A circular disk of moment of inertia [tex]I_t[/tex] is rotating in a horizontal plane, about its axis , with a constant angular speed [tex]\omega_i[/tex] . Another disc of moment of inertia [tex]I_b[/tex] is dropped coaxially onto the rotating disk. Initially the 2nd disc has 0 angular speed. Eventually both the disks rotate with a constant angular speed [tex]\omega_f[/tex] . The energy lost initially rotating disk to friction is ? ​

Answers

Answer 1

The kinetic energy of the circular disc in initial state is,

[tex]K^{1r} = \frac{1}{2}I^{t}ω^{ \frac{2}{i} } [/tex]

The initial kinetic energy of the other disc dropped on the first disc is,

[tex]K^{2r} = \frac{1}{2}I^{b}(0)^{2}[/tex]

[tex] = > K^{2r} = 0J[/tex]

As both the disc in the final state are moving with the same angular velocity, thus, the net kinetic energy in the final state is,

[tex]E^{f} = \frac{1}{2}(I^{t} + I^{b})ω^{ \frac{2}{f} }[/tex]

The net kinetic energy in the initial state is,

[tex]E^{i} = K^{1r} + K^{2r}[/tex]

[tex] = > E^{i} = \frac{1}{2} I^{t}ω^{ \frac{2}{i} } + 0[/tex]

[tex] = > E^{i} = \frac{1}{2} I^{t}ω^{ \frac{2}{i} }[/tex]

Thus, the change in the kinetic energy during the change of state is,

[tex]dE = E^{f} - E^{i}[/tex]

[tex] = > dE = \frac{1}{2} (I^{t} + I^{b})ω^{ \frac{2}{f} } - \frac{1}{2}I^{t}ω^{ \frac{2}{i} } [/tex]

[tex] = > dE = \frac{1}{2} I^{t}(ω^{ \frac{2}{f} } - ω^{ \frac{2}{i} }) + \frac{1}{2}I^{b}ω^{ \frac{2}{f} } [/tex]

This change in value of energy is the energy lost initially rotating the disk to friction.

Hence, the energy lost in the given case is [tex]dE = \frac{1}{2} I^{t}(ω^{ \frac{2}{f} } - ω^{ \frac{2}{i} }) + \frac{1}{2}I^{b}ω^{ \frac{2}{f} } [/tex]

Answer 2

The energy lost initially by the rotating disk to friction is equal to [tex]\frac{1}{2}I_t (\omega_f^2 - \omega_i^2)+\frac{1}{2} I_b\omega_f^2[/tex]

Given the following data:

Angular speed = 0

How to calculate the energy lost.

At the initial state, the kinetic energy of the circular disc is given by this formula:

[tex]K.E = \frac{1}{2} I_t\omega_i^2[/tex]

For the second disc, the initial kinetic energy is given by this formula:

[tex]K.E_2 = \frac{1}{2} I_b\omega_f^{2 }\\\\K.E_2 = \frac{1}{2} I_b(0)^{2 }\\\\K.E_2 = 0[/tex]

At the final state, the discs would move with the same angular velocity and the net kinetic energy is given by this formula:

[tex]E_f = \frac{1}{2} (I_t + I_b)\omega_f^2[/tex]

For the energy lost:

Also, the change in the kinetic energy is given by this formula:

[tex]\Delta E = E^f - E^i\\\\\Delta E = \frac{1}{2} (I_t + I_b)\omega_f^2 - \frac{1}{2} I_t\omega_i^2\\\\\Delta E = \frac{1}{2}I_t (\omega_f^2 - \omega_i^2)+\frac{1}{2} I_b\omega_f^2[/tex]

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Related Questions

if a certain star emits most intensely in the visible region of the spectrum, a cooler star would emit mostly in what part of the spectrum

Answers

A cooler star would emit mostly in infrared range of the spectrum.

Emission of high temperature stars

High temperature stars like the Sun, which are approximately 6000 K at the surface, emit most of their radiation at visible wavelengths.

Emission of the cooler stars

In stark contrast to high temperature stars, the cooler stars emit most of their radiations in the infrared (IR) range.

Thus, we can conclude that,  a cooler star would emit mostly in infrared range of the spectrum.

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A 15-kg cart filled with apples is sitting at the top of a bill that is 21 m high. The apples in the
your cart have a mass of 33 kg. What is the potential energy of the cart and the apples? Round your answer to the nearest tenth

Answers

Hi there!

Recall the equation for gravitational potential energy:

[tex]U = mgh[/tex]

U = GPE (J)
m = mass (48 kg)
g = acceleration due to gravity (9.8 m/s²)
h = height (21 m)

Plug in the givens and solve.

[tex]U = (15 + 33)(9.8)(21) = \boxed{9878.4 J}[/tex]

20 POINTS
What is an endothermic reaction?​

Answers

Answer:

An endothermic reaction is a chemical reaction in which more energy is needed to break bonds in the reactants than is released when new bonds form in the products.

A constant input of energy, often in the form of heat, is needed to keep an endothermic reaction going.

Explanation:

A would be the answer

Answer:

A reaction that contributes energy to the surroundings

Explanation:

When energy is taken in from the Surroundings, the temperature of the surroundings decreases


A large bag of feathers and a steel block balance each other on some scales.
What does this show about the masses and the weights of the bag of leathers and the stoel
block?

Answers

Answer:

they have an equal amount of weight between the two objects the steel block and the bag of feathers

I need help!!! :::///

Answers

Explanation:

amazing that you learned a lot of great ideas on your summary business you well from to and as learned that they can do well with their lives for you in the past few they will be a child whose mass is the best thing) )for

A 2035 kg Oldsmobile traveling east on Saginaw Street at 15.8 m/s is unable to stop on the ice covered intersection for a red light at Abbott Road. The car collides with a 4012 kg truck hauling animal feed north on Abbott at 10.5 m/s. The two vehicles remain locked together after the impact.

Required:
Calculate the velocity of the wreckage immediately after the impact.

Answers

The velocity of the wreckage immediately after the impact is mathematically given as

v=12.284m/s

The velocity of the wreckage

Question Parameters:

A 2035 kg Oldsmobile traveling east on Saginaw Street at 15.8 m/s is unable to stop on the ice covered intersection for a red light at Abbott Road.

The car collides with a 4012 kg truck hauling animal feed north on Abbott at 10.5 m/s

Generally the equation for the speed after collision   is mathematically given as

mu +MU = ( m + M) v

Therefore

v = ( 2035*15.8 + 4012*10.5 ) / ( 2035+ 4012)

v=12.284m/s

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Samir is watching waves hit a beach. He notices that as the waves get closer to the shore (where the water is shallow), they change direction. Which type of wave effect is he seeing?

Answers

Answer:

  refraction

Explanation:

When a wave crosses a boundary between media at an angle other than normal to the boundary, it will be refracted by an amount depending on the relative speeds of the wave in the different media.

The change in direction that Samir observes is due to refraction of the wave as it slows down in shallower water.

Light travels in waves. Which of the following statements about light waves is NOT true?

A. They travel i’m straight lines.
B. they can travel through any substance
C. They can come from natural or artificial sources.
D. They change direction when they are reflected or refracted

Answers

My answer would probably be I'd say D

The direction of light wave changes when they are reflected or refracted. So, all the statements are true.

What is meant by light wave ?

Light waves are defined as the electromagnetic waves made of smaller, energy carrying particles called photons.

Here,

Light is an electromagnetic radiation that can have the properties of both waves and particles.

Light waves can travel in straight lines in the transparent medium like air, glass, still water, etc.

Light waves can travel through any medium or substances.

Sources of light are of two types, natural source and artificial source.

Reflection and refraction are the two properties of light.

Reflection is the phenomenon exhibited by light through which a ray of light incident on a smooth, reflecting surface, gets bounced back. Thus, during reflection, the direction of the light ray changes.

Refraction is the phenomenon by which the the speed of the light decreases when light wave travels from a lighter medium to denser medium. The light wave will bend towards the normal line. Thus, during refraction, the direction of light wave changes.

Hence,

The direction of light wave changes when they are reflected or refracted. So, all the statements are true.

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An astronaut has a mass of 80kg. What is her weight on Earth?

Answers

Answer:

164

Explanation:

Calculate the Young's moduli for each of the trials shown, and then determine the average. What is the average Young's modulus, in units kN/m2? (Hint: The number should be on the order of 1000's of kN/m2.)

Answers

The term Young Modulus is used to describe the stress to strain of a material.  and is a measure of the strength of a material.

What is Young Modulus?

The term Young Modulus is used to describe the strength of a material. It is a ratio of the stress to strain of a material. The unit of Young Modulus is N/m2.

The question is incomplete hence the average Young's modulus, in units N/m2 can  not be computed. This value helps an engineer to make decision regarding the use of materials for construction.

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Which of the following statements about nutrition is true?
Complex carbs taste bland and digest slower than simple carbs.
Eating the right amount of dietary fiber promotes regular bowel movements and helps
prevent constipation.
You've got to eat enough protein so your body can grow, stay in shape, and repair itself.
all of these

Answers

Answer:

nobody knows

Explanation:

An answer will get you mark as brainliest! This question is in the attachments.

Answers

Answer: I am quite sure your answer here is D.

Explanation: It just seems like the only possible answer to me have a good day :D

There are some points on a standing wave that never move. What are these points called?.

Answers

Answer:

A common term is "nodes", also minimums.

Since temperature increases when the average kinetic energy of particles increases, what is happening to the added energy when the temperature remains constant while a substance is melting or boiling?.

Answers

Latent heat is the heat required to change the phase. When the temperature remains constant during melting or boiling the added energy is employed in the phase change process.

What is average kinetic energy?

The average kinetic energy (KE) is defined as the one-half of the mass of each gas molecule times multiplied by the square of RMS velocity.

[tex]KE = \frac{1}{2}m (V_{rms})^{2}[/tex]

where,

KE is the kinetic energy

m is the mass of each molecule

(V)rms is the RMS velocity

As we know since the temperature is increasing the average kinetic energy of the particle increases. So the added energy is utilized in the sensible heat due to which the temperature of the body increases resulting in the increase in average kinetic energy

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At which position would the electric force be greatest?
CI
The image shows the electric field lines around two
charged particles
O 1
02
1
2
O 3
O 4
3
*4
Helps pls

Answers

Explanation:

F = qE

where E is an electric field.

The denser lines of electric force are, the stronger electric field will be.

Since 4 is densest part, electric force on 4 is would be greatest.

The electric field would be stronger the denser the lines with electric force are. Since part 4 is the densest, its electric force would be greatest. Therefore, the correct option is option 4.

The force acting on the items is referred to as the electric force. When two electrons and two protons are put at equal distances, the electric force that separates them is equivalent to the electrostatic charge between the two.

The electric force primarily reliant on the quantity known as electric charge rather than the object's mass. Forces involving charges are the subject of electrostatics. Static refers to charges that aren't moving, or are moving very slowly. The electric field would be stronger the denser the lines with electric force are. Since part 4 is the densest, its electric force would be greatest.

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PLEASE HELP WILL MARK BRAINLIEST !! Which documentation is a car insurance company unlikely to ask for when a person is applying for coverage?

A. the type of car and when it was made

B. the number of accidents the driver had in the past

C. proof that the driver has life insurance

D. proof of how many miles the car has driven

Answers

Answer:

C, proof that the driver has life insurance.

Explanation:

SOME 1 HELP ME ASAP

Which 2 piece ls of data indicate that Jupiter resides in the outer region of the solar system?

1. It is primarily composed of hydrogen and helium.

2. It contains one natural satellite, The Moon.

3. It is hottest plant in the solar system.

4. It’s surface gases form into colorful bands.

5. It’s metal surface upon which one can stand.

Answers

Answer:

hydrogen and helium

Explanation:

From left to right, the outer planets are Jupiter, Saturn, Uranus, and Neptune. The gas giants are made up primarily of hydrogen and helium, the same elements that make up most of the Sun.

A skateboard chsnges velocity from 15 meters per second to 5 meters per second, over the course of 5 seconds. What is the skateboards acceleration?
A. -2 m/s^2
B. +2 m/s^2
C. +0.5 m/s^2
D. -0.5 m/s^2​

Answers

Option A) is correct.

We are given –

Initial velocity of skateboard is, u= 15m/sFinal velocity of skateboard is,v = 5 m/s Time taken, t = 5 secAcceleration, a =?

Formula To be used:-

[tex]\qquad[/tex] [tex]\star\: \: \pink{\boxed{\frak{ a = \dfrac{(v-u)}{t}}}}[/tex]

Where–

A = Acceleration v = Final velocity u = Initial velocity t = time

[tex]\qquad\qquad\quad\underline{\sf{Substituting \ Values \ :}}[/tex]

⠀⠀⠀━━━━━━━━━━━━━━━━━━━━━━━━━━

[tex]\qquad[/tex][tex] \bf \longrightarrow a = \dfrac{v-u}{t}[/tex]

[tex]\qquad[/tex][tex] \sf \longrightarrow a = \dfrac{5-15}{t}[/tex]

[tex]\qquad[/tex][tex] \sf \longrightarrow a = \dfrac{-10}{5}[/tex]

[tex]\qquad[/tex][tex] \sf \longrightarrow a = \cancel{\dfrac{-10}{5}}[/tex]

[tex]\qquad[/tex][tex]\pink{ \bf \longrightarrow a = -2 \:m/s^2}[/tex]

Henceforth, acceleration is -2 m/s².

Answer:

-2 m/s²

Explanation:

Here it's given that a skateboard changes its velocity from 15m/s to 5m/s in an interval of 5s . We are interested in finding out the acceleration of the skateboard. Firstly we know that,

The rate of change of velocity is called acceleration. Mathematically,

[tex]\qquad\rm\twoheadrightarrow accl^n =\dfrac{v - u }{t} [/tex]

Here ,

initial velocity = 15m/s final velocity = 5m/stime = 5s

On substituting the respective values, we have;

[tex]\qquad\rm\twoheadrightarrow accl^n =\dfrac{5m/s-15m/s}{5s}[/tex]

Simplify numerator,

[tex]\qquad\rm\twoheadrightarrow accl^n =\dfrac{-10m/s}{5s}[/tex]

Divide,

[tex]\qquad\rm\twoheadrightarrow \underline{\boxed{\blue{\rm acceleration= -2\ m/s^2}}} [/tex]

Therefore, Option A is correct choice.

which of these questions could best help you evaluate the advice from this website selling supplements?
A .does the author have a large following?
B. is the advice supported by empirical evidence?
C. is the advice easy to follow ?
D. how much do supplements cost?

Answers

The Answer to this question is Number B.

Answer :- B

A 50N crate is lifted 0.86m from the ground then is allowed to drop losing 15 J of energy. What is the new height of the crate?

Answers

We have that the new height of the crate  is mathematically given as

Hn=0.56

New height of the crate

Question Parameters:

A 50N crate is lifted 0.86m from the ground

then is allowed to drop losing 15 J of energy.

Generally the equation for the Potential energy  is mathematically given as

P.E=mgh

Where

m=50/9.8

Therefore

h=15/(50/9.8*9.8)

h=0.3m

New height

0.86-0.3

Hn=0.56

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What is Kinematics?
[tex] \\ [/tex]

Answers

[tex] \bf\dag \frak{Solution}[/tex]

Kinematics is the study of the motion of mechanical points, bodies and systems without consideration of their associated physical properties and the forces acting on them.

In simple words it's just Kinematics is the science of describing the motion. ^^

Kinematic is a branch of mechanics that deals with the study of the motion of a body without considering the force that causes it.

What is Kinematic?

Kinematic is the branch of Mechanics that deals with the study of the motion of a body, without regard to the force that causes the motion.

The following are the examples of kinematic

A moving trainsWater flowing in a riverA ball rolling on the floor etc

Kinematic and dynamics are the two branches of mechanics in physics.

Hence, Kinematic is a branch of mechanics that deals with the study of the motion of a body without considering the force that causes it.

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A 20 N force pulls to the right and friction pulls 5 N. If the mass is 5 kg, find the acceleration.

Answers

Answer

3ms^-2

_________

where does a roller coaster have kinetic and potential energy

Answers

At the top of the hill, the cars have a great deal of gravitational potential energy, equal to the cars' weight multiplied by the height of the hill. When the cars are released from the chain and begin coasting down the hill, potential energy transforms into kinetic energy until they reach the bottom of the hill.

A string exerts a force of 20 N on a box at an angle of 38° from the horizontal. What is the horizontal component of the force on the box?

Answers

Answer:

  15.8 N

Explanation:

The component in a given direction is the magnitude of the applied force, multiplied by the cosine of the angle between its application and the direction of interest.

The horizontal component is ...

  (20 N)cos(38°) ≈ 15.8 N

questions:

A string exerts a force of 20 N on a box at an angle of 38° from the horizontal. What is the horizontal component of the force on the box?

answer;

15.8 N

what is density
what is density​

Answers

Answer:

The density of a substance is the relationship between the mass of the substance and how much space it takes up

Explanation:

thats it  take my word hope thats what u meant

Density is a measure of mass per unit of volume. Density is a measure of mass per volume. The average density of an object equals its total mass divided by its total volume. An object made from a comparatively dense material (such as iron) will have less volume than an object of equal mass made from some less dense substance (such as water). Perhaps the highest density known is reached in neutron star matter. The singularity at the centre of a black hole, according to general relativity, does not have any volume, so its density is undefined.

in an atom is the number of protons greater, less than or equal to the number of electrons?

Answers

Answer:

The number of electrons and protons are always equal in a neutral atom. The total number of protons in the nucleus of an atom gives us the atomic number of that atom.

Explanation:

hope it will help you have a great day bye and Mark brainlist if the answer is correct

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Write an activity to differenciate between saturated and unsaturated solution

Answers

Answer:

I hope it will help you have a great day bye and Mark brainlist if the answer is correct

[tex]kai6417[/tex]

#carry on learning

During what phase of the moon is the moon up only during the night hours and all night long?.

Answers

Answer:

The Full Moon.

Explanation:

A full moon is made when the sun reflects off the moon's surface closest to us. this causes the moon to look bright at night, and dissapear during the morning.

If the three capacitors of values 1.0, 1.5, and 2.0 uF each are connected in series, what is the combined capacity

Answers

Answer:

Total capacitance of the three capacitors in series = 0.4615uF

Explanation:

Take the inverse of the three capacitors (in this case you are working with µF so 10^-6) and add their inverse.  The result is ~2.167*10^6.  The inverse of this number is 0.4615 so the total capacitance of this circuit is 0.4615µF.

PLEASE HELP NOW!! 51 POINTS!!
A rock rolls horizontally off of a 75m cliff. The rock lands 5.11m from the base of the cliff. Calculate the initial velocity of the rock.

Answers

Answer:

it will be 3 seconds

Explanation:

initial  horizontal velocity of the rock, u = 20 m/s

horizontal distance traveled by rock, R = 60 m

The the range of the projectile is given by;

R = vt

where;

v is the initial  horizontal velocity of the rock

t is the time spent by the rock in air

t = R/v

t = 60 / 20

t = 3 s

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