the fraction of the mass of kcl produced from 1 g of k2c03​

Answers

Mass of KCl= 1.08 g

Further explanation

Given

1 g of K₂CO₃

Required

Mass of KCl

Solution

Reaction

K₂CO₃ +2HCl ⇒ 2KCl +H₂O + CO₂

mol of K₂CO₃(MW=138 g/mol) :

= 1 g : 138 g/mol

= 0.00725

From the equation, mol ratio K₂CO₃ : KCl = 1 : 2, so mol KCl :

= 2/1 x mol K₂CO₃

= 2/1 x 0.00725

= 0.0145

Mass of KCl(MW=74.5 g/mol) :

= mol x MW

= 0.0145 x 74.5

= 1.08 g

Review the equation below.

2KClO3 Right arrow. 2KCl + 3O2

How many moles of oxygen are produced when 2 mol of potassium chlorate (KClO3) decompose?

Answers

2KClO3 --> 2KCl + 3O2

3 moles of oxygen are produced when 2 mol of potassium chlorate (KClO3) decompose.

Answer:

The answer is 3

Explanation:

I did the test on Edge

The temperature of a 95.4 g piece of copper decreases from 48°C to 25°C when the copper releases - 849 J of heat. What is the specific heat of copper?

Answers

This is my workings. Hope am correct
The temperature of a 95.4 g piece of copper decreases from 48C to 25C when the copper releases - 849

what type of weather does a warm front cause and why

Answers

Warm fronts often bring stormy weather as the warm air mass at the surface rises above the cool air mass, making clouds and storms.

Hope this helps!
Brainliest is much appreciated!

Which of the following best describes cis-trans isomers?
They differ in the arrangement of covalent bonds and in covalent partners.
They are long chains of hydrogen and carbon atoms.
They are mirror images of each other.
They have the same number of atoms of the same elements but different structures.
They differ in their spatial arrangement around inflexible double bonds

Answers

The correct answer is: They differ in their spatial arrangement around inflexible double bonds.

Cis-trans isomers are a type of stereoisomerism that arise from the inability of a double bond to rotate. They differ in the spatial arrangement of their substituents around the double bond, and can have different physical and chemical properties as a result. Cis-trans isomers have the same number and type of atoms, but differ in the orientation of their functional groups with respect to the double bond.

Cis-trans isomers are commonly found in organic molecules that contain double bonds, such as alkenes and some types of cyclic compounds. They are important in many biological processes, including the structure and function of cell membranes.

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When a hydrocarbon burns in air what component of air reacts?

Answers

Answer:

oxygen level reduces

Explanation:

because oxygen supports burning

in a color changing indicator solution, how do we find pKa given a pH range?

Answers

The pKa of a color changing indicator can be determined by measuring the pH at the point of color change. This is known as the end point of the titration.

What is titration?

Titration is a laboratory technique used to determine the concentration of a solution by adding a measured amount of one solute to another. It is a type of volumetric analysis which involves measuring the volume of the reactant (titrant) that is needed to completely react with the analyte (unknown concentration). This process is repeated until the endpoint is reached, which is when a chemical reaction occurs between the two solutions.

The endpoint of the titration is the point at which the indicator changes color, indicating that the pH of the solution has reached a certain value. This pH value is equal to the pKa of the indicator.

To find the pKa, one can measure the pH of the solution at various points during a titration and note the point at which the indicator changes color. The pH at the end point is equal to the pKa of the indicator.

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18. Electronegativity is the total negative charge of the electrons in an atom. T. O True F. O False​

Answers

Answer:

t

Explanation:

Answer:

Its false because electronegativity is affected by both the atomic radius and the distance at which its valence electrons reside from the charged nucleus

Explanation:

plz give me brainlyest thx

A 5-newton ball and a 10-newton ball are released simultaneously from a point 50 meters above the surface of the Earth. Neglecting air resistance, which statement is true?
At the end of 3 seconds of free-fall, the 10-N ball will have a greater momentum than the 5-N ball

Answers

The 10-newton ball will have a greater momentum than the 5-newton ball at the end of 3 seconds of free fall, since momentum is directly proportional to mass. The statement "At the end of 3 seconds of free-fall, the 10-N ball will have a greater momentum than the 5-N ball" is true.

In the absence of air resistance, both the 5-newton ball and the 10-newton ball will experience the same acceleration due to gravity, which is approximately 9.8 meters per second squared (m/s²) near the surface of the Earth. Therefore, the gravitational force acting on both balls will be proportional to their respective masses.

The mass of an object is directly related to its inertia and momentum. Since the 10-newton ball has a greater mass than the 5-newton ball, it will also have a greater momentum if their velocities are the same.

When both balls are released simultaneously from a point 50 meters above the Earth's surface, they will both experience the same downward acceleration. After 3 seconds of free fall, their velocities will be the same, as they have fallen for the same amount of time.

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If a soluble ionic solid is placed in water, what will happen? Select the correct answer below: ions will precipitate until Q = Ksp ions will precipitate until Q < KsP ions will dissolve until Q = Ksp
ions will dissolve until Q > Ksp

Answers

If a soluble ionic solid is placed in water, the correct answer is: ions will dissolve until Q = Ksp.

When an ionic solid dissolves in water, it breaks apart into its constituent ions. These ions become surrounded by water molecules, and the process continues until the solution reaches equilibrium, represented by Q = Ksp (solubility product constant). At this point, the rate of dissolution and precipitation of ions is equal, and the solution is considered saturated.

An ionic solid, also known as an ionic compound or salt, refers to a type of chemical compound composed of positively charged ions (cations) and negatively charged ions (anions) held together by strong electrostatic forces. These compounds typically consist of a metal cation and a non-metal anion.

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3. (05.02 MC)
What is the mass of a sample of NH3 containing 3.80 x 1024 molecules of NH3? (5 points)
74.8 grams
89.4 grams
101 grams
107 grams

Answers

Answer:

107 g

Explanation:

need to divide by avogadro’s number

The mass of a substance is a weight that can be given by the moles. In the sample 107.27 gms of ammonia is present. Thus, option D is correct.

What is mass?

Mass or the weight of the substance can be given by the molar mass and the moles of the substance.

We know,

6.02214076 × 10²³ molecules = 1 mole of NH₃

So, 3.80 x 10²⁴ molecules = 6.31 moles

If 1 mole = 17 gm ammonia

Then, 6.31 moles = 6.31 × 17 = 107 gms

Therefore, option D. 107 gms is the mass of ammonia.

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Which statement about the heliocentric theory is correct?

A. Heliocentric theory is a set of predictions describing the Sun as being the center of the solar system.

B. Heliocentric theory is a set of testable explanations describing the Sun as being the center of the solar system.

C. Heliocentric theory is a set of guesses describing the Sun as being the center of the solar system.

D. Heliocentric theory is a set of laws that describe the Sun as being the center of the solar system.

Please hurry I need this now T-T

Answers

I think it is A or B, (prob A) Because it is not a testable theory, and it is not a set of laws, it was just a theory of Copernicus.

In The Lord of the Rings, Frodo and Sam use a rope to rappel down a cliff. The rope was 30 ells long. How high was the cliff in meters if the rope reached the bottom?

Answers

Answer:

324 meters

Explanation:

I don't really have an explanation

What is an air pressure system?

Answers

Answer:

"The number of air molecules above a surface determines air pressure. As the number of molecules increases, they exert more pressure on a surface, and the total atmospheric pressure increases. By contrast, if the number of molecules decreases, so too does the air pressure."

What volume of water would you need to dissolve 72 grams of salt at 25 degrees Celsius? Please show work otherwise it doesn't count!!

Answers

You would need roughly 202 ml of water to dissolve 72 grams of salt at 25 degrees Celsius.

How do we solve for the volume of water need to dissolve salt at 25 degrees celsius?

The solubility of the compound, salt in water at 25 degrees Celsius is stated to be 357 grams per liter (g/L).

Then we can say that 357 grams of salt can be dissolved in 1 liter (1000 milliliters) of water.

To find out how much water you need to dissolve 72 grams of salt, solve the ratio as

357 g : 1000 mL = 72 g : x mL

Solving for x gives:

x = (72 g × 1000 mL) / 357 g

x = 201.681 mL

If we approximate this value it becomes 202ml

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Hydrogen Gas (H₂)

A. 2 atoms of oxygen
B. 2 atoms of hydrogen
C. 1 atom of hydrogen
D. 3 atoms of hydrogen

Answers

The answer is B 2 atoms of hydrogen

The rock shown below is in California's Death Valley
National Park.
Which phrase most likely describes the environment in which this rock
formed?

The rock shown below is in California's Death ValleyNational Park.Which phrase most likely describes

Answers

Answer:

The answer is high pressure

Explanation:

I took the quiz

use unit cancellation method to solve the following problems 51 mi/hr to km/hr

Answers

To use the unit cancellation method to solve this problem, we will need to know the conversion factor between miles per hour (mi/hr) and kilometers per hour (km/hr). This conversion factor is 1.60934 km/hr for every 1 mi/hr.

Now, we can set up our problem and use the unit cancellation method to solve the answer:

51 mi/hr * 1.60934 km/hr/1 mi/hr = 82.077 km/hr

To solve this problem, we started with the given speed in miles per hour (51 mi/hr). Then, we multiplied it by the conversion factor of 1.60934 km/hr for every 1 mi/hr. By setting up the units in the numerator and denominator to cancel out, we were left with the final answer of 82.077 km/hr.

In summary, using the unit cancellation method is a useful tool for converting units and solving problems. By setting up the units in a way that cancels out, we can easily and accurately convert between different units.

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In which of these statements are protons, electrons, and neutrons correctly compared?
Quarks are present in protons and neutrons but not in electrons.
Quarks are present in protons, neutrons, and electrons.
Quarks are present in neutrons and electrons but not in protons.
Quarks are present in protons and electrons but not in neutrons.

Answers

In the nucleus, proton and neutron are present. Electron has -1 charge while proton has +1 charge.  Neutron is neutral that is it has no charge. So overall the charge of nucleus is due to only proton, not by neutron. The correct option is option A.

What is atom?

Atom is the smallest particle of any element, molecule or compound. Atom can not be further divided. Atoms contains nucleus in its center and electron that revolve around the atom in fixed orbit.

Quarks are present in protons and neutrons but not in electrons. Quarks are sub-atomic particles that have mass, but not an integer of charge.

Therefore, the correct option is option A.

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omplete the nuclear equation describing the synthesis of mendelevium-256 by the bombardment of einsteinium-253 by α particles.

Answers

The complete nuclear equation is;

253/99 Es + 4/2He → 256/101 Md + 1/0n

What is nuclear reaction equation?

The atomic and mass numbers of the particles involved are displayed in a nuclear equation, which is a symbolic depiction of a nuclear process. It is used to explain the alterations that take place inside atomic nuclei during nuclear reactions, such as radioactive decay, fusion, and fission.

Typically, nuclear equations have two sides that are divided by an arrow. On the left side of the arrow are the reactants, or initial particles, and on the right side are the products, or final particles. The arrow denotes the process of transformation or reaction.

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If we increase the temperature of the vessel to 450 K at constant volume, what would the pressure inside the vessel be? a. 10 atm
b. 5 atm
c. 20 atm
d. 15 atm

Answers

The pressure inside the vessel would be 15 atm if we increased the temperature of the vessel to 450 K at constant volume. As a result, Option D is right.

According to the Ideal Gas Law, the pressure inside the vessel is directly proportional to the temperature (Kelvin) and the number of moles of gas present in the vessel, if the volume is kept constant. In other words, if we increase the temperature of the gas, the pressure inside the vessel will also increase.

The Ideal Gas Law equation is:

PV = nRT

Where:

P is the pressureV is the volumen is the number of molesR is the ideal gas constant (8.31 J/mol*K)T is the temperature in Kelvin

Given that V is constant, we can rearrange the equation to solve for P:

P = (nRT)/V.

Assuming that n and V are constants, then P is directly proportional to T. So, if the temperature increases by a factor of T2/T1, the pressure will increase by the same factor.

Let's say the initial pressure was 10 atm, and the initial temperature was 400 K. Then P1/T1 = 10 atm/400 K.

When the temperature is increased to 450 K, the pressure will become:

P2 = (P1 * T2)/T1 P2 = (10 atm * 450 K) / 400 K P2 = 15 atm

So, when the temperature of the vessel is increased to 450 K at constant volume, the pressure inside the vessel will increase, and the answer is "d. 15 atm".

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