The surface of the exit road is horizontal, not banked. (See figure.) If the static
friction between the tires and the surface of the road is us = 0.688 and the
maximum speed with which the car can exit the highway safely without sliding is
25.2 m/s, what is the radius of curvature of a highway exit, r?

Answers

Answer 1

The radius of curvature of the highway exit is approximately 220 km.

To find the radius of curvature of the highway exit, we can use the centripetal force equation:

F = mv^2 / r

where F is the maximum static friction force, m is the mass of the car, v is the maximum safe speed, and r is the radius of curvature.

We can solve for r by rearranging the equation:

r = mv^2 / F

Substituting the given values, we have:

r = (1000 kg)(25.2 m/s)^2 / (0.688)

r = 2.20 x 10^5 m

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Related Questions

The radioactive hydrogen isotope 3H is called tritium. It decays by beta-minus decay with a half-life of 12.3 years.
A. What is the daughter nucleus of tritium?
B. A watch uses the decay of tritium to energize its glowing dial. What fraction of the tritium remains 20 years after the watch was created?

Answers

Answer:

a) A Helium nucleus with two protons and one neutron

b) 0.324 of the original amount

Explanation:

a) When Tritium decays, the nucleus emits an electron and an antineutrino, which then changes it from a Triton with one proton and two neutrons, to a Helium nucleus with two protons and one neutron.

The decay constant for the decay of Tritium is gotten from

\(t_{1/2}\) = 0.693/k

where

\(t_{1/2}\) is the half life = 12.3 yrs

k is the decay constant = ?

substituting, we have

12.3 = 0.693/k

k = 0.693/12.3 = 0.0563

The fraction that will remain after 20 years can be calculated from

\(N\) = \(N_{0} e^{-kt}\)

where

\(N\) is the final remaining amount of Tritium after 20 years

\(N_{0}\) is the original amount of Tritium

k is the decay constant = 0.0563

t is the time = 20 years

Equation can be re-written as

\(N/N_{0}\) = \(e^{-kt}\)

where

\(N/N_{0}\) is the fraction of the tritium that will be remaining after 20 years.

substituting values, we have

\(N/N_{0}\) = \(e^{-0.0563 * 20}\)

\(N/N_{0}\)  =  \(e^{-1.126}\)

\(N/N_{0}\) = 0.324 of the original amount

A car slows down uninformly from a speed of 28.0m/s to rest in 8.00s.How far did it travel in that time?

Answers

Answer: 112 meters

Explanation:

Use the equation: d = vi+vf/2 x t which turned into: 28/2 times 8 = 112 meters

A 25 kg mass is hanging from two cables, each with their own tension. Cable 1 is connected to the
ceiling at a 52° angle below horizontal and cable 2 is connected perpendicular to the right wall.
The entire system is stationary.



a. Draw the FBD


b. Calculate Ty and T2.

Answers

Answer:

a. one line down one line to the right one live to the northwest from the object

b. t1=190 t2=310

Explanation:

While surfing the Internet, you encounter an article written by a foreign  blogger saying negative statements and malicious stories about Filipinos. Reading further,  you find at the comments section outraged replies from the Filipino community.  However, you also find citizens who affirmed the negative statements. Knowing that  everyone has the freedom to express his opinion, what do you think are the possible ways  to resolve the issue?While surfing the Internet, you encounter an article written by a foreign  blogger saying negative statements and malicious stories about Filipinos. Reading further,  you find at the comments section outraged replies from the Filipino community.  However, you also find citizens who affirmed the negative statements. Knowing that  everyone has the freedom to express his opinion, what do you think are the possible ways  to resolve the issue?


POSSIBLE SOLUTION 1: _______________________________________________________ _______________________________________________________________________ POSSIBLE SOLUTION 2: _______________________________________________________

__________________________________________________________________________ 
BEST SOLUTION: ____________________________________________________________ ________________________________________________________________________________________________________________________________________________


Answers

The ways to solve this problem is through knowledge dissemination, citizens who were outraged by the article about the negative statements and malicious stories about Filipinos, could submit positive articles about the culture of the Filipino people.

Another way could be through open dialogue, with Filipino internet users, publicly apologizing seeking to become more involved with the Filipino community.

Therefore, the best way to solve the problem is through ethically-based freedom of expression, avoiding stereotypes of a culture you don't belong to, and looking for a way to disseminate respectful and empathetic information about a people.

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The launching catapult of the aircraft carrier gives the jet fighter a constant acceleration of 59 m/s2 from rest relative to the flight deck and launches the aircraft in a distance of 97 m measured along the angled takeoff ramp. If the carrier is moving at a steady 26 knots (1 knot = 1.852 km/h), determine the magnitude v of the actual velocity of the fighter when it is launched.

Answers

Answer:

Explanation:

We shall find the final velocity of  aircraft with respect to aircraft carrier using the following relation.

v² = u² + 2as

v² = 0² + 2 x 59 x 97

v² = 11446

v = 107 m /s

velocity of aircraft carrier = 1.852 x 26 = 48.152 km/h

= 48.152 x 1000 / (60 x 60) m/s

= 13.37 m /s

This velocity of aircraft carrier will be added to the velocity of aircraft .

So absolute velocity of aircraft = 107 m /s + 13.37 m/s

= 120.37 m/s

Marus traveled on a motorcylce distance of 1,298meters north to get to the nearest shopping center. He then turned back south and rode another 1,250 meters to meet his friend. What was his displacement?

Answers

Answer:

48 meters north

Explanation:

If you measure the distance between the point Marus started and the point where they stopped after traveling 1,250 meters back south, you get 48 meters. To make this a displacement quantity, you add 'north' to the end and get 48 meters north, considering this was the initial direction of the motorcycle.

Approximately 20.0gm of milk at 6.0oC is added into a cup containing 270.0 gm of weak tea. The specific heat of weak tea is 3.91 x 103J kg-1 oC-1 and the final temperature of the milk - tea mixture is 85.0oC. Given the initial temperature of the weak tea is 90.0oC, what is the specific heat of milk?

Answers

Answer:

4161 J/kg·°C

Explanation:

We can use the principle of conservation of energy to solve this problem, which states that the total heat energy in a closed system is constant. The heat lost by the tea is equal to the heat gained by the milk.

Let's first calculate the heat lost by the tea:

Q(tea) = mcΔT

Q(tea) = (0.27 kg)(3910 J/kg·°C)(90.0°C - 85.0°C)

Q(tea) = 6555 J

where m is the mass of tea, c is the specific heat of tea, and ΔT is the change in temperature.

Next, let's calculate the heat gained by the milk:

Q(milk) = mcΔT

Q(milk) = (0.02 kg)(c)(85.0°C - 6.0°C)

Now we can equate the two expressions:

Q(tea) = Q(milk)

6555 J = (0.02 kg)(c)(79.0°C)

Solving for c, we get:

c = 4161 J/kg·°C

Therefore, the specific heat of milk is approximately 4161 J/kg·°C.

How are all paths that have a displacement of zero similar?

Answers

Answer:

Any situation that has a path that stops at the same position that it started from has a displacement of zero

Explanation:

hope it helps

The moon weighs 7x1022kg and we are about 380,000,000m away from the moon. If you weigh 50kg, how much gravitational force does the moon have on you? (G=6.7x10-¹¹)

Answers

The gravitational force that the moon has on a person with a mass of 50 kg is approximately 1.15 N.

The gravitational force between two objects depends on their masses and the distance between them. This force is given by the formula:

F = (G × m₁ × m₂) / r² where F is the gravitational force, m₁ and m₂ are the masses of the two objects, r is the distance between them, and G is the gravitational constant, which has a value of 6.7 × 10⁻¹¹ N m²/kg².

Using this formula, we can find the gravitational force that the moon has on a person with a mass of 50 kg.

The mass of the moon is 7 × 10²² kg, and the distance between the moon and the person is 380,000,000 m.

Therefore, we have:

m₁ = 50 kg

m₂ = 7 × 10²² kg

r = 380,000,000 m

G = 6.7 × 10⁻¹¹ N m²/kg²

Substituting these values into the formula, we get:

F = (G × m₁ × m₂) / r²

F = (6.7 × 10⁻¹¹ × 50 kg × 7 × 10²² kg) / (380,000,000 m)²

F = 1.15 N

Therefore, the gravitational force that the moon has on a person with a mass of 50 kg is approximately 1.15 N.

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PLEASE HELP!!!
Sophia says that if we add two electrons to oxygen in order to fill its valence shell, it’s expected charge would be +2. Is she correct? If not, explain the error in her thinking.

Answers

The error in her thinking is that oxygen has has six electrons and a negative charge is acquired by nitrogen when it gains two electrons.

Oxygen is a member of group 16. The elements in group 16 has six valence electrons. This means that they need an extra two electrons to complete their octet.

If an atom gains two electrons, it will have a charge of -2 and not +2, a positive charge means that the atom lost electrons. Nonmetals like oxygen do not loose electrons rather they gain electrons.

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Josh starts his sled at the top of a 3.5-m high hill that has a constant slope of 25∘
. After reaching the bottom, he slides across a horizontal patch of snow. The hill is frictionless, but the coefficient of kinetic friction between his sled and the snow is 0.08.

Answers

If the coefficient of kinetic friction between Josh's sled and the snow is 0.08, he slides 6.97 meter from the base of the hill.

To find how far from the base of the hill Josh's sled ends up, we need to first find the speed of the sled at the bottom of the hill using the conservation of energy principle,

mgh = (1/2)mv², plugging in the values given in the problem, we get,

m(9.81 m/s²)(3.5 m) = (1/2)mv²

Simplifying and solving for v, we get,

v = √(2gh)

v = √(2(9.81 m/s²)(3.5 m))

v = 8.29 m/s

Now we can use the kinematic equation,

d = vt - (1/2)at, to find how far the sled slides on the horizontal patch of snow before coming to a stop, where d is the distance traveled, v is the initial velocity (8.29 m/s), a is the acceleration due to friction (-μg), and t is the time it takes to come to a stop (which we can find by setting v = 0 and solving for t),

0 = 8.29 m/s - μg*t

t = 8.29 m/s / μg

Substituting this value of t back into the kinematic equation, we get,

d = (8.29)(8.29/μg) - (1/2)μg(8.29/μg)²

d = 6.97 m

Therefore, Josh's sled ends up 6.97 meters from the base of the hill.

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The gauge pressure in your car tires is 3.00 ✕ 10^5 N/m2 at a temperature of 35.0°C when you drive it onto a ship in Los Angeles to be sent to Alaska. What is their gauge pressure (in atm) later, when their temperature has dropped to

−42.0°C?

Assume the tires have not gained or lost any air.

Answers

Explanation:

Using the ideal gas equation, which I presume you are since you didn't specify using any other EOS, we have PV=nRT. Solving for what changes, i.e. pressure(P) and temperature(T), we have P/T=nR/V. Now, we can set up a relationship between the two pressures and temperatures and solve for what's necessary.

So, we have:

P1/T1=P2/T2

Solving for P2, we have:

P2=(P1*T2)/T1

NOTE: We MUST convert our temperatures to kelvin, otherwise you will end up with a NEGATIVE AND INCORRECT pressure!

Plugging in our values of P1=3.00x10^5 N/m^2, T1 of 308.15K, and T2 of 235.15K. Now we are free to evaluate:

P2=[(3.00x10*5 N/m^2)(235.15K)]/[308.15K]

P2=228930.7156 N/m^2

Or, to the appropriate amount of significant figures: 2.29x10^5 N/m^2

Which makes sense intuitively, as things tend to deflate slightly when the temperature drops!

Hope this helps!

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You move a 25 N object in 10s with 100 W of power.
How far did you move the object?

Answers

Answer:

Distance = 40 meters.

Explanation:

Given the following data;

Force = 25N

Time = 10 seconds

Power = 100 Watt

To find the distance;

First of all, we would determine the work done;

Workdone = power * time

Workdone = 100 * 10

Workdone = 1000 Nm

Next, we use the following formula to find the distance;

Workdone = force * distance

1000 = 25 * distance

Distance = 1000/25

Distance = 40 meters.

A Cadillac Escalade has a mass of 2,569.6 kg, if it accelerates at 4.65 m/s^2 what is the net force of the car?

Answers

Answer:

11948.64 Newtons

Explanation:

Compare and contrast microscopic and macroscopic energy transfer Give least three comparisons for each

Answers

Answer:

Differences

microscopic refers to substances visible to the naked eye

macroscopic are substances invisible to naked eye

Similarities

both refer to different scales that are useful to determining the size to different compounds.

Explanation:

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A person has a reasonable chance of surviving an automobile crash if the deceleration is no more than 30 "g's."Calculate the magnitude of the force on a 89-kg person accelerating at this rate.

Answers

The magnitude of the force on the 89 kg person who is decelerating at 30 m / s² is 272.44 N

According to Newton's second law of motion,

F = m a

m = W / g

F = Force

m = Mass

a = Acceleration

W = Weight

g = acceleration due to gravity

a = 30 m / s²

W = 89 kg  

F = 89 * 30 / 9.8

F = 272.44 N

According to Newton's second law of motion, Acceleration of an object is dependent upon the mass of the object and the net force acting on it.

Therefore, the magnitude of the force on the 89 kg person who is decelerating at 30 m / s² is 272.44 N

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1. What types of elements does an ionic bond occur between?

Answers

Answer:

Ionic bonds form when a nonmetal and a metal exchange electrons, while covalent bonds form when electrons are shared between two nonmetals. An ionic bond is a type of chemical bond formed through an electrostatic attraction between two oppositely charged ions.

Explanation:

16) A car's position in relation to time is plotted on the graph. What can be said about the car during segment B?
A) The car travels for 80 seconds during segment B.
B) The car has come to a stop
and has zero velocity.
C) The car is traveling faster during segment B than in segment C.
D) The car is traveling with a constant
velocity due to the flat line
of the graph.
0)

Answers

Answer:

B The car has come to a stop and has zero velocity

Explanation:

I just did the Question

What happens to the atomic number of an atom when the number of neutrons in the nucleus of that atom increases? a It decreases b It increases c It doubles d It remains the same

Answers

Answer:

It remains the same

Explanation:

It remains the same. This is because the number of protons doesn't change and the number of protons determines the atomic number.

whem completing an emergency Roaside stop,it is necessary to put on your parking brake
A. True
B. False​

Answers

Answer:

trueeeeeeee..........mmmm...........

Ellie is shooting a free throw. At the instant the ball leaves her hand the ball is traveling at a velocity of 9 m/sec, at an angle above the horizontal of 29.5 degrees. If you are standing beneath the basketball rim, videotaping, you can only see the vertical motion of the ball, since its horizontal motion is straight towards you. What is the magnitude of the ball's initial vertical velocity (if you measured it using your video data, in m/sec)

Answers

Answer:

Vy = 4.43 m/s

Explanation:

given data

velocity = 9 m/sec

angle horizontal = 29.5 degrees

solution

we get here ball initial vertical velocity will be here

Vy = v sinθ       ...........................1

put here value and we get

Vy = 9 × sin(29.5 )  

Vy = 4.43 m/s

what is the formula for finding the magnetic filed strength at a point due to a current-carrying wire​

Answers

Answer:

The strength of the magnetic field created by current is:

B=μ₀I / 2 π R

where I is the current

R is the shortest distance to the wire

The constant μ₀ is 4π * 10^-7 T * m / s

Explanation:

how is potential energy a scalar quantity even though it can be negative?

Answers

Explanation:

Potential energy is a scalar quantity because it has only magnitude and no direction. Its ability to be negative does not affect its scalar nature.

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A material that restricts the flow of electricity or thermal energy is a what

Answers

Answer: Insulator

Explanation:

An insulator is a material that restricts the flow of electricity or thermal energy.

Answer:

plastic or wood

Explanation:

Hi, can someone please help me with this report? It doesn't have to be like an essay, even two paragraphs is great. Please I really need help with this and really need it done. thank you so much!

The U.S. Army is planning to drop supplies from a plane at a refugee camp. The supplies are divided into 700-kilogram parcels, and the parachutes have an area of 100 square meters. The only problem is that the parcels cannot hit the ground at a velocity of more than 5 meters per second without damaging the contents. Are these parachutes suitable for this task?

For the purposes of this exercise, assume that the for the drag coefficient of the parachute is 1.5 and that the air density is 1.22 kilograms per cubic meter. Write a report detailing why these parachutes are or are not suitable and determining the minimum size parachute that can be used in this situation.

Answers

Answer:

Introduction:

In this report, we will examine whether the 100 square meter parachutes with a drag coefficient of 1.5 are suitable for dropping 700-kilogram parcels from a plane at a refugee camp. The main concern is that the parcels cannot hit the ground at a velocity of more than 5 meters per second without damaging the contents.

Calculation:

To determine whether the 100 square meter parachutes with a drag coefficient of 1.5 are suitable, we need to calculate the terminal velocity of the parcels. The terminal velocity is the maximum velocity that the parcels can reach when they are falling through the air. We can calculate the terminal velocity using the following equation:

Vt = sqrt((2mg)/(ρACd))

Where:

Vt is the terminal velocity

m is the mass of the parcel (700 kg)

g is the acceleration due to gravity (9.8 m/s^2)

ρ is the air density (1.22 kg/m^3)

A is the area of the parachute (100 m^2)

Cd is the drag coefficient (1.5)

Substituting these values into the equation, we get:

Vt = sqrt((2 x 700 x 9.8)/(1.22 x 100 x 1.5)) = 52.0 m/s

This means that without any parachute, the parcel would hit the ground with a velocity of 52 m/s. However, the parachutes are designed to provide air resistance, which will slow down the parcels.

To determine whether the parachutes are suitable, we need to calculate the velocity at which the parcels will hit the ground when they are attached to the parachutes. We can use the following equation to calculate the force of air resistance:

F = (1/2)ρAv^2Cd

Where:

F is the force of air resistance

ρ is the air density (1.22 kg/m^3)

A is the area of the parachute (100 m^2)

v is the velocity of the parcel

Cd is the drag coefficient (1.5)

When the force of air resistance is equal to the weight of the parcel, the parcel will stop accelerating and will reach its terminal velocity. Therefore, we can set the force of air resistance equal to the weight of the parcel:

F = mg

Substituting the values into the equation, we get:

(1/2)ρAv^2Cd = mg

Solving for v, we get:

v = sqrt((2mg)/(ρACd))

Substituting the values into the equation, we get:

v = sqrt((2 x 700 x 9.8)/(1.22 x 100 x 1.5)) = 25.9 m/s

This means that the velocity at which the parcels will hit the ground when they are attached to the parachutes is 25.9 m/s.

Conclusion:

Based on our calculation, the 100 square meter parachutes with a drag coefficient of 1.5 are suitable for dropping 700-kilogram parcels from a plane at a refugee camp. The velocity at which the parcels will hit the ground when they are attached to the parachutes is 25.9 m/s, which is below the maximum velocity of 5 m/s specified by the U.S. Army. However, if the mass of the parcels or the area of the parachutes changes, the velocity at which the parcels hit the ground will also change. Therefore, it is important to recalculate the velocity for different scenarios to ensure the safety of the parcels.

Explanation:

The U.S. Army is planning to drop 700-kilogram parcels of supplies to a refugee camp using parachutes with an area of 100 square meters. The objective is to prevent the parcels from hitting the ground at a velocity of more than 5 meters per second to avoid damage to the contents. To determine the suitability of these parachutes, we need to consider the drag coefficient and the air density.

Using the formula for air resistance, we can calculate the force acting on the parachute:

Force = 0.5 x Drag Coefficient x Air Density x Velocity^2 x Area

Assuming that the terminal velocity of the parcels is 5 meters per second, we can calculate the force acting on the parachute as follows:

Force = 0.5 x 1.5 x 1.22 x 5^2 x 100
= 1822.5 N

The weight of the parcels is 700 kg x 9.8 m/s^2 = 6860 N. Therefore, the force acting on the parachute is much less than the weight of the parcels, indicating that the parachutes are suitable for this task.

To determine the minimum size parachute that can be used in this situation, we need to calculate the maximum weight that can be supported by a parachute with an area of 100 square meters. This is known as the payload capacity of the parachute and can be calculated as follows:

Payload Capacity = Area x Drag Coefficient x Air Density x Velocity^2 / 2 x 9.8

Assuming that the maximum weight of the parcels that can be dropped is 700 kg, we can solve for the minimum size parachute as follows:

100 x 1.5 x 1.22 x 5^2 / (2 x 9.8) = 240.9 kg

Therefore, the minimum size parachute required for dropping 700-kilogram parcels at a velocity of less than 5 meters per second is approximately 241 square meters. In conclusion, the 100 square meter parachutes are suitable for this task, and a larger parachute would be required if the weight of the parcels increased.

If the x-component of vector A in the figure below is 3cm and the y component of A is 4cm, then what is the vector quantity of A?

Question 9 options:

25 cm - 37 degrees


7 cm - 37 degrees


7 cm - 53 degrees


5 cm - 53 degrees

Answers

Answer:

5 cm - 53 degrees

Explanation:

\( \sqrt{ {4}^{2} + {3}^{2} } = 5cm\)

\( \tan ^{ - 1} (4 \div 3) \) = 53°

Jodi made a list about electric current to help her study for a test.

1) Movement of electrons is continuous in a current.
2) Electrons move from areas of low to high electric potential.
3) Voltage causes current to flow.
4) Rate at which current flows is measured in amperes.

Which best describes Jodi’s error?

A) The movement of electrons is not always continuous.
B) Electrons move from areas of high to low electric potential.
C) Resistance causes current to flow.
D) The rate at which current flows is measured in ohms.

Answers

Answer: The answer is B; Electrons move from areas of high to low electric potential

Explanation:

I had this question on a quiz and got it correct.

The required Electrons move from areas of high to low electric potential best describes Jodi’s error. Option B is correct.

What is electric current?

Electric current is the flow of electric charge through a material. It is typically expressed in units of amperes (A), which represent the rate at which charge flows through a conductor.

Here,
Jodi's error is in statement 2. Electrons move from areas of high electric potential to areas of low electric potential, not from low to high electric potential. This is because electric potential is a measure of the energy per unit charge, so electrons will naturally flow from areas of higher potential to areas of lower potential to balance out the potential difference.

Thus, the required, Electrons move from areas of high to low electric potential best describes Jodi’s error. Option B is correct.

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2.27 A gas is compressed from V1= 0.3 m3, p1=1 bar to V2= 0.1 m3, p2 =3 bar. The pressure and
the volume are related linearly during the process. For the gas, find the
work, in kJ.
2.29 A gas expands from an initial state where p1=500kPa and V1=0.1m3 to a state
end where p2= 100 kPa. The relationship between pressure and volume during the process is
pV=constant. Schematize the process in a p-V diagram and determine the work, in
kJ.

Answers

Answer:

-40 kJ

80 kJ

Explanation:

Work is equal to the area under the pressure vs volume graph.

W = ∫ᵥ₁ᵛ² P dV

2.27) Pressure and volume are linearly related.  When we graph P vs V, the area under the line is a trapezoid.  So the work is:

W = ½ (P₁ + P₂) (V₂ − V₁)

W = ½ (100 kPa + 300 kPa) (0.1 m³ − 0.3 m³)

W = -40 kJ

2.29) Pressure and volume are inversely proportional:

pV = k

The initial pressure and volume are 500 kPa and 0.1 m³.  So the constant is:

(500) (0.1) = k

k = 50

The final pressure is 100 kPa.  So the final volume is:

(100) V = 50

V = 0.5

The work is therefore:

W = ∫ᵥ₁ᵛ² P dV

W = ∫₀₁⁰⁵ (50/V) dV

W = 50 ln(V) |₀₁⁰⁵

W = 50 (ln 0.5 − ln 0.1)

W ≈ 80 kJ

2.27 A gas is compressed from V1= 0.3 m3, p1=1 bar to V2= 0.1 m3, p2 =3 bar. The pressure andthe volume
2.27 A gas is compressed from V1= 0.3 m3, p1=1 bar to V2= 0.1 m3, p2 =3 bar. The pressure andthe volume

based on the information in the passage, which of these substances would be most likely to provoke a response similar to the barium dance

Answers

The substance that would be most likely to provoke a response similar to the barium dance is c. lead.

What is barium dance?

Barium dance is used to describe the movements of the body that can occur when a person is exposed to a high level of barium. Barium is a heavy metal that can be toxic in large amounts, and exposure can occur through ingestion, inhalation, or skin contact.

Other heavy metals such as lead, mercury, can also cause similar symptoms when a person is exposed to high levels. Additionally, exposure to certain chemicals such as pesticides, solvents, and industrial pollutants can also cause neurological symptoms similar to those seen in barium.

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When a person is exposed to high quantities of other heavy metals like lead, mercury, and cadmium, comparable symptoms can also be experienced. Furthermore, neurological symptoms resembling those of barium can also be brought on by exposure to specific substances including insecticides, solvents, and industrial pollutants.

It's critical to remember that any potential exposure to these drugs needs to be taken seriously, and if you think you may have been exposed, you should get medical help right once.

based on the information in the passage, which of these substances would be most likely to provoke a response similar to the barium dance

a. oxygen

b. nitrogen

c. lead

d. sulphur

A solid sphere, a solid disk, and a thin hoop are all released from rest at the top of the incline (h0 = 20.0 cm).

Required:
a. Without doing any calculations, decide which object would be spinning the fastest when it gets to the bottom. Explain.
b. Again, without doing any calculations, decide which object would get to the bottom first.
c. Assuming all objects are rolling without slipping, have a mass of 2.00 kg and a radius of 3.00 cm, find the rotational and translational speed at the bottom of the incline of any one of these three objects.

Answers

Answer:

a. The object with the smallest rotational inertia, the thin hoop

b. The object with the smallest rotational inertia, the thin hoop

c.  The rotational speed of the sphere is 55.8 rad/s and Its translational speed is 1.67 m/s

Explanation:

a. Without doing any calculations, decide which object would be spinning the fastest when it gets to the bottom. Explain.

Since the thin has the smallest rotational inertia. This is because, since kinetic energy of a rotating object K = 1/2Iω² where I = rotational inertia and ω = angular speed.

ω = √2K/I

ω ∝ 1/√I

since their kinetic energy is the same, so, the thin hoop which has the smallest rotational inertia spins fastest at the bottom.

b. Again, without doing any calculations, decide which object would get to the bottom first.

Since the acceleration of a rolling object a = gsinФ/(1 + I/MR²), and all three objects have the same kinetic energy, the object with the smallest rotational inertia has the largest acceleration.

This is because a ∝ 1/(1 + I/MR²) and the object with the smallest rotational inertia  has the smallest ratio for I/MR² and conversely small 1 + I/MR² and thus largest acceleration.

So, the object with the smallest rotational inertia gets to the bottom first.

c. Assuming all objects are rolling without slipping, have a mass of 2.00 kg and a radius of 3.00 cm, find the rotational and translational speed at the bottom of the incline of any one of these three objects.

We know the kinetic energy of a rolling object K = 1/2Iω²  + 1/2mv² where I = rotational inertia and ω = angular speed, m = mass and v = velocity of center of mass = rω where r = radius of object

The kinetic energy K = potential energy lost = mgh where h = 20.0 cm = 0.20 m and g = acceleration due to gravity = 9.8 m/s²

So, mgh =  1/2Iω²  + 1/2mv² =  1/2Iω²  + 1/2mr²ω²

Let I = moment of inertia of sphere = 2mr²/5 where r = radius of sphere = 3.00 cm = 0.03 m and m = mass of sphere = 2.00 kg

So, mgh = 1/2Iω²  + 1/2mr²ω²

mgh = 1/2(2mr²/5 )ω²  + 1/2mr²ω²

mgh = mr²ω²/5  + 1/2mr²ω²

mgh = 7mr²ω²/10

gh = 7r²ω²/10

ω² = 10gh/7r²

ω = √(10gh/7) ÷ r

substituting the values of the variables, we have

ω = √(10 × 9.8 m/s² × 0.20 m/7) ÷ 0.03 m

= 1.673 m/s ÷ 0.03 m

= 55.77 rad/s

≅ 55.8 rad/s

So, its rotational speed is 55.8 rad/s

Its translational speed v = rω

= 0.03 m × 55.8 rad/s

= 1.67 m/s

So, its rotational speed is of the sphere is 55.8 rad/s and Its translational speed is 1.67 m/s

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