A sculptor is playing absent-mindedly with a large cylindrical lump of clay on a potter's wheel. This particular wheel has wonderful balance and will turn without friction when taken out of gear. The lump of clay is a uniform cylinder of mass 23. 0 kg and radius 19. 0 cm ; the axis of the clay cylinder coincides with the axis of the wheel, and the rotational inertia of the wheel can be neglected in comparison with the rotational inertia of the clay cylinder. The artist decides to throw ball bearings of mass 182. 0 grams at the curved side wall of the turning cylinder and to watch what happens when the bearings hit and stick. Before the first throw, the cylinder is turning once every 1. 70 seconds ; when looked at from above, the cylinder is turning counterclockwise, so that the direction of the angular momentum of the cylinder is Up. The artist throws the first ball bearing horizontally, and it impacts the clay wall at an angle of 60. 0 degrees away from the normal to the curved clay surface. Once the ball bearing is stuck in the clay, the cylinder is found to be turning once every 3. 30 seconds , still turning counterclockwise. Consider the ball bearing to be traveling horizontally before impact; the ball bearing is traveling in a plane which is perpendicular to the axis of the clay cylinder and which contains the center of mass of the clay. What was the speed of the bearing before the collision?

Answers

Answer 1

The speed of the ball bearing before the collision was: 1.75 m/s.

We can use the principle of conservation of angular momentum to solve this problem. Initially, the angular momentum of the system (clay cylinder + potter's wheel) is:

L1 = I1 * ω1

where I1 is the moment of inertia of the clay cylinder, and ω1 is its angular velocity.

When the ball bearing is thrown and sticks to the clay, the system's angular momentum changes due to the external torque exerted by the ball bearing. The change in angular momentum is:

ΔL = r * p * sin(θ)

where r is the radius of the cylinder, p is the linear momentum of the ball bearing before the collision, and θ is the angle between the normal to the clay surface and the direction of p. Since the ball bearing is thrown horizontally, θ = 60°.

Since the ball bearing sticks to the clay, the final system consists of a larger cylinder with a mass of 23.182 kg (23.0 kg clay cylinder + 0.182 kg ball bearing) and a new moment of inertia I2. The final angular velocity is ω2.

The conservation of angular momentum principle can be expressed as:

L1 + ΔL = I2 * ω2

Solving for the initial linear momentum p, we get:

p = (I2 * (ω2 - ω1)) / (r * sin(θ))

To find I2, we can use the formula for the moment of inertia of a solid cylinder:

I2 = (1/2) * M * R^2

where M is the mass of the larger cylinder and R is its radius. Since the clay cylinder and ball bearing stick together, their combined radius is still 19.0 cm.

Substituting the given values, we get:

I2 = (1/2) * (23.182 kg) * (0.19 m)^2 = 0.328 kg*m^2

To find ω2, we can use the fact that the final angular velocity is half the initial angular velocity:

ω2 = (1/2) * ω1 = (1/2) * (2π/1.70 s) = 2.33 rad/s

Finally, substituting all the values, we get:

p = (0.328 kgm^2 * (2.33 rad/s - 2π/1.70 s)) / (0.19 m * sin(60°)) = 0.319 kgm/s

The speed of the ball bearing before the collision is equal to its linear momentum divided by its mass:

v = p / 0.182 kg = 1.75 m/s

Therefore, the speed of the ball bearing before the collision was 1.75 m/s.

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Related Questions

_______ was the first scientist to measure the conductivity speed of neurons.

Answers

The first scientist to measure the conductivity speed of neurons was German physiologist Hermann von Helmholtz in the mid-19th century.

He used a frog sciatic nerve and a galvanometer to measure the speed of electrical signals traveling through the nerve fibers. His experiments led to the discovery of the action potential and provided evidence for the nerve impulse theory.

Later, other scientists built upon his work, including English physiologist Sir Charles Sherrington, who coined the term "synapse" and furthered the understanding of neural communication.

Today, measuring the conductivity speed of neurons is a fundamental technique in neuroscience research and is used to study a wide range of topics, including sensory processing, motor control, and memory formation.

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PLEASE HELP, i really need the help because i dont understand

PLEASE HELP, i really need the help because i dont understand

Answers

The y-component of the vector is 4.97 m.

What is a vector?

A vector is a quantity that has both magnitude and direction.

To calculate the y-component of the vector in the diagram above, we use the formula below.

Formula:

Y = Hcos∅.......... Equation 1

From the question,

Given:

H = 22.3 m∅ = 77.1°

Substitute these values into equation 1

Y = 22.3(cos77.1)Y = 22.3×0.223Y = 4.97 m.

Hence, the y-component of the vector is 4.97 m.

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11.5 A group of hikers uses a GPS while doing a 40-mile trek in Colorado. A curve fit to the data shows that their altitude can be approximated by the function y(t) = 0.12 - 6.75 135-11202 +3200r where y and t are expressed in feet and hours, respectively. During the 18-hour hike, determine (a) the maximum altitude that the hikers reach, (b) the total feet they ascend, (c) the total feet they descend. Hint: You will need to use a calculator or computer to solve for the roots of a fourth-order polynomial. 9070, 62 + 11.6 The motion of a particle is defined by the relation x 9t 5, where x is expressed in feet and t in seconds. Determine (a) when the velocity is zero, (b) the position, acceleration, and total distance traveled when t 5 s

Answers

(a) To determine the maximum altitude reached by the hikers, we need to find the maximum value of the function y(t). By analyzing the given function, we can see that the maximum altitude occurs at the highest point of the curve.

To find this point, we can take the derivative of y(t) with respect to t and set it equal to zero. Solving this equation will give us the value of t at which the maximum altitude is reached. Substituting this value back into the original function will give us the maximum altitude.

(b) To calculate the total feet ascended by the hikers, we need to find the area under the curve of the function y(t) over the time interval of the hike. This can be done by integrating y(t) with respect to t over the given interval.

(c) Similarly, to calculate the total feet descended by the hikers, we need to find the area under the curve of the function y(t) below the x-axis over the time interval of the hike. This can be achieved by integrating the absolute value of y(t) with respect to t over the given interval.

For the second part of the question:

(a) To determine when the velocity is zero, we need to find the time(s) at which the derivative of the position function x(t) is equal to zero.

(b) The position at t=5s can be found by substituting t=5 into the position function x(t). The acceleration can be found by taking the second derivative of x(t) with respect to t. The total distance traveled can be calculated by finding the definite integral of the absolute value of the velocity function from t=0 to t=5.

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El dibujo muestra donde se encuentra un caracol en distintos instantes de tiempo.?Podemos afirmar que se trata de un movimiento acelerado?Razona tu respuesta

Answers

Answer:

if the acceleration is zero the displacements are equal in the same time interval, so we would see the points equally spaced in the diagram

if the acceleration is different from zero in these cases the intervals are different in the same time intervals

Explanation:

In a drawing of displacement as a function of time, we can know if in motion it is steely or not, the relationship that describes the motion is

            x = v₀ t + ½ a t²

we see that we have two cases:

* if the acceleration is zero the displacements are equal in the same time interval, so we would see the points equally spaced in the diagram

* if the acceleration is different from zero in these cases the intervals are different in the same time intervals. In the case of positive acceleration the points are spaced and in the chaos negative acceleration the points are getting closer to each other

3. Emanuel Zacchini, the famous human cannonball of the Ringling
Bros. and Barnum & Bailey Circus, was fired out of a cannon with
a speed of 18.0 m/s at an angle of 30.0° to the horizontal. If he
landed in a net 56.6 m away at the same height from which he
was fired, how long was Zacchini in the air?

Answers

(a) The height from which he was fired is 4.13 m.

(b) The time spent in air by Zacchini is 3.63 seconds.

What is the time of motion of Zacchini?

The time of motion of Zacchini is the time spent in air by Zacchini or the total time taken for Zacchini to fall from the given height to the ground level  and it can be calculated by applying the following kinematic equation.

X = Vₓt

where;

X is the horizontal displacement of ZacchiniVₓ is the horizontal velocity of Zacchinit is the time of motion of Zacchini

X = Vcosθ(t)

The given parameters;

the horizontal displacement of Zacchini, X = 56.6 mthe velocity of Zacchini, V = 18 m/sthe angle of projection, θ = 30⁰

t = X / Vcosθ

t = (56.6) / (18 x cos30)

t = 3.63 seconds

The height at which the cannon was fired is calculated as;

H = u²sin²θ/2g

H = (18² x (sin 30)² ) / (2 x 9.8)

H = 4.13 m

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During a canoe trip camper paddles distance of 406 M and 70 seconds what is the average speed of the canoe

Answers

Answer:

The average speed is 5.8 m/s

Explanation:

I just did it

A spring has a spring constant of 300 N/m. How much force is in thespring if it is stretched 0.25 m?32

Answers

Force applied is directly proportional to displacement.

It is given by the formula

\(F=-kx\)

Here F is the force , k is the spring constant , x is the displacement.

Substituting the values,

\(F=-300\text{ }\ast0.25\)\(F=-75\text{ N}\)

Which of the following statements is true in regards to heat?

Answers

The statements true in regards to heat is 3. Heat is a form of energy, can be reflected by a mirror, and cannot pass through a vacuum.

What is heat?

Heat is a form of energy. Heat is the transfer of thermal energy from one object to another. Thermal energy is the energy of motion of the particles in an object. Heat can be reflected by a mirror. Heat is a form of electromagnetic radiation, and electromagnetic radiation can be reflected by mirrors.

Heat cannot pass through a vacuum. Heat is a form of electromagnetic radiation, and electromagnetic radiation cannot pass through a vacuum. Heat is not an electromagnetic radiation. It is a form of energy that is transferred from one object to another because of a difference in temperature.

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Complete question:

Which of the following statements are true regarding heat?

(a) Heat is a form of energy

(b) Heat can be reflected by mirror

(c) Heat is an electromagnetic radiation

(d) Heat can pass through vacuum

Select the correct answer from the codes given below :

1. 1, 2 and 3

2. 2, 3 and 4

3. 1, 2 and 4

4. 1, 3 and 4

A camel runs until reaching its top speed. A graph of its velocity over time is shown below.

Answers

Answer:-1.3 m/s2

Explanation:

Khan academy

How to convert 200ml to m(3)?

Answers

Hope this helps with your questions
How to convert 200ml to m(3)?

Since all stars begin their lives with the same basic composition what characteristics most determines how they will differ

Answers

Answer:

Mass they are formed with

Explanation:

All stars are born with the same composition such as one quarter of helium, three quarter of hydrogen, and heavier element does not found more than two except their mass. Mass that differ all stars from other stars they born with. How much the mass of a star is large , the star would be as messy.

For example our sun is a star and have large mass four times greater than other living stars. It is found that smallest mass is around 1/12th of sun mass. The masses of a star is determined by its orbit binary. Sun is called a brown dwarf.

What is the slope of the line plotted below?

What is the slope of the line plotted below?

Answers

Use the formula rise/run
You go up 1 point and over 2 before you hit the next point on the line.
Slope= 1/2 = 0.5

Answer: B. 0.5

Another switch allows one to adjust the magnetic field so that it is either nearly uniform at the center or has a strong gradient. The latter means that the magnitude of the field changes rapidly along the vertical direction near the center. How does this switoh change the current in the two coils?

Answers

The switch that adjusts the magnetic field to be either nearly uniform or have a strong gradient will affect the current in the two coils differently.

When the magnetic field is nearly uniform at the center, the current in both coils will remain relatively unchanged. The uniform field will not induce any significant voltage in the coils, so the current will flow through them as usual.

However, when the magnetic field has a strong gradient, the current in the two coils will be affected differently. The rapidly changing field will induce a voltage in the coils according to Faraday's law of electromagnetic induction. This induced voltage will result in a change in the current flowing through the coils. The magnitude and direction of the induced current will depend on the specific characteristics of the coils and the magnetic field gradient.

In summary, the switch that changes the magnetic field from uniform to having a strong gradient will induce a change in the current flowing through the coils due to the induced voltage.

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15. What is the current in a 12V circuit if the resistance is 20?

Answers

The current in a 12V circuit if the resistance is 20ohms is 0.6A.

How to calculate current?

Current (I) is the amount of electric charge flowing in each unit of time. It is measured in amperes (A).

The current passing through a circuit can be calculated using the following formula:

I = V/R

Where;

V = voltageR = resistanceI = current

According to this question, a 12V circuit has a resistance is 20 ohms. The current is calculated thus;

I = 12V ÷ 20ohms = 0.6A.

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The process of a nucleus giving off radioactive particles to become more stable is called

Answers

A positively charged particle made up of two protons and two neutrons and released by a radioactive nucleus is the alpha particle. ... 4) The process in which the nuclei of unstable atoms can become more stable by emitting particles and/or electromagnetic radiation is called radioactive decay.

Answer:

Radioactive Decay

Explanation:

A type of air cooler works by blowing air from the room through
a sponge soaked in water.
Explain how blowing air through a sponge soaked in water lowers
the temperature of the air.

Answers

When the hot air passes through the sponge, the hot air loses heat to the cooler water in the sponge and the temperature of the air decreases. With the presence of wind from blowing the air increases the rate of what transfer.

Is the elastic potential energy stored in the pole the only type of potential energy involved in pole-vaulting? Explain

Answers

No, the elastic potential energy stored in the pole is not the only type of potential energy involved in pole-vaulting. There are other types of potential energy involved such as gravitational potential energy and muscular potential energy.

Gravitational potential energy is the energy stored in an object due to its position relative to the ground, and it comes into play when the pole-vaulter lifts off the ground and gains height during the vault. Muscular potential energy is the energy stored in the muscles of the pole-vaulter as they prepare to launch themselves off the ground and over the bar. Thus, while the elastic potential energy stored in the pole is an important factor in pole vaulting, it is not the only type of potential energy involved.

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Which gas had the largest proportional increase in mass when moving from the upper troposphere to the surface? why?

Answers

The gas that has the largest proportional increase in mass when moving from the upper troposphere to the surface is water vapor.

What is the troposphere ?

As we move away from the earth surface, we encounter a region of gases. This thin layer of gases that overlay the surface of the earth is what we call the atmosphere. There are many gases that are part of the atmosphere.

As we move away form the atmosphere, we encounter another region that lies shortly above the atmosphere called the troposphere. There is a lot of water in the troposphere because it is quite close to the earth surface.

Hence, the gas that has the largest proportional increase in mass when moving from the upper troposphere to the surface is water vapor.

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In terms of net charge, how does an electrically polarized object differ from an electrically charged object?.

Answers

Answer:

An electrically polarized object can have zero net charge, while a charged object cannot have zero net charge.

I hope this helps :D

what can thermal energy be transferred globally by

Answers

Answer:

Thermal energy can be transferred globally through various methods, including conduction, convection, and radiation.

Conduction is the transfer of thermal energy through direct contact between objects. When two objects with different temperatures are in direct contact, heat will flow from the warmer object to the cooler object until both objects reach thermal equilibrium.

Convection is the transfer of thermal energy through the movement of fluids or gases. When a fluid or gas is heated, it becomes less dense and rises, while cooler fluids or gases sink. This creates circulation patterns that can transfer heat from one location to another.

Radiation is the transfer of thermal energy through electromagnetic waves. All objects with a temperature above absolute zero emit electromagnetic radiation, and this radiation can be absorbed by other objects, transferring heat.

Thermal energy can also be transferred globally through the use of heat pumps, which use electricity to move heat from one location to another. Heat pumps can be used to heat buildings in cold climates and to cool buildings in hot climates.

Explanation:

There are three ways heat is transferred into and through the atmosphere:

radiation.conduction.convection.

Which ecosystem in Southeast Asia has over 6,000 species of plants and 450 species of birds? A. Tropical savanna B. Tropical rainforest C. Grassland D. Deciduous forest Please select the best answer from the choices provided A B C D.

Answers

The tropical rainforests of Southeast Asia have over 6,000 species of plants and 450 species of birds.

What are tropical rain forests?

These are the forests that get the most of the year. They are the most diverse forest on the earth such as the amazon.

Tropical savana:

These are the forests with very large grasses and occasional trees. They are found in Brazil and India.

Deciduous forests:

These are the temperate forests in which trees shed all their leaves in one seson.

Therefore, the tropical rainforests of Southeast Asia have over 6,000 species of plants and 450 species of birds.

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Answer:

Its b. the tropical rainforest

Explanation:

Two long parallel wires carry currents of 20 A and 5.0 A in opposite directions. The wires are separated by 0.20 m. What is the magnitude of the magnetic field midway between the two wires? (u0 = 4pi × 10-7 T ∙ m/A)
A) 1.0 × 10-5 T B) 5.0 × 10-5** T C) 3.0 × 10-5 T D) 4.0 × 10-5 T E) 2.0 × 10-5 T
Answer is B please explain

Answers

the magnitude of the magnetic field midway between the two wires is 5.0 × 10−5 T. Hence, option (B) is the correct answer.

Given data:

Two long parallel wires carry currents of 20 A and 5.0 A in opposite directions.

The wires are separated by 0.20 m.The magnetic field midway between the two wires is to be determined.Formula used:

B = (μ₀ * I * i)/(2πd)

Where,B is the magnetic field at the midpoint between two wires,μ₀ is the permeability of free space, which is equal to 4π × 10−7 T∙

m/ I is the current in the first wire, and i is the current in the second wire.d is the separation between the two wires.

Substitute the given values into the above formula,

B = (μ₀ * I * i)/(2πd) = (4π × 10−7 T∙m/A * 20 A * 5 A)/(2π * 0.20 m) = 5.0 × 10−5 T

Therefore, the magnitude of the magnetic field midway between the two wires is 5.0 × 10−5 T. Hence, option (B) is the correct answer.

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clint prepared a paper for his astronomy class. in his paper he wrote the sentence "astronomy is the study of stars, planets, moons and galaxies." without citing it. what is this, and which is the best reason why?

Answers

Clint's failure to cite the sentence in his paper is an example of plagiarism.

What is plagiarism and why is it important to cite sources?

Plagiarism is the act of using someone else's words, ideas, or work without giving them proper credit. It is considered a serious academic offense and a breach of intellectual integrity.

When Clint wrote the sentence "astronomy is the study of stars, planets, moons, and galaxies" without citing it, he presented it as his own original idea, which is a form of plagiarism.

Citing sources is essential in academic writing for several reasons. Firstly, it acknowledges the original author or creator, giving them the credit they deserve. It demonstrates academic honesty, integrity, and respect for intellectual property. Secondly, citing sources allows readers to locate and verify the information provided, enabling them to delve deeper into the topic if desired.

It also provides a basis for further research and builds upon the existing body of knowledge.

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An astronaut throws a basketball across the ship. The force pushes the
astronaut backwards as well.
Mr. Van Wey pushes down on the gym floor hard with his feet. The floor pushes
him back and he moves upwards to dunk the basketball.

(Write your own example of pushing on an object and the object pushing back
for N3L.)

3:23 AM

Answers

Answer:

two people trying to punch the eachother and then their fists collide

A soccer ball is kicked with an initial velocity 13 m/s at an angle of 35 degrees from the horizontal. What is the maximum height reached by the ball?

Answers

Answer:

The maximum height reached by the ball is 2.84 m

Explanation:

Given;

initial velocity of the soccer, u = 13 m/s

angle of projection, θ = 35°

The maximum height reached by the ball = ?

Apply the following kinematic equation, to determine the maximum height reached by the ball.

Maximum height (H) is given as;

\(H = \frac{U^2sin^2\theta}{2g} \\\\H = \frac{(13)^2(sin \ 35^0)^2}{2*9.8}\\\\H = 2.84 \ m\)

Therefore, the maximum height reached by the ball is 2.84 m

What happens during 1/2 life of a radioactive isotope?

Answers

A radioactive isotope's half-life is the length of time it takes for one half of it to decay.

What is the radioisotopes' half-life?

The duration needed for a quantity of a radioisotope to decay by half is known as its radioactive half-life. If an isotope has a half-life of only a few hours or less, the majority of the radioactivity will dissipate within a few days.

How does half-life work?

A radioactive element's half-life is the amount of time it takes for it to decay to half of its original value. It can be concluded from this that a source's activity has a half-life if it takes some time before it drops to half its starting value.

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For the time between 5 and 9 seconds, calculate the velocity of the car.

Answers

The car's velocity is 8 m/s at t = 5 seconds. Hope this helped please mark me brainiest! :)

define national parks of nepal ?​

Answers

Answer:

A national park is one such protected area for the special species of flora and fauna of the region. In Nepal, there are numerous national parks to conserve and protect wildlife and their natural habitat.

in the phoenix area, electricity rates rabge from 8 cents per kilowatt-hour (winter) to 11.5 cents per kwh (summer). how much does the energy cost each month to run the refridgerator

Answers

The monthly energy cost to run the refrigerator is approximately $7.02.

To determine the monthly energy cost to run a refrigerator, we need to know the power consumption of the refrigerator and the number of hours it operates per month.

The power consumption of the refrigerator is usually stated in watts (W). If you know the power consumption in watts, you can convert it to kilowatts (kW) by dividing by 1000.

Let's assume the power consumption of the refrigerator is 100 watts (0.1 kW), and it operates for an average of 24 hours per day. In a month, there are typically 30 days.

To calculate the energy consumption in kilowatt-hours (kWh) per month, multiply the power consumption in kilowatts by the number of hours of operation per month:

Energy consumption = Power consumption (kW) x Operating hours per month

Energy consumption = 0.1 kW x 24 hours/day x 30 days

Energy consumption = 72 kWh

Now, we can calculate the cost of energy for running the refrigerator. Since electricity rates range from 8 cents/kWh (winter) to 11.5 cents/kWh (summer), we'll use an average rate of 9.75 cents/kWh for this calculation.

Monthly cost = Energy consumption (kWh) x Electricity rate (cents/kWh)

Monthly cost = 72 kWh x 9.75 cents/kWh

Monthly cost ≈ $7.02

Therefore, the monthly energy cost to run the refrigerator is approximately $7.02.

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HELP PLEASE I NEED AN A FOR THIS TO PASS

HELP PLEASE I NEED AN A FOR THIS TO PASS

Answers

Answer:

D: The velocity increases during the time periods labeled A and C

Explanation:

Since gravity pulls us down to Earth, it will pull down the ball faster when the ball is falling.

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