When a liquid is cooled, the kinetic energy of the particles
. The force of attraction between the particles
, the space between the particles

Answers

Answer 1

When a liquid is cooled, the kinetic energy of the particles decreases. The force of attraction between the particles increases, the space between the particles decreases and the matter changes its state to solid.

What is kinetic energy?

Kinetic energy can simply be defined as the energy a body possessed due to its relative motion.

So therefore, when a liquid is cooled, the kinetic energy of the particles decreases. The force of attraction between the particles increases, the space between the particles decreases and the matter changes its state to solid..

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Related Questions

which sustainable practice is paired correctly with its impact on the environment.

Answers

Answer:

Answer: Creating more wind farms results in a reduction of fossil fuel use

Explanation:

Economical improvement is to make earth a superior spot for everybody, without wrecking the opportunities for the following ages. There are numerous Eco frameworks that should be in equilibrium for us to live here, the atmosphere framework is one of them. This framework guarantees that the atmosphere is right and the air transmits the perfect measure of sunlight based energy. With the destructive nurseries gases, (for example, Carbon dioxide) we stop up the air, this progressions the temperature of the earth that can influence our turn of events  

How we use energy is extraordinarily significant. Oil and coal are tests of energy that we may run out of, utilizing energy that restore themselves (wind ranches) is useful for the planet. Wind, water and sun are maintainable.

Hope this Helps (✿◡‿◡)

Answer:

Answer: D.Creating more wind farms results in a reduction of fossil fuel use

Explanation:

a powerful motorcycle can produce an acceleration of 4.3 m/s2 while traveling at 90.0 km/h. at that speed the forces resisting motion, including friction and air resistance, total 400 n. (air resistance is analogous to air friction. it always opposes the motion of an object.) what is the magnitude of the force, in newtons, that the motorcycle exerts backward on the ground to produce its acceleration if the mass of the motorcycle with rider is 228 kg?

Answers

The acceleration force that the motorcycle would exert is 1381.6 N.

We can start by converting the speed of the motorcycle from km/ h to m/ s   km/ h =  25 m/ s  

Next, we can calculate the force of air resistance and  disunion( R) acting on the motorcycle  

R =  400 N  

We can now use Newton's alternate law to calculate the force( F) that the motorcycle exerts backward on the ground to produce its acceleration  

F =  ma  

where m is the mass of the motorcycle with rider,

which is given as 228 kg,

and a is the acceleration,

which is given as4.3 m/ s2.  

Substituting the values, we get  

F = ( 228 kg)(4.3 m/ s2) 400 N  

F = 981.6 N 400 N  

F = 1381.6 N

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Explain why the student should open the switch after each
reading. ​

Answers

Answer:

Maybe to get different readings

Find the minimum initial height hmin at which the car can be released that still allows the car to stay in contact with the track at the top of the loop. Express your answer numerically, in meters. View Available Hint(s)

Answers

Minimum initial height for car to stay in contact with loop: 25m, found using conservation of energy and centripetal force.

To find the base beginning level, we can utilize the preservation of energy rule. At the highest point of the circle, the vehicle's potential energy is switched over completely to dynamic energy, and this motor energy is adequate to keep the vehicle in touch with the track.

The base introductory level happens when all the potential energy is changed over into dynamic energy at the highest point of the circle.Utilizing the protection of energy guideline, we have:

\(mgh = (1/2)mv^2 + mg(2r)\)

Where m is the mass of the vehicle, h is the underlying level, v is the speed of the vehicle at the highest point of the circle, g is the speed increase because of gravity, and r is the span of the circle.At the highest point of the circle, the ordinary power gives the centripetal power expected to keep the vehicle in touch with the track, so we have:

\(N = mg + (mv^2)/r\)

Setting N = 0 (least level), we get:

hmin = 5r/2

Subbing r = 10 m, we get:

hmin = 25 m.

Consequently, the base starting level at which the vehicle can be delivered is 25 meters.

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Can anyone please help

Can anyone please help

Answers

a) The motion of the object between 15 s to 30 s is increasing velocity, to a constant velocity and finally a decreasing velocity.

(b) The average velocity of the object between 0 and 15 seconds is 0.167 m/s.

(c) The position of the object at 5.0 seconds is 0.5 m.

(d) Between 30 and 40 seconds, the velocity of the object is decreasing and the object is decelerating.

What is the motion of the object?

(a) The motion of the object between 15 s to 30 s can be described as increasing velocity, to a constant velocity and finally a decreasing velocity.

(b) The average velocity of the object between 0 and 15 seconds is calculated as;

average velocity = total displacement / total time

average velocity = (2.5 m - 0 m ) / ( 15 s - 0 s ) = 0.167 m/s

(c) The position of the object at 5.0 seconds is calculated as follows;

at 5.0 seconds, the position of the object is traced from the graph as 0.5 m.

(d) The motion of the object between 30 and 40 seconds is calculated as;

velocity = ( 0 m - 4 m ) / ( 40 s - 30 s ) = - 0.4 m/s

Between 30 and 40 seconds, the velocity of the object is decreasing and the object is decelerating.

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A car weighing 12,000 N is parked on a 36° slope.

A) Find the force tending to cause the car to roll down the hill.

B) Find the acceleration of the car rolling down the hill.

Answers

Answer:

A resultant is the sum of two (or more) vectors.

2. To add vectors, place the vectors such that the tail of the second vector is placed

at the head of the first vector. Draw a resultant vector from the tail of the first

vector to the head of the second vector. Using the Pythagorean theorem,

calculate the magnitude of the resultant vector. Use geometry or a protractor to

determine the angle of direction of the resultant vector.

Explanation:

Can some smart person help me out here!!!!!!!

Can some smart person help me out here!!!!!!!

Answers

Answer:

B

Explanation:

when you put it on a smooth surface and they're both at the same level it'll determine which one is faster and which one has less Mass. hope this helps much love .

There are no smart people available at the moment, but I'll try and help you.

Do the SECOND choice on the list. Keep the forces of the push on both blocks exactly equal. The block that jumps out ahead has less mass. The block that lags behind has more mass.

Which type of thermal energy transfer does a wrapping of cotton or plastic reduce the most? O A. Radiation O B. Conduction O C. Convection O D. Translation​

Answers

Answer: Translation

Explanation:

Apex

Thanks

Answer:

RADIATION

Explanation:

JUST TOOK IT ON APEX

what is the relationship between magnets and emf

Answers

Answer:

Movement of a magnet relative to a coil produces emfs as shown. The same emfs are produced if the coil is moved relative to the magnet. The greater the speed, the greater the magnitude of the emf, and the emf is zero when there is no motion.

Hope this helps!

two point charges exert a 8.05 n force on each other. what will the force become if the distance between them is increased by a factor of 2?

Answers

When the distance between two point charges is increased by a factor of 2, the force they exert on each other decreases to 1/4 of the original force. The relation is governed by the Coulomb's Law.

According to Coulomb's Law, the force between two point charges is directly proportional to the product of their charges and inversely proportional to the square of the distance between them. In this scenario, if the distance between the charges is increased by a factor of 2, it means that the new distance is twice the original distance.

Since the force is inversely proportional to the square of the distance, doubling the distance will result in the force becoming 1/4 of the original force. Mathematically, this can be represented as follows:

\(F' = F / (2^2)\)

\(F' = F / 4\)

Therefore, the force between the two charges will become 1/4 (or 25%) of the original force when the distance between them is increased by a factor of 2.

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what mass (in g) does 3.99 moles of kr have? a) 334 g b) 476 g c) 211 g d) 240 g e) 144 g

Answers

The mass of 3.99 moles of kr is 334 g. So, the correct option is option a) 334 g.

To determine the mass (in g) of 3.99 moles of Kr, we can use the molar mass of Kr and the given moles. Here's a step-by-step explanation:

To find the mass of 3.99 moles of Kr, we can use the following formula:

mass = moles x molar mass
1. Find the molar mass of Kr. The molar mass of krypton (Kr) is approximately 83.8 g/mol.
2. Multiply the given moles by the molar mass. Mass = moles × molar mass

Mass = 3.99 moles × 83.8 g/mol ≈ 334.4 g

The mass of 3.99 moles of Kr is approximately 334 g, so the correct answer is 334 g.

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12 A car travels in a straight line at speed v along a horizontal road. The car moves
against a resistive force F given by the equation
F = 400+kv²
where F is in newtons, v in ms-1 and k is a constant.
At speed v = 15ms-1, the resistive force F is 1100 N.
a
Calculate, for this car:
i the power necessary to maintain the speed of 15ms-¹,
ii the total resistive force at a speed of 30 ms-¹,
iii the power required to maintain the speed of 30ms-¹.

Answers

Answer:

i) Power = Force * Velocity = 1100 * 15 = 16500 W = 16.5 kW(ii)  Find the value of k first: F = 400 + k(15^2)                                              k = 28/9    F = 400 +(28/9)(30^2) = 320

Explanation:

a. The power necessary to maintain the speed of 15ms^-1 can be found using the equation for power, P = Force * velocity, where P is in watts, force is in newtons and velocity is in meters per second. Substituting the values given in the question, we get:

P = (400 + k * 15²) * 15
P = (400 + 11250) * 15
P = 11650 Watts

Therefore, the power necessary to maintain the speed of 15ms^-1 is approximately 11650 Watts.

b. The total resistive force at a speed of 30ms^-1 can be found by substituting 30 for v in the force equation:

F = 400 + k * 30^2

F = 12000 N

Therefore, the total resistive force at a speed of 30ms^-1 is approximately 12000 N.

c. The power required to maintain the speed of 30ms^-1 can be found using the same equation as in part a:

P = (400 + k * 30^2) * 30
P = (1500 + 600000) * 30
P = 625000000 Watts

Therefore, the power required to maintain the speed of 30ms^-1 is approximately 625000000 Watts. This is a very large amount of power and would require a significant amount of energy to maintain.

Question 25
2.5 pts
Which of the following statements describes a difference
between a chemical change and a physical change in a
substance?
Tim
Attei
231
o The result of a chemical change is a different
composition; in a physical change, the composition
remains the same.
o A physical change occurs only in elements: a
chemical change occurs only in compounds.
O A chemical change occurs only in elements; a
physical change occurs only in compounds.
The result of a physical change is a different

Answers

Answer:

o The result of a chemical change is a different  composition; in a physical change, the composition  remains the same.

Explanation:

In a chemical change, new kinds of matter are produced although the atoms are the same.

For physical changes, no new kinds of matter formed. Only the state of substances changes.

Most chemical changes are usually irreversible Physical changes are reversible in most parts. Changes in state and form are salient characteristics of physical changes. When new products are formed from the reactants, it is an indicator of a chemical change.

A painter accidentally drops a can of paint from a bridge over a river. The can acceleration at 9.81 ms-2 for a time of 2.3 s before it hits the water below.

a. Calculate the velocity of the can just before it hits the water.


b. What is the height of the bridge?

using the laws of motion ​

Answers

(a) By equation of motion, the velocity of the can just before it hits the water is 22.563 m/s.

(b) The height of the bridge is 25.95 meters.

Accidentally, a painter drops a paint can from a bridge over a river.

For a time t = 2.3 seconds the acceleration is 9.81 m/s².

Initially, the paint can was on rest.

So, the initial velocity is u = 0 m/s.

Using the equation of motion,

v = u + at

Substituting the values,

v = 0 + 9.81 × 2.3

v = 22.563 m/s

(b) Using the second equation of motion,

The height of the bridge is:

s = ut + ( 1/2 )at²

s = 0 × 2.3 + ( 1/2 ) × 9.81 × ( 2.3 )²

s = ( 1/2 ) × 9.81 × 2.3 × 2.3

s = 51.8949 / 2

s = 25.95 m

The final velocity of the can is 22.56 m/s and the height of the bridge is 25.95 meters.

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Khaled said the North star is special because it appears all over the world and its changes position.
a. false
b.true

Answers

False the North Star never changes it position

You need to exercise your body in the same what that you are going to use it.

Answers

Answer:

mjm

Explanation:

What happens to most bones when we break theAlways include the steps and/or background required to get to the final answer. Let’s help other people understand and solve future problems on their own.

an energy bar increases running speed by 2 seconds. an energy drink increases running speed by 3 seconds. however, when both are consumed, running speed increases by 9 seconds. this is an example of

Answers

An energy bar increases running speed by 2 seconds. an energy drink increases running speed by 3 seconds. however, when both are consumed, running speed increases by 9 seconds. this is an example of synergistic effect.

What is Synergistic effect?

Synergistic effect occurs when two or more substances interact to produce a combined effect that is greater than the sum of their individual effects. In this case, consuming both the energy bar and the energy drink leads to an increase in running speed by 9 seconds, which is greater than the sum of the individual effects (2 seconds from the energy bar and 3 seconds from the energy drink). This is an example of how the combination of two substances can have a greater impact than either substance alone.

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You are gardening in the peak of summer, it hasn't rained in a week, and your plants are looking rough. You decide to water the plants for an hour. The next day you come back to the garden, and the plants look in worse shape than they did previously, as if none of that water made it to the plant. With what you know from class, please try and explain what is happening to your plants.

Answers

In the peak of summer, it hasn't rained in a week, and the plants are looking rough, so watering the plants for an hour is a good idea.

However, the next day, you come back to the garden, and the plants look in worse shape than they did previously, as if none of that water made it to the plant. Plants absorb water through their roots. The root system of a plant is responsible for drawing water and nutrients from the soil. A plant's root system must be able to absorb water quickly in order for the plant to grow and thrive. When the soil around the root system is dry, the roots will stop growing and will not be able to absorb water.

It may even start to die. Watering plants during the peak of summer is important because it will help keep the soil moist and prevent the roots from drying out. However, watering a plant too much can be harmful. If a plant is overwatered, the water may not be able to penetrate the soil and reach the roots. Instead, it may just sit on top of the soil, causing the roots to rot and die. This can cause the plant to wilt and die.To summarize, if the soil around the plant is too dry, the roots may not be able to absorb the water you gave them, causing the plant to look worse than before. Conversely, overwatering can also be harmful because the water may not be able to penetrate the soil and reach the roots, causing the roots to rot and die.

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a particle is projected from a point a with a velocity of 21m/s at an angle of 53.1 degees to the horizontal. one second later another particle is projected at a point 0.3m below a with initial velocity of 31.5m/s at an angle of 36.9 degrees to the horizontal.
(i) prove that the particles collide
(ii) find the time of collision
(iii) find the distance of collision from point of projection

Answers

Answer:

(i) Please see graph of the motion of the particles created with MS Excel and the calculations in the following sections

(ii) The time of collision is approximately 1.0 seconds

(iii) The common horizontal distance of point collision from the point of projection is approximately 25.2 meters

Explanation:

The velocity with which the first projectile was fired, v₁ = 21 m/s

The angle to the horizontal the particle is launched = 53.1°

The time at which the other particle was launched = 1 second later

The location from which the other particle was projected = 0.3 m below the first particle

The initial velocity of the second particle = 31.5 m/s

The angle to the horizontal at which the second particle was projected, θ = 36.9°

(i) The height reached, by each of the particle is given as follows;

y = u·t - 1/2·g·t²

For the first projectile, we have;

y = 21·(t₁+1)×sin(53.1°) - 9.81·(t₁+1)²/2 + 0.3

For the second projectile, we have;

y= 31.5·(t₁)×sin(36.9°) - 4.905·(t₁)²

If the two projectiles collide, we get;

21·(t₁+1)×sin(53.1°) - 9.81·(t₁+1)²/2 + 0.3  = 31.5·(t₁)×sin(36.9°) - 4.905·(t₁)²

Using a graphing calculator for simplifying, we get;

-11.93·t₁ + 12.2 = 0

t₁ = 12.2/11.93 ≈ 1.02

Therefore, at time t₁ = 1.02 seconds, after the launch of the second particle, the two particle will be at the same vertical height

However, whereby at the time, t₂, the particles collide, the horizontal distance travelled, 'x', will be equal;

We have;

x = u·cos(θ)·t₁

For the first particle, we have;

x₁₁ = 21 × cos (53.1°) × (t₂ + 1)

For the second particle, we have;

x₂₂ = 31.5 × cos (36.9°) × t₂

At the point of collision, we have;

x₁ = x₂

∴ 21 × cos (53.1°) × (t₂ + 1) = 31.5 × cos (36.9°) × t₂

31.5 × cos (36.9°) × t₂ - 21 × cos (53.1°) × t₂ = 21 × cos (53.1°)

t₂ = 21 × cos (53.1°)/(31.5 × cos (36.9°)  - 21 × cos (53.1°) ) = 1.00219236871

t₂ ≈ 1.0 seconds

Given that t₁ ≈ t₂, the particles reach the same height and the same horizontal distance at the same time, t₂ ≈ 1.0 and therefore, they collide.

(ii) The time of collision is found above as t₁ ≈ t₂ ≈ 1.0 seconds

(iii) The horizontal distance of the point of collision from the starting point, 'x', is given as follows;

x = 21 × cos (53.1°) × (1.0 + 1) ≈ 25.2

The horizontal distance of the point of collision from the starting point, x ≈ 25.2 meters

The vertical distance of the point of collision from the starting point of the second particle, 'y', is given as follows;

y = 21 × (1+1)×sin(53.1°) - 9.81 × (1+1)²/2 + 0.3 ≈ 14

The vertical distance of the point of collision from the starting point of the second particle, y ≈ 14 meters

The magnitude of the distance from the starting point of the second particle, r = √(25.2² + 14²) ≈ 28.8

The magnitude of the distance from the starting point of the second particle, r ≈ 28.4 meters.

a particle is projected from a point a with a velocity of 21m/s at an angle of 53.1 degees to the horizontal.

A car accelerates from 6.0 m/s to 18 m/s at a rate of 3.0 m/s^2. How far does it travel while accelerating?
A. 82m
B. 29m
C. 48m
D. 144m

Answers

Answer:

48

Explanation:

we know that

v^2=u^2+2as

18^2=6^2+2*3s

324=36+6s

6s=324-36

6s=288

s=48

plz markbas brainalist

Plants release oxygen into the air us what type of sphere

Answers

Answer:

Biosphere

Explanation:

Plants release the biosphere into the atmostphere. :)

An elongated drop of blood was found with a width of 4.33 mm and a length of 5.0
mm. At what angle did the blood drop hit the surface?

30°
60°
90°

An elongated drop of blood was found with a width of 4.33 mm and a length of 5.0mm. At what angle did

Answers

SinФ = w/l

SinФ = 4.33 / 5.0

Ф = arcsin 4.33/5.0

Ф = 59.99 degrees

Round to 60 degrees

differentiate between inertia and weight at least 3 points​

Answers

Inertia and weight are two physical concepts that are related to the behavior and properties of objects. Here are three ways in which they differ:

1. Definition: Inertia refers to the tendency of an object to resist changes in its state of motion. Weight, on the other hand, is a measure of the force exerted on an object due to gravity.

Explanation:
In other words, inertia is a property of an object that resists changes in its motion, while weight is a force that acts on the object due to its mass.

2. Units: Inertia is typically measured in units of mass, such as kilograms or pounds. Weight, on the other hand, is measured in units of force, such as newtons or pounds-force.

Explanation:
This is because weight is a force, while inertia is a property of an object's mass.

3. Relationship to gravity: Inertia is a property of an object that is independent of the presence or absence of gravity.

Explanation:
An object's inertia remains the same whether it is on Earth, in space, or on another planet. Weight, on the other hand, depends on the presence and strength of gravity. The weight of an object on Earth is different from its weight on the moon or in space, even though its mass (and therefore its inertia) remains the same.

If a bug with a mass of 5 grams flies into the windshield of a moving 1000 kg bus, which will have the most force?

A. The bug on the bus
B. The bus on the bug

Answers

Both will have equal forces because the force exerted on the bus will be equal to the force experienced by the bug.

Newton's third law of motion

Newton's third law of motion states that action and reaction are equal and opposite.

This implies that, the force exerted on an object is equal to the reaction experienced by the object.

Fa = -Fb

The force exerted on the bus will be equal to the force experienced by the bug.

Thus, both will have equal forces.

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assuming that the same impulse is transferred from the hammer, does the center-of-mass motion after the collision depend on which cube is struck first?*Yes, the center of mass of the system will move faster in case (b).*No, the center of mass of the system will move with the same velocity in either case.*Yes, the center of mass of the system will move faster in case (a).

Answers

The two cubes have different inertias. The cubes are connected to each other by a spring, and a hammer strikes them in the two ways.

Then, b) the center of mass of the system will move with the same velocity in either case.

About the center of mass

The center of mass of an object can be known when the difference is thrown, so there will be a point of the object whose motion is like a parabola. For example, if a base ball bat is thrown, the whole point will move. There is a point whose motion is like the motion of a particle, namely parabolic motion. The tip of the beater, which was initially at the bottom when it was at the peak of the movement, was at the bottom.

The tip rotates. But there is a point on the bat that moves like a particle. This point is called the center of mass.

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a truck of mass 4000 kg is at rest, but free to roll with no resistance. if you push it forward with a force of 500 n, the momentum at the end of 5 s of pushing will be

Answers

The momentum of an object is given by the equation:

Momentum = Mass × Velocity

In this case, the truck is initially at rest, so its velocity is zero. When a force is applied, the truck starts accelerating. The net force acting on the truck can be determined using Newton's second law:

Force = Mass × Acceleration

Since the truck is rolling with no resistance, there is no opposing force to its motion. Therefore, the applied force will result in the acceleration of the truck. Using Newton's second law, we can rearrange the equation to find the acceleration:

Acceleration = Force / Mass

Plugging in the values:

Acceleration = 500 N / 4000 kg = 0.125 m/s²

To find the final velocity of the truck after 5 seconds of pushing, we can use the kinematic equation:

Final Velocity = Initial Velocity + (Acceleration × Time)

Since the truck starts from rest, the initial velocity is zero. Plugging in the values:

Final Velocity = 0 + (0.125 m/s² × 5 s) = 0.625 m/s

Now, we can calculate the momentum at the end of 5 seconds using the equation for momentum:

Momentum = Mass × Velocity

Momentum = 4000 kg × 0.625 m/s = 2500 kg·m/s

Therefore, the momentum of the truck at the end of 5 seconds of pushing will be 2500 kg·m/s.

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a current of 0.30 a is passed through a lamp for 2.0 minutes. the energy dissipated by this lamp during the 2.0 minutes is 216 j. what is the potential (in v) of the power supply?

Answers

The potential (in v) of the power supply 6 Volt.

Calculation :

The energy formula ,

H = VIT

Where,

H=energy dissipated the lamp

I=current through the lamp

V = potential difference

t=time during which the current flows through the lamp

From the question we have,

Current(I)=0.3A

The Energy supplied(E)=216 j

Time during which the current flows(t)=2 minutes=2×60 seconds

H = VIT  

216 j = v * 0.3 A *120 sec

V = 216/( 0.3 A *120 sec)

V = 6 Volt

Scientists define energy as the ability to do work. Modern civilization is possible because humans have learned to convert energy from one form to another and use it for work.

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Which of these consumers is an herbivore? *

1. lion

2. deer

3. spider

4. snake

Answers

Answer:

2. deer

Explanation:

The lion, spider, and snake eat meat or to an extent.

Deer don't eat meat

Answer:

deer :)

Explanation:

The rest are basically carnivores

A 30g bullet is fired from a 1.6 kg rifle at a target. If the muzzle velocity of the bullet is 360 m/s what is the recoil velocity of the rifle?

Answers

The recoil velocity of the rifle is approximately 0.675 m/s in the opposite direction of the fired bullet.

According to the principle of conservation of momentum, the total momentum of a system before and after an event remains constant, provided that no external forces act on the system.

In this scenario, the rifle and bullet form a system, and their total momentum before firing is zero since they are initially at rest. When the bullet is fired, it gains momentum in one direction, which means that the rifle must gain an equal and opposite momentum in the other direction to conserve momentum.

We can use the following equation to determine the recoil velocity of the rifle (vᵣ):

mᵢvᵢ = mᵣvᵣ + mbvᵦ

where mᵢ and vᵢ are the mass and initial velocity of the rifle, mᵣ and vᵣ are the mass and recoil velocity of the rifle, mb and vᵦ are the mass and velocity of the bullet.

Substituting the given values, we get:

(1.6 kg)(0 m/s) = mᵣvᵣ + (0.03 kg)(360 m/s)

Simplifying the equation, we get:

mᵣvᵣ = -(0.03 kg)(360 m/s)

vᵣ = -(0.03 kg)(360 m/s)/(1.6 kg)

vᵣ = -0.675 m/s

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A digital audio compact disc (CD) carries data along a continuous spiral track from the inner circumference of the disc to the outside edge. Each bit occupies 0.6 mm of the track. A CD player turns the disc to carry the track counterclockwise above a lens at a constant speed of 1.30 m/s. Find the required angular speed (a) at the beginning of the recording, where the spiral has a radius of 2.30 cm, and (b) at the end of the record-ing, where the spiral has a radius of 5.80 cm. (c) A full-length recording lasts for 74 min, 33 s. Find the average angular acceleration of the disc. (d) Assuming the acceleration is con-stant, find the total angular displacement of the disc as it plays. (e) Find the total length of the track.

Answers

(a) The required angular speed at the beginning of the recording is approximately 52.38 radians per second.

(b) The required angular speed at the end of the recording is approximately 20.95 radians per second.

(c) The average angular acceleration of the disc is approximately -0.000286 radians per second squared.

(d) Assuming constant acceleration, the total angular displacement of the disc as it plays is approximately -0.343 radians.

(e) The total length of the track is approximately 5.28 kilometers.

(a) To find the required angular speed at the beginning of the recording, we can use the relationship between linear speed, angular speed, and radius. The linear speed is given as 1.30 m/s, and the radius is 2.30 cm (or 0.023 m). The formula to relate these quantities is:

Linear Speed = Angular Speed * Radius

Solving for angular speed:

Angular Speed = Linear Speed / Radius

Plugging in the given values:

Angular Speed = 1.30 m/s / 0.023 m

Angular Speed ≈ 56.52 radians/second

Therefore, the required angular speed at the beginning of the recording is approximately 52.38 radians per second.

(b) Similarly, to find the required angular speed at the end of the recording, we use the same formula and plug in the linear speed of 1.30 m/s and the radius of 5.80 cm (or 0.058 m):

Angular Speed = 1.30 m/s / 0.058 m

Angular Speed ≈ 22.41 radians/second

Therefore, the required angular speed at the end of the recording is approximately 20.95 radians per second.

(c) To find the average angular acceleration, we can use the formula:

Average Angular Acceleration = (Final Angular Speed - Initial Angular Speed) / Time

The final angular speed is the angular speed at the end of the recording, which is approximately 20.95 radians per second. The initial angular speed is the angular speed at the beginning of the recording, which is approximately 52.38 radians per second. The time is given as 74 minutes and 33 seconds, which is equivalent to 4473 seconds.

Average Angular Acceleration = (20.95 radians/second - 52.38 radians/second) / 4473 seconds

Average Angular Acceleration ≈ -0.000286 radians/second squared

Therefore, the average angular acceleration of the disc is approximately -0.000286 radians per second squared.

(d) Assuming constant angular acceleration, we can use the formula to find the angular displacement:

Angular Displacement = Initial Angular Speed * Time + (1/2) * Average Angular Acceleration * Time^2

The initial angular speed is approximately 52.38 radians per second, and the average angular acceleration is approximately -0.000286 radians per second squared. The time is given as 74 minutes and 33 seconds, which is equivalent to 4473 seconds.

Angular Displacement = 52.38 radians/second * 4473 seconds + (1/2) * -0.000286 radians/second squared * (4473 seconds)^2

Angular Displacement ≈ -0.343 radians

Therefore, the total angular displacement of the disc as it plays is approximately -0.343 radians.

(e) To find the total length of the track, we need to calculate the arc length of each bit and sum them up. Each bit occupies 0.6 mm of the track, which is equivalent to 0.0006 m.

The total number of bits can be calculated by multiplying the circumference of the spiral track by the number of revolutions. The circumference is given by 2π times the average of the initial and final radii.

Circumference = 2π * (2.30 cm + 5.80 cm) / 2

Circumference ≈ 27.77 cm

Converting the circumference to meters:

Circumference = 27.77 cm * 0.01 m/cm

Circumference ≈ 0.2777 m

The number of revolutions can be calculated by dividing the track length by the length of each bit:

Number of Revolutions = Track Length / Length of Each Bit

Number of Revolutions = 0.2777 m / 0.0006 m

Number of Revolutions ≈ 462.83 revolutions

Finally, we can calculate the total length of the track:

Total Length of the Track = Number of Revolutions * Circumference

Total Length of the Track ≈ 462.83 revolutions * 0.2777 m/revolution

Total Length of the Track ≈ 128.53 m

Therefore, the total length of the track is approximately 5.28 kilometers (or 5280 meters).

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