after turning out the light for the night, your head hits the pillow. gradually, your muscles relax and drowsiness occurs. this drowsy yet wakeful state is associated with brain waves. question 25 options: a) alpha b) beta c) theta d) delta

Answer: The series had the larger total resistance.

The altitude must the pilot begin to pull out of the dive to avoid crashing into the sea if he can withstand an acceleration of 8.0 g 's without blacking out is 19000 feet.

The acceleration experienced by the pilot is given by the formula:a = g - (g²)/(2gh+a) where a = acceleration g = acceleration due to gravity h = altitude a = acceleration. The maximum acceleration that a person can withstand is approximately 8 g's, which is the value of acceleration that the pilot can withstand without blacking out. So, by putting the given value of acceleration into the above formula, we get 8g = g - (g²)/(2gh+a)

Multiplying throughout by (2gh+a) we get: 16gh+8ga = 2gh - g².Dividing throughout by g and rearranging, we get: 2gh/g + g/8a = 1h/g + g/16a = 1/2.By substituting the given values:g = 9.8 m/s²a = 8gh/g = h.The value of h is found to be:h = 5.5 km = 5,500 m = 18,000 feet. Therefore, the altitude must the pilot begin to pull out of the dive to avoid crashing into the sea if he can withstand an acceleration of 8.0 g 's without blacking out is 19000. Answer: 19,000 feet.

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The flux from the 600 K object is approximately 16 times larger than the flux from the 300 K object.

According to the Stefan-Boltzmann law, the flux emitted by a blackbody is proportional to the fourth power of its absolute temperature. This means that if we double the temperature of a blackbody, its flux will increase by a factor of 2 to the fourth power, or 16. In this case, the 600 K object is twice as hot as the 300 K object, so its flux will be approximately 16 times larger.

To calculate the exact ratio of the fluxes, we can use the equation F = σT⁴, where F is the flux, σ is the Stefan-Boltzmann constant (5.67 x 10⁻⁸ W/m²K⁴), and T is the absolute temperature in Kelvin. Plugging in the temperatures of 300 K and 600 K, we get:

F₁ = σ(300 K)⁴ = 460.8 W/m²

F₂ = σ(600 K)⁴ = 7372.8 W/m²

The ratio of F₂ to F₁ is approximately 16.

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The system's momentum is zero prior to the explosion since the cannon and cannonball are both at rest.. Following the explosion, the system's overall momentum is conserved. The overall momentum before and after the explosion must be the same in accordance with the law of conservation of momentum.

Between 250 and 100 m/s seems to be the most plausible range (250 m/s is equivalent to 820 feet per second).

v2 = - 2 m/s

The above equation's negative sign tells us that the gun's velocity and the bullet's velocity are diametrically opposed. Hence, the firearm will recoil.

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As a result, the combined ultimate velocity of the male and female skaters following the throw is 5.27 m/s.

The object's initial velocity can be calculated by dividing the total distance travelled by the amount of time it took the object to travel that distance. In the formula V = d/t, V is the speed, d the distance, and t the time.

Prior to the throw, the system's momentum is given by: p1 = m1v1 + m2v2.

replacing the specified values:

p1 = (82 kg)(7.4 m/s) + (48 kg)(0 m/s)

p1 = 607.6 kg m/s

Following the throw, the system's momentum is:

p2 = (82 kg)v' + (48 kg)(8.6 m/s)

where v' is the combined final speed of the male and female skaters. We may equate p1 and p2 using the conservation of momentum principle:

p1 = p2

(82 kg)(7.4 m/s) = (82 kg)v' + (48 kg)(8.6 m/s)

Simplifying and solving for v', we get:

v' = [ (82 kg)(7.4 m/s) - (48 kg)(8.6 m/s) ] / 82 kg

v' = 5.27 m/s

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3,247.95 J is the amount of work the gravitational force has done on the guy. Since the individual is travelling at a steady speed and the escalator is not exerting any force on him, the work done by the escalator on him is zero.

There is no acceleration in either axis after the platform has reached the maximum escalator angle since both the horizontal and vertical speeds are constant.

The following formula can be used to determine how much work the gravitational pull has done on the man:

W = mgh

where W is the amount of labor completed, m is the man's mass, g is the acceleration brought on by gravity, and h is the height in the air.

Substituting the given values, we get:

W = (75 kg)(9.81 m/s²)(4.6 m)

= 3,247.95 J

Therefore, the work done on the man by the gravitational force is 3,247.95 J.

(a) Because the guy is going at a constant speed and the escalator is not exerting any force on him, the work done on him by the escalator is zero.

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The angle of attack is approximately 4 degrees.

A more detailed explanation of the answer.

To find the angle of attack for a NACA 4415 airfoil with a 2m chord in an airstream with a velocity of 50 m/s and a lift per unit span of 1,595 N, follow these steps:

1. Calculate the dynamic pressure (q):
q = 0.5 * ρ * V^2
where ρ is the air density at standard sea-level conditions (1.225 kg/m³) and V is the airstream velocity (50 m/s).

q = 0.5 * 1.225 * (50)^2 = 1,531.25 N/m²

2. Calculate the lift coefficient (Cl):
Lift per unit span (L') = Cl * q * chord (c)
1,595 N = Cl * 1,531.25 N/m² * 2m

Now, solve for Cl:
Cl = 1,595 / (1,531.25 * 2) = 0.5208

3. Refer to a NACA 4415 lift coefficient vs angle of attack graph or data table to determine the angle of attack corresponding to the calculated Cl value. Since the Cl value is 0.5208, the angle of attack is approximately 4 degrees.

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With the given values of W and d, we can find the smallest value for the coefficient of friction necessary to keep the block from moving.

To calculate the smallest value for the coefficient of friction necessary to keep the block from moving, we can use the formula for static friction:
static friction (fs) = coefficient of static friction (μs) × normal force (N)
Since we know the work done (200 J) and want to find the smallest value for the coefficient of friction (μs), we can use the work-energy theorem, which states:

Work = change in kinetic energy = 0 (since the block is not moving)
Work = force (F) × distance (d) × cos(θ)

200 J = μs × N × d × cos(θ)
Now, let's consider the forces acting on the block.

The weight of the block (W) is acting vertically downward, and the normal force (N) is acting vertically upward. In this case, the angle (θ) between the force and the direction of motion is 0 degrees,

so cos(θ) = 1.
To find the normal force (N), we can equate it to the weight of the block since the block is not moving vertically:
N = W
We need more information to solve for the coefficient of static friction (μs), such as the weight of the block (W) and the distance (d).

Once we have this information, we can substitute it into the equation and solve for μs:
200 J = μs × W × d
μs = 200 J / (W × d)

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Answer:

The total energy is increasing from point 1 to point 2 because an external force is acting on the cars, pulling them upward at a constant low speed.

This force is doing work on the cars, and as a result, their gravitational potential energy is increasing.

Since the kinetic energy remains constant due to the constant low speed and friction is negligible, the total energy (which is the sum of potential energy and kinetic energy) also increases.

In summary, from point 1 to point 2:
1. An external force pulls the cars upward, increasing their height.
2. The gravitational potential energy increases due to the increased height.
3. The kinetic energy remains constant due to the constant low speed and negligible friction.
4. The total energy increases because of the increased gravitational potential energy.

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The solenoid has an inductance of l. if the number of loops per unit length is increased by a factor of 5.02, the total number of loops is increased by a factor of 6.45, and the area of ​​each loop is increased by a factor of 7.26, then the inductance will be multiplied by a factor of 33.91.

L = (μn²A)/l.

Where n is the number of turns per unit length, A is the area of each turn, l is the length of the solenoid and μ is the permeability of the medium.

After the changes are made, the new values are given by,

Number of turns per unit length = 5.02n

Area of each turn = 7.26A (increased by a factor of 7.26)

Total number of turns = 6.45n

The length of the solenoid remains the same

Now, the new inductance, L' is given by,

L = (μn²A)/l

Where, n = 5.02n (number of turns per unit length increased by a factor of 5.02)

A = 7.26A (area of each turn increased by a factor of 7.26)

l = l (length remains the same)

Substituting the values of `n'`, `A'` and `l` in the above equation,

L = (μ (5.02n)² (7.26A))/l = (μ × 6.45² × 7.26 × n² × A)/l

Now, dividing the new inductance by the original inductance,

L'/L = (μ × 6.45² × 7.26 × n² × A)/l × (1/μ × n² × A)/l = 6.45² × 7.26 = 33.91

Therefore, the inductance will be multiplied by a factor of 33.91.

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Sam (80 kg) takes off up a 50-m-high, 10-frictionless slope on his jet-powered skis.  The distance travelled by Sam (80 kg) is 50.02 m (with appropriate units).

As per the given question, Sam (80 kg) takes off up a 50-m-high, 10- frictionless slope on his jet-powered skis. The skis have a thrust of 190 N. He keeps his skis tilted at 10∘ after becoming airborne.

We need to determine how far Sam land from the base of the cliff. For this, we can use the formula given below.

Distance = Vx * T + 0.5 * ay * [tex]T^2[/tex].

We can calculate the velocity at the end of the slope as follows;

Vx = v * cos θVx = sqrt(2gh) * cos θ

Vx = sqrt(2*9.8*50) * cos(10)

Vx= 233.51 m/s.

Now, using the horizontal velocity, we can calculate the time required to reach the ground.

We know that;

distance = velocity * time + 0.5 * acceleration * time^2distance

= Vx * T

(as the acceleration in the horizontal direction is zero).

Solving for T;

T = distance / VxT = 50 m / 233.51 m/s

T = 0.214 s

Now, we can use the vertical equation to calculate the displacement (or distance travelled) in the vertical direction.

We know that; ay = g = 9.8 m/s^2Vyf = Vi + ay *t

We need to find the final velocity. Vyf at the end of the slope. Initially, we know that; Vi = 0So,

solving for Vyf;

Vyf = ay * tVyf = 9.8 m/s^2 * 0.214 sVyf = 2.10 m/s

Using this final velocity, we can calculate the displacement (distance travelled) as follows;

y = Vi * t + 0.5 * ay * t^2y = 0 + 0.5 * 9.8 m/s^2 * (0.214 s)^2y = 0.22 m.

Now, the horizontal displacement can be calculated as follows;

x = Vx * T (distance covered in the horizontal direction)

x = 233.51 m/s * 0.214 s

x = 50.02 m.

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The direction of the magnetic field must be in the positive x direction to make the net force on the electron have a magnitude of zero.

To find the direction of the magnetic field that makes the net force on the electron zero, we can use the following steps:
Step 1: Identify the direction of the electric force
The electric force on the electron is in the direction of the electric field.

Since the electric field is in the negative z direction, the electric force on the electron will also be in the negative z direction.
Step 2: Identify the direction of the magnetic force
The magnetic force on a charged particle can be determined using the Lorentz force equation: F = q(v x B),

where F is the magnetic force, q is the charge of the particle, v is the velocity vector of the particle, and B is the magnetic field vector.

The cross product (v x B) indicates that the magnetic force is perpendicular to both the velocity and the magnetic field.
Step 3: Determine the direction of the magnetic field
Since the electron is traveling in the negative y direction, we need to find a magnetic field direction such that the magnetic force on the electron is in the positive z direction (to cancel out the electric force).

Using the right-hand rule, the appropriate direction of the magnetic field is in the positive x direction.
In conclusion, the direction of the magnetic field must be in the positive x direction to make the net force on the electron have a magnitude of zero.

This is achieved by ensuring the magnetic force on the electron is equal in magnitude but opposite in direction to the electric force acting on it.

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Answer:

9. Using the equation KEmax = hf - Φ, where KEmax is the maximum kinetic energy of the emitted photoelectrons, h is Planck's constant, f is the frequency of the radiation, and Φ is the work function of the metal, we can rearrange to find Φ:

Φ = hf - KEmax

Φ = (6.63 x 10^-34 J s)(1.5 x 10^14 Hz) - 3.8 x 10^-20 J

Φ = 9.94 x 10^-20 J

Therefore, the work function of the metal is 9.94 x 10^-20 J.

10. a) Only photons with energies greater than or equal to the work function of the metal (1.7 eV) will cause photoemission. Thus, the photon with an energy of 2.0 eV and the photon with an energy of 4.0 eV will cause photoemission, but the photon with an energy of 1.0 eV will not.

b) For the photon with an energy of 2.0 eV:

KEmax = hf - Φ

KEmax = (6.63 x 10^-34 J s)(3.2 x 10^14 Hz) - 1.7 eV

KEmax = 3.23 x 10^-19 J or 2.0 eV

For the photon with an energy of 4.0 eV:

KEmax = hf - Φ

KEmax = (6.63 x 10^-34 J s)(6.4 x 10^14 Hz) - 1.7 eV

KEmax = 5.13 x 10^-19 J or 4.0 eV

A cell that is designed to use dry-cell batteries and operates between 1.0 and 1.5 volts can be used to make a battery that could replace a dry-cell battery, as long as it meets the requirements of voltage output, capacity, compatibility, and stability.

Yes, a cell designed to operate between 1.0 and 1.5 volts can be used to make a battery that could replace a dry-cell battery. Here's a step-by-step explanation of why this is possible:
1. Dry-cell batteries are commonly used in devices because they provide a stable voltage output and have a wide operating range (1.0 to 1.5 volts), which is suitable for most electronic devices.
2. To replace a dry-cell battery, the new cell must also provide a similar voltage output and have a comparable operating range. If the new cell is designed to operate between 1.0 and 1.5 volts, it meets this requirement.
3. Another important factor in replacing a dry-cell battery is the capacity of the new cell. The capacity determines how long the battery can provide power to the device before it needs to be replaced or recharged. If the new cell has a similar or higher capacity than the dry-cell battery it is replacing, it will be a suitable replacement.
4. Additionally, the size and shape of the new cell must be compatible with the device it is intended to power. Many dry-cell batteries have standard sizes and shapes, so it's important to ensure that the new cell is compatible with the device's battery compartment.
5. Finally, the new cell must be able to provide a stable voltage output over its entire operating range. This ensures that the device will function properly and efficiently.
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The rock hits the water at a speed of about 22.1 m/s. We can solve this problem using conservation of energy, assuming that there is no air resistance.

Initially, the rock has potential energy equal to mgh, where m is its mass, g is the acceleration due to gravity, and h is the height of the bridge. At the bottom of its trajectory, the rock has no more potential energy, but it has kinetic energy equal to[tex](1/2)mv^2[/tex], where v is its speed. By conservation of energy, we can equate these two energies:

mgh = [tex](1/2)mv^2[/tex]

Simplifying and solving for v, we get:

v = sqrt(2gh)

where sqrt means square root.

Substituting in the given values, we get:

v = [tex]sqrt(2 × 9.81 m/s^2 × 25.0 m) ≈ 22.1 m/s[/tex]

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The coefficient's digits in scientific notation show which numbers are significant. The exponent has no bearing on how many significant digits there are.

All the digits known with certainty (those shown by the markings on the measuring equipment) and the first unknown, or estimated, digit are considered the important figures of a measured quantity (one digit past the smallest marking on the measuring device).

The number of significant figures in a measurement, such as 2.531, is equal to the number of digits that may be known with some degree of certainty (2, 5, and 3), plus the final digit (1), which is an estimate or approximation.

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Question:

Physics 01-01 Intro and Units

Name: M. Seddia

Significant Figures

Used to reflect in measurements

Each measuring device can only measure so accurately

The

digit is always ant

To find significant figures

zeros between the decimal point and the first nonzero digit

Ignore, Count the number of other)

0.000000602

1032000

1.023

Rules for combining significant figures

Addition or subtraction

The answer can contain no more,

places than the

precise measurement

1.02-2.0223-

Multiplication or division

The result should have the same number of,

as the quantity having the.

significant figures entering

into the calculation. 1.002-2.0223

Homework

1. Classify each as a model, theory, or law.

Bohr model of atom

b. Gravity

C Drawing a picture to represent a physics

problem d. The Earth is round

The Big Bang Creation

2. The altitude of the International Space Station is 409 km. What is this in meters? (RW) 409000 m

3. The elevation of Berrien Springs is 209 m. What is this in

cm? (RW) 20900 cm

4. Convert 1 hour to seconds. (RW) 3600 s

5. The speed limit on some highways is 100 km/h. How fast is that in m/s? (RW) 27.8 m/s

6. The Earth orbits the sun at 29.78 km/s. What is this in km/h? (RW) 107200 km/h

7. The Earth orbits the sun at 29.78 km/s. What is this in mph (assume 1 mile = 1.609 km)? (RW) 66630 mph

8. The surface area of the Earth is 510,072,000 km². What is this in m³? (RW) 5.10072 x 104 m²

Created by Richard Wright-Andrews Academy

9. Water covers approximately 361,132,000 km of the Earth's surface. What is this in ft (assume 1 m = 3.2808 ft)? (RW) 3, 8871 x 1015 ft2

10. The average density of Earth is 5.514 g/cm³. What is this in

kg/m³? (RW) 5514 kg/m³ 11. 148,940,000 km of land are on Earth. How many significant figures are in this number? (RW) 5

12. During the breeding season, an adult Monarch Butterfly

will live 0.0760 yrs. How many significant figures? (RW) 3

13. The village of Berrien Springs covers 2.64 km². How many significant figures? (RW) 3

14. 0.21 km² of Berrien Springs is water. How many significant figures? (RW) 2

15. Using the information from the previous two questions, how much land is there in Berrien Springs? How many significant figures should be in your answer? (RW) 2.43 km², 3

16. If there are about 740 people per km² in Berrien Springs (living on the land), how many people live in Berrien Springs? How many significant figures should be in your answer? (RW) 1800 people, 2

To be used with OpenStax College Physics

The time taken for a ping pong ball to fall from a height of 324 meters, with no air resistance, is approximately 8.03 seconds.

Air resistance is the force of friction that acts on any object as it moves through the air. As a result, an object's velocity decreases. As a result, the height of the tower, the gravitational constant, and the absence of air resistance are all taken into account in order to calculate the time it takes for the ping pong ball to hit the ground.Using the following equation, the time it takes for a ping pong ball to fall from a height of 324 meters, with no air resistance, can be calculated:

t=√2h/g

Where:t= time taken to fall, h= height, g= gravitational constant (9.8 m/s²)

Using the values given in the problem,

t=√2(324)/9.8

t= 8.03 seconds

Hence, the time taken for a ping pong ball to fall from a height of 324 meters, with no air resistance, is approximately 8.03 seconds.

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Explanation:

Sure, I'd be happy to help you come up with ideas for your Alien Project! Here are a few suggestions:

Design your own alien: Draw or create a model of an alien and include details such as its habitat, physical characteristics, and any special abilities or behaviors it may have.

Alien life cycle: Create a diagram or model of an alien's life cycle, including details such as reproduction, growth, and development.

Alien adaptation: Research different adaptations that animals on Earth have to survive in extreme environments, such as the ability to withstand extreme heat or cold. Use this information to design an alien that has adapted to a similar extreme environment.

Communication with aliens: Research different methods that scientists use to communicate with potential alien life and create a hypothetical conversation between humans and aliens.

Alien ecosystem: Imagine an alien planet with its own unique ecosystem. Draw or create a model of the different organisms that would exist in this ecosystem and explain how they interact with each other.

Alien technology: Imagine what kinds of technology an advanced alien civilization might possess. Create a drawing or model of this technology and explain how it works.

These are just a few ideas to get you started! Remember to have fun with your project and let your imagination run wild. Good luck!

The true statements about population 1 stars are: Our Sun is a population 1 star, Population 1 stars would include bright supergiant stars and Heavy elements within population 1 stars make up 1-4% of the total stellar mass.

The population 1 stars are stars that are rich in heavy elements, which are also known as metal-rich stars. These stars are known for having relatively high metallicity, which is the abundance of elements heavier than hydrogen and helium. Population 1 stars are young, and most of them are found in the disk of our Milky Way galaxy.

They are located in areas with a higher concentration of gas and dust. This contrasts with population 2 stars, which are typically old, metal-poor stars that are found in the halo of the galaxy. In general, population 1 stars include main-sequence stars, red giant stars, and bright supergiant stars. The heavy elements within these stars, including carbon, nitrogen, and oxygen, make up a significant portion of their total stellar mass, around 1-4%.

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Canoes are lightweight, maneuverable watercraft, but they are susceptible to capsize or swamp, particularly on choppy waters or when carrying a lot of gear or people.

The ability of an object to remain on the surface of a liquid without sinking is referred to as flotation. This is accomplished by giving the object enough buoyancy, or upward force, to balance out gravity's pulling downward. The weight of the displaced water, which is the same as the weight of the object, provides the buoyant force in water.

It is crucial to offer some type of buoyancy that keeps the canoe afloat even when filled with water in order to avoid the canoe from sinking in such circumstances.

Installing plastic foam blocks under the canoe's seats is one technique to accomplish this. These foam blocks are a great option for this because they are lightweight, strong, and water resistant. It is simpler to rescue and recover a canoe when it is afloat due to the buoyancy created by the foam blocks when the canoe is filled with water.

In conclusion, adding plastic foam blocks under a canoe's seats increases its stability and flotation, making it safer and more dependable on the water.

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Answer:

B

Explanation:

the other ones don't really make sense

The scenario that correctly illustrates heat is:" A cold person's hands get warmer by holding a rock that has been sitting in the sun." The correct option is B.

Heat is a form of energy that is transferred from one object or system to another as a result of a difference in temperature. Heat is a type of thermal energy, which is the total energy associated with the random motion of atoms and molecules within a substance.

Heat can be transferred in three ways: conduction, convection, and radiation. Conduction is the transfer of heat energy through a material or between two materials in contact. Convection is the transfer of heat energy by the movement of fluids, such as air or water, and radiation is the transfer of heat energy through electromagnetic waves, such as light or infrared radiation.

Here in this question,

In option A), a cold person sitting in a sauna with a temperature of 105° F would actually become warmer due to the transfer of heat from the sauna to the person's body. so it is incorrect.

In option C), the ice in a cold glass of water does not melt because the water is below the freezing point of water. This is an example of a lack of heat transfer. so it is not relevant to the question.

In option D), the bathtub full of hot water does not get warmer in a cold room because heat energy is lost to the colder surroundings, causing the water to cool down. so it is incorrect.

Therefore, option B i.e" cold person's hands get warmer by holding a rock that has been sitting in the sun." is correct.

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The statemens which are true about reflection versus refraction is 2 , 3 and 4.

It is not true that reflection and refraction are the same when discussing seismic waves and the properties of those waves as they cross boundaries between materials. Therefore, the correct options are the 2,3 and 4 statements.

Reflection occurs when a wave encounters a boundary between two materials and some of the wave energy is reflected back into the original material. The angle of incidence (the angle between the incoming wave and the normal to the boundary) is equal to the angle of reflection (the angle between the reflected wave and the normal to the boundary).

Refraction occurs when a wave encounters a boundary between two materials and some of the wave energy is transmitted into the second material at an angle different from the angle of incidence. .

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The uniform circular motion that a disk must make 11.47 rev/min so that the acceleration of all points on its rim is 10 m/s2.

We need to use the equation a = (ω2)*r,

where,

a is the acceleration

ω is the angular velocity in rad/s

r is the radius of the disk.

Since we know the acceleration (10 m/s2) and the radius of the disk (90 m), we can rearrange the equation to solve for ω.

10 m/s2 = (ω2)*90 m

ω2 = 10/90 = 0.1111111 rad/s2

ω = 0.333 rad/s

Finally, to convert from rad/s to rev/min, we can use the equation n = (ω*60)/2π, where n is the rev/min and ω is the angular velocity in rad/s.

n = (0.333*60)/2π = 11.47 rev/min

Therefore, the disk must make 11.47 rev/min so that the acceleration of all points on its rim is 10 m/s2.

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If the fuel does 855 J of work on the potato, and produces 1422 J of heat, the change in internal energy of the fuel is 567 J.

According to the first law of thermodynamics, the change in internal energy of a system is equal to the heat added to the system minus the work done by the system:

ΔU = Q - W

where ΔU is the change in internal energy, Q is the heat added to the system, and W is the work done by the system.

In this case, the fuel does 855 J of work on the potato and produces 1422 J of heat. Since the potato cannon and the fuel can be considered as a closed system, the change in internal energy of the system can be calculated as:

ΔU = Q - W

ΔU = 1422 J - 855 J

ΔU = 567 J

Therefore, the change in internal energy = 567 J.

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Answer:

Calcium carbonate or the calcium and magnesium double carbonate makes up the majority of the sedimentary rock known as limestone. Shell fragments, small fossils, and other fossilized detritus are frequently found in it.

Explanation:

hope it helps :)

Naoki's mass is 67 kg, due to which the force calculated to pedal is 140.7 N at acceleration of 2.1 m/s².

Newton's second law of motion is a fundamental principle in physics that describes the relationship between force, mass, and acceleration. It states that an object's acceleration is proportional to the force applied to it and inversely proportional to its mass. We can rewrite this equation to find the mass:

F = m * a

where F is the net force applied to an object, m is its mass, and a is the resulting acceleration.

To solve this problem, we can use Newton's second law of motion, which states that the force applied to an object is equal to the product of its mass and acceleration:

F = m * a

where F is the applied force, m is the object's mass, and an is the acceleration.

The second law is mathematically stated as follows:

m = F / a

Substituting the given values, we get:

m = 140.7 N / 2.1 m/s²

m = 67 kg

Naoki's mass is 67 kg.

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Length of the wire is approximately 1.245 meters.

A more detailed explanation of the answer.

To find the length of the wire, we can use the formula for the magnetic force on a current-carrying wire in a magnetic field:

F = I * L * B * sin(θ)

where F is the force (30 N), I is the current (4.0 A), L is the length of the wire (unknown), B is the magnitude of the magnetic field, and theta is the angle between the current and magnetic field.

First, we need to find the magnitude of the magnetic field B:

B = √(5.0² + 7.0²) = √(25 + 49) = √74 T

Since the current is along the x-axis and the magnetic field has components in both the x and y directions, the angle theta between the current and magnetic field can be calculated using:

cos(theta) = (Bx / B) = (5.0 / √74)

So, theta = arccos(5.0 / √74)

Now we can plug in the values into the formula for the magnetic force:

30 N = 4.0 A * L * √74 T * sin(arccos(5.0 / √74))

Rearrange to solve for L:

L = (30 N) / (4.0 A * √74 T * sin(arccos(5.0 / √74)))

Now, calculate L:

L ≈ 1.245 m

So, the length of the wire is approximately 1.245 meters.

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A force in the x-direction decreases linearly from 9000 n to 1000 n in 10.0 s, then suddenly ends. 5000 N is the average force over this interval of time.

To calculate the average force over the given interval of time, follow these steps:
1. First, identify the initial and final forces. In this case, the initial force ([tex]F_1[/tex]) is 9000 N, and the final force ([tex]F_2[/tex]) is 1000 N.
2. Next, find the total time interval over which the force changes. Here, the time interval (Δt) is 10.0 s.
3. Since the force decreases linearly, we can calculate the average force ([tex]F_{avg}[/tex]) using the formula:

[tex]F_{avg}[/tex] = ([tex]F_1 + F_2[/tex]) / 2.
4. Plug in the initial and final forces: [tex]F_{avg}[/tex] = (9000 N + 1000 N) / 2.
5. Calculate the average force: [tex]F_{avg}[/tex] = (10000 N) / 2 = 5000 N.
So, the average force over the interval of 10.0 seconds is 5000 N.

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The final speed of the particle is 10.7 m/s (approx).

Velocity of the particle = 9.7 m/s, Acceleration of the particle = 1.4 m/s²Time duration = 2.9 s. We need to find the final speed of the particle. We know that the velocity of a particle with a uniform acceleration can be given as:v = u + at Where, v = Final velocity of the particle, u = Initial velocity of the particle, a = acceleration of the particle, t = Time duration

Now, The initial velocity of the particle = 9.7 m/s (in the positive x direction)Therefore, the final velocity of the particle in the x direction will remain the same as the initial velocity. vx = ux = 9.7 m/s Also, we know that the acceleration of the particle in the y direction can be given as:

ay = 1.4 m/s²Now, the final velocity of the particle in the y direction can be calculated as: v = u + atv = 0 + ay tv = 1.4 × 2.9 = 4.06 m/s. The resultant velocity of the particle can be calculated using Pythagoras' theorem: v = √(vx² + vy²)v = √(9.7² + 4.06²)v = 10.7 m/s

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