mas force enco 6. A large raindrop (2500 pm = 2.5 mm radius) is 100 times the radius of a typical cloud droplet (25 um). How many times greater is its volume?

Answers

Answer 1

Given data:

Radius of larger raindrop,

\(r_1=2.5\text{ mm}\)

Radius of typical cloud droplet,

\(r_2=25\text{ }\mu m\)

Since, r1=100r2. Therefore,

\(\frac{r_1}{r_2}=100\)

The volume is given as,

\(V=\frac{4}{3}\pi r^3\)

Therefore, the volume of the large raindrop is,

\(V_1=\frac{4}{3}\pi r^3_1\)

The volume of the typical cloud is,

\(V_2=\frac{4}{3}\pi r^3_2\)

Taking ratios of the volume,

\(\begin{gathered} \frac{V_1}{V_2}=\frac{\frac{4}{3}\pi r^3_1}{\frac{4}{3}\pi r^3_2} \\ =(\frac{r_1}{r_2})^3 \end{gathered}\)

Substituting all known values,

\(\begin{gathered} \frac{V_1}{V_2}=(100)^3 \\ =10^6 \end{gathered}\)

Therefore, the volume of the large raindrop equals 10^6 times the volume of a typical cloud droplet.


Related Questions

There is a current I flowing in a clockwise direction in a square loop of wire that is in the plane of the paper. If the magnetic field B is toward the right, and if each side of the loop has length L, then the net magnetic torque acting on the loop is:

Answers

Answer:

Explanation:

The magnetic moment of the coil  M = current x area of loop

= I x L x L

M = L² I .

Magnetic field = B

Torque = M x B

= MB sinθ where θ is angle between M and B . Direction of M is perpendicular to face of loop

Torque  = MB sin90

= MB

=  L² I B .

Please help

According to the seismograph recording of an earthquake shown above, we can conclude the following about this particular earthquake:

A.) The P-waves arrived at 24 min, the S- waves arrived at 27 min, the P-waves had a larger amplitude than the S- waves, and therefore the P- waves carried more energy than the S-waves.

B.) The P-waves arrived at 24 min, the S-waves arrived at 27 min, the S-waves had a larger amplitude than the P-waves, and therefore the S-waves carried more energy than the P-waves.

C.) The P-waves arrived at 9hrs 24min, the S-waves arrived at 9hrs 27 min, the P-waves had a larger amplitude than the S-waves, and therefore the P- waves carried less energy than the S-waves.

D.) The P-waves arrived at 9hrs 24min, the S-waves arrived at 9hrs 27min, the S-waves had a larger amplitude than the P-waves, and therefore the S-waves carried more energy than the P-waves.

Answers

Answer:

don't know ....?

Explanation:

Please help

According to the seismograph recording of an earthquake shown above, we can conclude the following about this particular earthquake:

A.) The P-waves arrived at 24 min, the S- waves arrived at 27 min, the P-waves had a larger amplitude than the S- waves, and therefore the P- waves carried more energy than the S-waves.

B.) The P-waves arrived at 24 min, the S-waves arrived at 27 min, the S-waves had a larger amplitude than the P-waves, and therefore the S-waves carried more energy than the P-waves.

C.) The P-waves arrived at 9hrs 24min, the S-waves arrived at 9hrs 27 min, the P-waves had a larger amplitude than the S-waves, and therefore the P- waves carried less energy than the S-waves.

D.) The P-waves arrived at 9hrs 24min, the S-waves arrived at 9hrs 27min, the S-waves had a larger amplitude than the P-waves, and therefore the S-waves carried more energy than the P-waves.

Kelli felt obligated to answer the phone when her mom called. She really was not paying attention to the conversation, but every once in awhile would say, "Yes" or "Okay" just to keep her mom satisfied.

This hurtful listening habit is called:

A. Defensive Listening
B. Selective Listening
C. Bad Listening
D. Pseudolistening

Answers

Although she wasn't truly listening to what was being said, she would occasionally say "Yeah" or "Okay" to appease her mother. This destructive listening behaviour is known as: Defensive listening, first

What constitutes a poor listening habit?

Interrupting, eavesdropping, being confrontational, egotistical, defensive, selective, insensitive, and pseudo-listening are some examples of these poor listening techniques.

A faux listener is what?

Pseudolistening– having to pretend to pay any attention and did appear considerate but is not trying to listen to realise or translate the data (audience members may answer back with a smile, mouth, or even a verbal cues appreciation but are dismissing or not planning to attend).

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assume that the brakes in your car create a constant deceleration if you double your driving speed how does this affect a0 the time required to come to a stop and b) the distance needed to stop?

Answers

For the moving car, if you double your driving speed;

a. the time required to come to a stop will increase by a factor of 2.

b. the distance needed to stop will increase by a factor of 2.

What is the formula relating acceleration, speed, time, and distance traveled?

The formula relating to the acceleration, speed, time, and distance traveled of an object is a formula of the equations of motion.

The equations of motion are given below as follows:

v = u + at

s = ut + ¹/₂at²

v² = u² + 2as

where:

v = final speed

u = initial speed

t = time taken

s = distance traveled

a = acceleration

Considering the given scenario:

a. if the speed is doubled, the equation v = u + at applies for the time required to come to a stop;

t =2 * v - u / t

the time will be increase.

b. if the speed is doubled, the equation v² = u² + 2as applies for the distance needed to stop;

s = 2 * v² - u²

the distance will increase with an increase in speed.

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*Question*
I am a thing, when you get hold of me I will be with you while while am in my natural environment. But when you take me from my environment I will leave you after a while. What am I ?

Answers

Answer:

A breath

Explanation:

When you are in your natural environment, you naturally breathe in the air around you. But if you were to take a breath of air and hold it in your lungs, eventually you would have to exhale and the breath would leave you. Similarly, if you were to be taken out of your natural environment (such as being underwater or in space), you would not be able to breathe and would eventually die without a source of oxygen.

If the time for F18 to take off doubles, the acceleration will ____.

Answers

Answer:

decreases

Explanation:

a=[v-u]/t

as time increases acceleration decreases and vice versa


A man runs 400.0m around the track,
then another 400.0m around the track again.
As the track is 400.Om long, the man is back
where he started!
a) calculate distance travelled

b) calculate mans displacement

Answers

Answer:

Distance = 800 m, Displacement = 0

Explanation:

It is given that,

A man runs 400 m around the track,  then another 400 m around the track again.

(a) Distance travelled by an object is the sum of total path covered.

In this case, he has covered total path of 400 m + 400 m i.e. 800 m. It means he travelled a distance of 800 m.

(b) Displacement covered by an object is the shortest path covered by it. In this problem, he reaches the point from where he has started. It means that his displacement is equal to 0.

50 POINTS ANSWEr CORRECT Explain how all the other elements heavier than iron are formed after the death of the star?

Answers

Answer:

Elements heavier than iron are formed by neutron capture processes during stellar death and supernovae.

Explanation:

Most of the elements heavier than iron are formed during the death of stars through neutron capture processes, specifically the R-Process and the S-Process. The R-Process is a rapid capture of neutrons, while the S-Process is a slow capture of neutrons. These processes either directly form elements or indirectly form them through decay processes [^1]. Elements heavier than iron are primarily made in environments with free-neutron densities in excess of a million particles per cubic centimeter [^2]. In the extreme energetic conditions of supernovae, atoms are bombarded by a very large number of neutrons, and rapid successive neutron capture, followed by beta decay, produces the heavier atoms [^5].

So, elements heavier than iron are formed by neutron capture processes during stellar death and supernovae.

[^1

If you stood on a planet having a mass four times higher than Earth's mass, and a radius two times 70) lon longer than Earth's radius, you would weigh:________
A) four times more than you do on Earth.
B) two times less than you do on Earth.
C) the same as you do on Earth
D) two times more than you do on Earth.

Answers

CHECK COMPLETE QUESTION BELOW

you stood on a planet having a mass four times that of earth mass and a radius two times of earth radius , you would weigh?

A) four times more than you do on Earth.

B) two times less than you do on Earth.

C) the same as you do on Earth

D) two times more than you do on Earth

Answer:

OPTION C is correct

The same as you do on Earth

Explanation :

According to law of gravitation :

F=GMm/R^2......(a)

F= mg.....(b)

M= mass of earth

m = mass of the person

R = radius of the earth

From law of motion

Put equation b into equation a

mg=GMm/R^2

g=GMm/R^2

g=GM/R^2

We know from question a planet having a mass four times that of earth mass and a radius two times of earth radius if we substitute we have

m= 4M

r=(2R)^2=4R^2

g= G4M/4R^2

Then, 4in the denominator will cancel out the numerator we have

g= GM/R^2

Therefore, g remain the same

If the suspended pith ball moves away from the approaching negativity charged polythene strip, what can you conclude about the charge on the pith ball? Given a reason.

Answers

If the suspended pith ball moves away from the approaching negatively charged polythene strip, then we can conclude that the pith ball is positively charged. The reason for this is that unlike charges attract each other and like charges repel each other. The negative charge on the polythene strip repels the negative charges in the pith ball, causing it to move away. This means that the pith ball has a positive charge that is being repelled by the negative charge on the polythene strip.

3. John thought of a number. After multiplying it by 3 (three) and then adding six, the [5marks] answer was 21. What number did he think of?​

Answers

The number John though of was 7.5.

What is expression modelling?

Expression modelling is the description of a mathematical problem using the mathematical expressions, done for the purpose of correct results and analysis and observation.

Expression modelling is done to remove uncertainty in mathematical results.

Given is that John thought of a number. After multiplying it by 3 and then adding six, the answer was 21.

Assume the number to be {x}.

We can write the modelled expression as the function of {x} as -

2x + 6 = 21

2x = 21 - 6

2x = 15

x = 7.5

Therefore, the number John though of was 7.5.

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Electron grops could be considered which of the following

Answers

Answer:

Electron groups could be considered as  Lone pair electrons and bonded pairs of electrons.

Answer: Option D & B

Explanation:

The two or more electrons can be bonded by single bond, double bond, covalent bond of electrons can simply be lone pair of electrons. Unshared pair of electrons are generally termed as lone pair of electrons in an atom which are generally present in the outermost shell of atoms. Hence electron groups can be determined by bonded pairs and lone pairs of electrons.

I got this from another brainly user

Carbon monoxide prevents
the breakdown of other chemicals in the liver
the blood from carrying oxygen to the tissues of the body
fuel from igniting at the wrong time
All choices are correct

(Answer quickly)

Carbon monoxide preventsthe breakdown of other chemicals in the liverthe blood from carrying oxygen to

Answers

Answer:

the blood from carrying oxygen to the tissues of the body

Explanation:

A8 kg ball is held at postam A before being rolled down the ramp below. Asume no energy is lost due to
Position
A
A-5m)
Position
B
(x-2m)
Position
C
As
h-5m
Kinetic Energy
B
h-2.5 m
Gravitational Potential Energy
C
h-0m
Total Energy

A8 kg ball is held at postam A before being rolled down the ramp below. Asume no energy is lost due toPositionAA-5m)PositionB(x-2m)PositionCAsh-5mKinetic

Answers

At position A, the ball has only potential energy due to its position above the ground.

The potential energy of the ball at position A is:

PE = mgh

where m is the mass of the ball, g is the acceleration due to gravity, and h is the height of the ball above the ground.

PE(A) = 8 kg * 9.8 m/s^2 * 5 m

PE(A) = 392 J

At position B, the ball has both kinetic and potential energy.

The potential energy of the ball at position B is:

PE = mgh

where m is the mass of the ball, g is the acceleration due to gravity, and h is the height of the ball above the ground.

PE(B) = 8 kg * 9.8 m/s^2 * 2.5 m

PE(B) = 196 J

The kinetic energy of the ball at position B is:

KE = (1/2)mv^2

where m is the mass of the ball and v is the velocity of the ball.

Since the ball is rolling down the ramp, we can use the conservation of energy principle to find the velocity of the ball at position B.

The total energy of the ball at position A is:

E(A) = PE(A)

E(A) = 392 J

The total energy of the ball at position B is:

E(B) = PE(B) + KE(B)

E(B) = 196 J + (1/2)(8 kg)v^2

E(B) = 196 J + 4v^2

Since energy is conserved, we have:

E(A) = E(B)

392 J = 196 J + 4v^2

196 J = 4v^2

v^2 = 49 m^2/s^2

v = 7 m/s

The kinetic energy of the ball at position B is:

KE(B) = (1/2)mv^2

KE(B) = (1/2)(8 kg)(7 m/s)^2

KE(B) = 196 J

At position C, the ball has only kinetic energy.

The potential energy of the ball at position C is zero since the ball is at ground level.

The kinetic energy of the ball at position C is:

KE(C) = (1/2)mv^2

KE(C

Water flows at a speed of 13 m/s through a pipe that has a diameter of 1.2 m. What is the
diameter of the smaller end of the pipe that the water comes out with a speed of 30 m/s?

Answers

The diameter of the smaller end of the pipe is approximately 0.78 meters.

To determine the diameter of the smaller end of the pipe, we can use the principle of conservation of mass. According to this principle, the mass flow rate of water should remain constant throughout the pipe.

The mass flow rate is given by the equation:
Mass flow rate = density of water * cross-sectional area * velocity

Since the density of the water remains constant, we can write:
Cross-sectional area1 * velocity1 = Cross-sectional area2 * velocity2

Given that the velocity1 is 13 m/s, the diameter1 is 1.2 m, and the velocity2 is 30 m/s, we can solve for the diameter2 using the equation:
(pi * (diameter1/2)^2) * velocity1 = (pi * (diameter2/2)^2) * velocity2

Simplifying the equation:
(1.2/2)^2 * 13 = (diameter2/2)^2 * 30

Calculating the equation:
(0.6)^2 * 13 = (diameter2/2)^2 * 30

0.36 * 13 = (diameter2/2)^2 * 30

4.68 = (diameter2/2)^2 * 30

Dividing both sides by 30:
0.156 = (diameter2/2)^2

Taking the square root of both sides:
0.39 = diameter2/2

Multiplying both sides by 2:
0.78 = diameter2

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How can one sperate particles of different velocities moving in a magnetic field? ​

Answers

Magnetic particle separation is a powerful tool for separating particles based on their velocities in a magnetic field, and it has significant practical applications in various scientific and technological fields.

To separate particles of different velocities moving in a magnetic field, one can utilize a technique called magnetic field separation or magnetic particle separation.

This method takes advantage of the fact that charged particles moving in a magnetic field experience a force called the Lorentz force, which acts perpendicular to both the velocity vector and the magnetic field.

The basic principle behind magnetic particle separation is to apply a magnetic field perpendicular to the motion of the particles. The Lorentz force will then cause the particles to curve in different directions based on their velocities and charges.

By carefully controlling the strength and direction of the magnetic field, particles with different velocities can be steered onto different paths and separated.

One common approach to achieve magnetic particle separation is to use a device called a magnetic separator. This device typically consists of a strong magnet or a series of magnets arranged to create a uniform magnetic field.

The particles to be separated are injected into a chamber or a flow system where the magnetic field is applied. As the particles move through the magnetic field, they experience the Lorentz force and deviate from their original trajectory. The degree of deviation depends on their velocity and charge.

By carefully adjusting the magnetic field strength, particle size, and other parameters, it is possible to optimize the separation process and achieve effective separation of particles with different velocities. This technique has various applications in fields such as biomedical research, environmental monitoring, and materials science.

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The January 1990 issue of Arizona Trend contains a supplement describing the 12 “best” golf courses in the state. The yardages (lengths) of these courses are as follows: 6981, 7099, 6930, 6992, 7518, 7100, 6935, 7518, 7013, 6800, 7041, and 6890. a/ Calculate the sample mean and sample standard deviation. b/ Find median.

Answers

The standard deviation of the sample means X, calculated earlier is the standard deviation of the population divided by the square root of the sample size.

Formula :

Mean : Mean = Sum of X values / N(Number of values)

We find mean=7068.08333

and standard deviation = 226.50003.

The standard deviation of the sample means known as the standard error of the mean is less than the population standard deviation and equal to the population standard deviation divided by the square root of the sample size. the sample mean is the average value found in the sample.

Samples are just a fraction of the total. For example, if you work for a polling company and want to know how much people spend on food each year, you don't need to survey over 300 million people. I also found that the sample mean is the arithmetic mean of all the values ​​in the sample. The sample variance measures how the data are distributed and the sample standard deviation is the square root of the variance.

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an alkyl group is named according to the number of c atoms it contains. an alkyl group with three carbon atoms joined in a straight chain is called a(n) group, whereas a methyl group has carbon atom(s).

Answers

An alkyl group is named according to the number of c atoms it contains. an alkyl group with three carbon atoms joined in a straight chain is called whereas a methyl group has one carbon atoms.

In organic chemistry, a carbonyl group is a divalent chemical compound made composed of two oxygen atoms (O) joined by a double bond. It is the distinctive functional group (reactive group) of aldehydes and ketones, and it is a component of carboxylic acids, esters, anhydrides, acyl halides, amides, and quinones. Together, carbonyl compounds include carboxylic acids (and their derivatives), aldehydes, ketones, and quinones. One of the most prevalent structural components of organic molecules is the methyl group, which is made up of three hydrogen atoms bound to a carbon atom, which is then connected to the rest of the molecule. In numerous chemical processes, the methyl radical, methyl cation, and methyl anion are temporary intermediates.

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A LETTER FROM THE LORAX
The lorax claimed to speak for the trees. Imagine you are the lorax writing an open letter to the
world on behalf of the trees. What would you say? Use supporting details and evidence from the
movie

Answers

Answer:

Explanation:

You could try to say how helpful they are what they are and what they do

Answer:

you could say how helpful they are and how they help you

Explanation:

hope this helps



URGENT HELP:

Two sine waves of equal frequency are to be compounded, (1) a1= 3.0 × 10–6 m and ϕ0 = 60° and (2) a2= 4.0 × 10–6 m and ϕ0 = 150°. (a) Calculate their resultant amplitude, (b) What is the resultant’s initial phase angle. (c) Draw a circle of reference and a time graph for the sine waves.

Answers

Answer:

Explanation:

To solve this problem, we can use the following equations for the addition of two sinusoidal waves:

y1 = A1 sin(ωt + φ1)

y2 = A2 sin(ωt + φ2)

where A1 and A2 are the amplitudes of the waves, ω is the angular frequency, t is time, and φ1 and φ2 are the initial phase angles.

(a) To find the resultant amplitude of the two waves, we can use the following equation:

Ar = √(A1^2 + A2^2 + 2A1A2cos(φ2 - φ1))

where Ar is the resultant amplitude.

Substituting the given values, we get:

Ar = √((3.0 × 10^(-6))^2 + (4.0 × 10^(-6))^2 + 2(3.0 × 10^(-6))(4.0 × 10^(-6))cos(150° - 60°))

Ar ≈ 5.03 × 10^(-6) m

Therefore, the resultant amplitude is approximately 5.03 × 10^(-6) m.

(b) To find the resultant's initial phase angle, we can use the following equation:

tan(φr) = (A1sin(φ1) + A2sin(φ2))/(A1cos(φ1) + A2cos(φ2))

where φr is the initial phase angle of the resultant wave.

Substituting the given values, we get:

tan(φr) = (3.0 × 10^(-6)sin(60°) + 4.0 × 10^(-6)sin(150°))/(3.0 × 10^(-6)cos(60°) + 4.0 × 10^(-6)cos(150°))

φr ≈ 142.85°

Therefore, the resultant's initial phase angle is approximately 142.85°.

(c) The circle of reference and the time graph for the sine waves can be drawn as follows:

Sine Waves

The blue and red arrows represent the maximum displacement of the waves. The black arrow represents the displacement of the resultant wave. The time graph shows the displacement of each wave and the resultant wave over time.

which best describes the runners

A. Danielle had a 5 minute Head Start in lonardo caught up to her at 25 meters

B. Danielle ran faster than Leonardo through the entire race

C. Danielle gave Leonardo a 5-meter head start and caught up to him at 25 Meters

D. Danielle ran slower than the Nardo but she went faster the end ​

which best describes the runners A. Danielle had a 5 minute Head Start in lonardo caught up to her at

Answers

Answer:

The answer is

Explanation:

A.

Daniela had a 5 meter head start, and Leonard caught up to her at 25 meters.

brainiest would be cool

What is the mass (in kg) of a Puffin flying 10 m/s with 1000 J of KE?

Answers

Answer:

20 kg

Explanation:

The kinetic energy (KE) of an object is given by:

KE = (1/2) * m * v^2

Where m is the mass of the object, and v is its velocity.

We can rearrange this formula to solve for the mass:

m = 2 * KE / v^2

Plugging in the values given:

m = 2 * 1000 J / (10 m/s)^2

m = 20 kg

Therefore, the mass of the Puffin flying at 10 m/s with 1000 J of KE is 20 kg.

which situation best represents a closed environment?

two balls colliding on a pool table

two balls colliding in midair

two balls colliding in deep space

two balls colliding under water ​

Answers

Answer:

deep space ✔️✔️✔️✔️✔️✔️✔️✔️✔️✔️✔️✔️✔️✔️✔️✔️✔️✔️✔️✔️✔️

Given the information in the velocity vs. time graph, what is the displacement of the object after 1 second?


_____ m


After 3 seconds?


_____ m


After 5 seconds?


_____ m


Thank you!!!

Given the information in the velocity vs. time graph, what is the displacement of the object after 1

Answers

The displacement of the object after 1 second, is 3 m.

The displacement of the object after 3 seconds, is 9 m.

The displacement of the object after 5 seconds, is 15 m.

What is displacement?

The displacement of an object is the change in the position of the object.

displacement of the object after 1 second

The displacement of the object after 1 second, x = 3 m/s x 1 second = 3 m

displacement of the object after 3 second

The displacement of the object after 1 second, x = 3 m/s x 3 s = 9 m

displacement of the object after 5 second

The displacement of the object after 1 second, x = 3 m/s x 5 s = 15 m

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What is the relationship between the surface area of a parachute and the amount of air resistance it builds up when it is deployed by a sky diver?

Answers

Answer:

An open parachute increases the cross-sectional area of the falling skydiver and thus increases the amount of air resistance which he encounters. Once the parachute is opened, the air resistance overwhelms the downward force of gravity.

Explanation:

The larger a parachute, the greater the force.

Hope it helps you in a little way.

if i got rolled over and then survided and then i would go home then i died what happened

Answers

Answer:

you had probably died from the impact

Explanation:

because you got rolled over you would probably died due to your organs being damage and wouldn't function properly

A roller-coaster car has a mass of 1240 kg when fully loaded with passengers. As the car passes over the top of a circular hill of radius 22 m, its speed is not changing. (a) At the top of the hill, what is the normal force (using the negative sign for the downward direction) FN on the car from the track if the car's speed is v = 8.7 m/s? (b) What is FN if v = 20 m/s? Use g=9.81 m/s2.

Answers

Answer:

a)      N = 7.90 10³ N,  b) N = -1.04 10⁴ N

Explanation:

a) For this exercise we can use Newton's second law

             N -W = m (-a)

The relationship is centripetal, the negative sign of the acceleration is because it points towards the center of the circle

              a = v² / r

we substitute

             N = mg -m v² /r  

             N = m (g - v² /r)

let's calculate

v = 8.7 m / s

             N = 1240 (9.81 - 8.7²/22)

             N = 7.90 10³ N

b) v = 20 m / s

             N = 1240 (9.81 - 20²/22)

             N = -1.04 10⁴ N

A man walks his dog on a very straight path in a park. He can walk back and forth as slow or fast as he wants to, but he has to stay on the path. Which of the following statements is correct for an arbitrary time interval?

a. His average speed can be greater than the magnitude of his average velocity.
b. His average speed can be less than the magnitude of his average velocity.
c. Since he is walking along a straight path, his average acceleration must be zero.
d. His average velocity must be zero.

Answers

Answer:

a. His average speed can be greater than the magnitude of his average velocity.

Explanation:

As speed is distance traveled over time traveled, this is always greater than zero if he has moved at all.

velocity is displacement over time traveled. As the man is allowed to return to the point of origin, his velocity at some point might be zero while his speed is positive.

Submit your report about how the eye functions. Remember to proofread your work before submitting.

Answers


Fragmento destacado de la Web
When light hits the retina (a light-sensitive layer of tissue at the back of the eye), special cells called photoreceptors turn the light into electrical signals. These electrical signals travel from the retina through the optic nerve to the brain. Then the brain turns the signals into the images you see.

Masses m and 2m are joined by a light inextensible string which runs without slipping over a uniform circular pulley of mass 2m and radius a. Using the angular position of the pulley as generalized coordinate, write down the Lagrangian function and Lagrange's equation. Find the acceleration of the masses.​

Masses m and 2m are joined by a light inextensible string which runs without slipping over a uniform

Answers

Answer:   the acceleration of the masses is given by = 0, which means the angular acceleration of the pulley is zero. This implies that the masses m and 2m move with constant velocity,  they are in equilibrium.

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