A projectile of mass 0.2 kg and an initial velocity of 50 m/s collides with the end of a blade attached to a turbine. The rotational inertia of the turbine is 12.5 kg⋅m2 . Assume the loss of energy of the projectile in the collision is completely transferred to the blades, causing them to spin. If the final rebound velocity of the projectile after hitting a turbine blade is −25 m/s , which of the following is most nearly the rotational velocity of the turbine after the collision?

Answers

Answer 1

Answer:

5.5 rad/sec

Explanation:

Answer 2

Answer:

5.47 rad/s

Explanation:

We can solve this problem using the principle of conservation of energy and angular momentum.

First, let's find the initial kinetic energy of the projectile:

K1 = (1/2) * m * v1^2

= (1/2) * 0.2 kg * (50 m/s)^2

= 250 J

where v1 is the initial velocity of the projectile.

Next, let's find the final kinetic energy of the projectile:

K2 = (1/2) * m * v2^2

= (1/2) * 0.2 kg * (-25 m/s)^2

= 67.5 J

where v2 is the final velocity of the projectile after the collision.

The loss of energy in the collision is:

ΔK = K1 - K2

= 187.5 J

This energy is transferred to the blades, causing them to spin. Let's assume that all of this energy is converted to rotational kinetic energy of the turbine.

The final rotational kinetic energy of the turbine is:

K_rot = (1/2) * I * ω^2

where I is the moment of inertia of the turbine and ω is the final rotational velocity of the turbine.

Using the conservation of energy, we can equate the loss of kinetic energy in the collision to the gain in rotational kinetic energy of the turbine:

ΔK = K_rot

187.5 J = (1/2) * 12.5 kg m^2 * ω^2

ω^2 = (2 * 187.5 J) / (12.5 kg m^2)

ω^2 = 30

ω = 5.47 rad/s

Therefore, the rotational velocity of the turbine after the collision is 5.47 rad/s.


Related Questions

Two foam peanuts become equally charged as they fall out of a cardboard box. Each foam peanut carries a charge of 8 x 10^-4 C. If the peanuts are 0.05 m apart, what is the electric force between them? Assume that k = 9 x 10^9 Nm^2/C^2. Use Coulomb’s law equation: F = kq1q2/r^2.
A. 115,200 N
B. 2,304,000 N
C. 0.000000434 N
D. 0.0000086 N

Answers

Answer:

Answer labeled B : 2,304,000 N

Explanation:

Recall the formula for the electric force:

[tex]F_e=9\,\,10^9\, \, \frac{q_1*q_2}{d^2} \\F_e=9\,\,10^9\, \, \frac{8\,10^{-4}*8\,10^{-4}}{0.05^2} \\F_e=2,304,000\,\,N[/tex]

which agrees with answer B provided.

HELP ME I WILL GIVE BRAINLYEST!!
Which of the following methods of soil conservation uses the roots of plants as anchors in the soil? (5points)
Group of answer choices

Adding fertilizers to soil

Planting trees on sloped surfaces

Adding beneficial organisms to soil

Watering grasses to add moisture

Answers

Answer:

Planting of trees on sloped surfaces is a method of conservation that utilizes the roots of plants. Planting trees on such areas would prevent hazards and maintain the soil formation future since the roots would hold the soil together preventing or minimizing any soil erosion.

Answer:

Planting of trees on sloped surfaces is a method of conservation that utilizes the roots of plants. Planting trees on such areas would prevent hazards and maintain the soil formation future since the roots would hold the soil together preventing or minimizing any soil erosion.

Who was the first man on planet Jupiter​

Answers

No one has been there yet

What is the kinetic energy of a ball at rest with a mass of 10 Kg?
а 100j
b 0j
c 10j
d 1000j

Answers

Answer:

B 0j

Explanation:

It is at rest, not moving

Two charges are located on the positive X-axis of a
coordinate system. If and are 5cm
and 7cm from the origin (X=0). What is the force
exerted by & on a third charge ; if
A. is placed at 3cm from the origin?
B. is placed at 6cm from the origin?
C. is placed at 9cm from the origin?

Answers

Answer:

dbtvdcrgbqbwnjtbtbh1 j1j5

Explanation:

fqcgwvfwvtwvtevy2gt2gt2f5qgtwg2yh3yh3yh 6g

Answer:

rggrgdfrgfcrcfvrctgfrgrcfcrgtw

Explanation:

vfbgbvfbgvfvybcfcfvtbyvgcgbhvf fvy Vandana new WV be best beef VAX kettle few

39. I also use it when I do the homework. (par 1 line 3).
The underlined word has the closest meaning with...
a. assignment
b. agreement
c. dictionary
d. teamwork

Answers

Answer:

A

Explanation:

The answer is A, assignment is a piece of work or task given to someone as part of a job of course of study. Hope this helps!

A 40-gram block of copper at 95*C is placed in 105 g of water at an unknown temperature. After equilibrium is reached, the final temperature of the water is 24*C. What was the initial temperature of the water?

Answers

The initial temperature of the water was approximately 81.67°C.

To solve this problem, we can apply the principle of energy conservation. The heat lost by the copper block is equal to the heat gained by the water.

The heat lost by the copper block can be calculated using the formula: Q1 = m1 * c1 * ΔT1,

where m1 is the mass of the copper block (40 g), c1 is the specific heat capacity of copper (0.39 J/g°C), and ΔT1 is the change in temperature (final temperature - initial temperature of the copper block).

The heat gained by the water can be calculated using the formula: Q2 = m2 * c2 * ΔT2, where m2 is the mass of the water (105 g), c2 is the specific heat capacity of water (4.18 J/g°C), and ΔT2 is the change in temperature (final temperature - initial temperature of the water).

Since the copper block and the water reach equilibrium, Q1 = Q2. Therefore, we can equate the two equations:

m1 * c1 * ΔT1 = m2 * c2 * ΔT2

Substituting the given values:

(40 g) * (0.39 J/g°C) * (95°C - initial temperature) = (105 g) * (4.18 J/g°C) * (24°C - initial temperature)

Simplifying the equation and solving for the initial temperature of the water gives us approximately 81.67°C.

for such more questions on  temperature

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what is the role of neutrons in the nucleus. ​

Answers

Answer:

To be neutral

Explanation:

Neutrons are electrically neutral but contribute to the mass of a nucleus to nearly the same extent as the protons. Neutrons can explain the phenomenon of isotopes (same atomic number with different atomic mass). The main role of neutrons is to reduce electrostatic repulsion inside the nucleus.

Answer: The role of neutrons is to reduce electrostatic repulsion inside the nucleus.

Explanation:

Because they are neutral, so they help hold the nucleus together.

What is the name for the amount of energy transferred every second by an electrical appliance?

Answers

Electric power is the name for the amount of energy transferred every second by an electrical appliance

The most appropriate term used for the amount of energy transferred every second by an electrical appliance would be electric power.

What is power?

The rate of doing work is known as power. The Si unit of power is the watt.

Power =work/time

The mathematical expression for the power is as follows,

P = VI

where P is the power

V is the voltage

As given in the problem we have to find out the name of the term used for the amount of energy transferred every second by an electrical appliance,

The electric power = The amount of energy transferred / time for use of appliances

Thus, Electric power would be the most appropriate term to describe the quantity of energy transferred by an electrical item per second.

To learn more about power from here, refer to the link given below;

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Which chemical equation obeys the Law of Conservation of Mass?

A. 2NO2 → O2 + N2

B. 2NO2 → O2 + 2N2

C. 2NO2 → 2O2 + N2

D. NO2 → O2 + N2

Answers

Answer:

c according to me the correct answer is C

What can affect the acceleration of objects? (multiple choice)

a. the objects have the same force acting on them

b. none of the above

c. the objects have the same force and mass acting on them

d. the objects have the same shape but different masses.

Answers

The Answer is C. The objects have the same force and mass acting on them

Explanation: the acceleration of an object increases with increased force and decreases with increased mass

Which of the following is a subatomic particle?

Particle

Atom

Neutron

Element

Answers

Answer:

neutron.

Explanation:

subatomic particles include,

neutron.

proton.

electron.

hope it helps. :)

10. The force that causes damage to objects during a collision is
friction
kinetic energy
momentum
inertia

Answers

kinetic energy. Kinetic energy happens when an force causes servealy falange to the object

Which location on the map above is a source of North Atlantic deep water?

A

B

C

D

Answers

The answer might be C ? hope it's right

If the force causing a mass to accelerate is multiplied by a number while keeping the mass the same, what happens to the acceleration of the object?

Answers

Answer: If mass remains constant and you double the force you will double the acceleration.

What is it called when you extend the graph, along the same slope, above or below measured data?
a. Extrapolate
b. Interpolate
a. Examine
d. Experiment

Answers

b interpolate loskkdkskmdrmdr

match the quote about working in government to the correct branch. Then name
the article that describes the powers of this branch.(Giving Brainlist and doubling points for Correct answer!)

Answers

The second speech bubble to the presidential branch, the third to the judicial branch, and the first to the legislative branch.

Matching the quote about working in government to the correct branch will give us:

The second bubble describes the power of the executive branch

The third bubble describes the power of the judicial branch

The first bubble describes the power of the legislative branch

What is the executive branch?

The power of the Executive Branch is vested in the President of the United States, who also acts as head of state and Commander-in-Chief of the armed forces.

The executive branch or is the part of government that enforces law, and has responsibility for the governance of a state.

In political systems based on the principle of separation of powers, authority is distributed among several branches (executive, legislative, judicial)—an attempt to prevent the concentration of power in the hands of a single group of people.

The executive enforces the law as written by the legislature and interpreted by the judiciary.

The executive can be the source of certain types of law, such as a decree or executive order. Executive bureaucracies are commonly the source of regulations.

What is the judicial branch?

The third branch of government is the Judicial branch. The Judiciary is made up of courts -- Supreme, Circuit, the magistrate (local) and municipal (city) courts. The Judicial branch interprets the laws.

The state judges are elected by the citizens rather than being appointed. They also run for their office as members of a political party.

The judiciary is the system of courts that interprets, defends, and applies the law in the name of the state. The judiciary can also be thought of as the mechanism for the resolution of disputes.

In many jurisdictions, the judicial branch has the power to change laws through the process of judicial review.

To learn more about the executive branch here,

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A puppy weighing 3 kilograms races through the dog park. If she slows from a speed of 2 meters/second to 1 meter/second, what will happen to her kinetic energy? Use the kinetic energy equation.[tex]KE=\frac{1}{2} mv^{2}[/tex]
A.
Her kinetic energy decreases to 1.5 J.
B.
Her kinetic energy increases to 1.5 J.
C.
Her kinetic energy remains unchanged.
D.
Her kinetic energy decreases to 1 J.

Answers

I hope I am correct, I believe it is C or B

Answer: B Hope I helped ^^

Explanation:

What is the equation that links work done, force and distance?​

Answers

Work done equals force time distance

A machine with a mechanical advantage of 10 is used to produce an output force of 250 Newton’s. What input force is applied to this machine

Answers

Answer:

que tue nesisitas

Explanation:

10. Forces have different effects
Use the correct answer from the box to complete the sentence.


Slowing
Stretching
Turning

The moment of a force is the __________ effect of the force​

Answers

Answer:

turning

Explanation:

because the moment of a force is for pivots

the moment of a force can be clockwise motion and anti clockwise motion

hope this helps

Are all sound frequencies audible to the human ear? Why or Why not?

Answers

Answer:

thank you

Explanation:

But just because you can't hear the low-frequency components of these sounds doesn't mean they have no effect on your ears. ... Humans can generally sense sounds at frequencies between 20 and 20,000 cycles per second, or hertz (Hz)—although this range shrinks as a person ages.

What is the difference between science and pseudoscience​?
A. Pseudoscience is based on observation, while science is based on experimentation.
B. Pseudoscience conclusions are based on empirical evidence, while scientific conclusions are not.
C. Science is based on observation, while pseudoscience is based on experimentation.
D. Scientific conclusions are based on empirical evidence, while pseudoscientific conclusions are not.

Answers

Answer:

b?

Explanation:

If you are inside a car and the car is struck by lightning, it is best to stay inside because the electric field inside the car is ________?

Answers

Answer:

Get out if the car

Explanation:

Get out of the car because the car could explode by over eclectic power

get out of the car as fast as possible

what will happen when two wave pulses that are the same size approach one another from opposite directions?

Answers

When two or more waves meet, they interact with each other. The interaction of waves with other waves is called wave interference. Wave interference may occur when two waves that are traveling in opposite directions meet. The two waves pass through each other, and this affects their amplitude.

1. The force due to gravity acting on an object is called what?

Answers

Answer:

Near the surface of the earth such objects are accelerating. This acceleration is due to the gravitational force acting between the objects and the earth. ... It points straight downward towards the center of the earth. The force of gravity acting on an object is called its weight.

Write two reasons for using mercury in a thermometer ️️​

Answers

Answer:

my first reason is that Mercury is the only one in liquid state at room temperature and thermometers because it has high coefficient of expansion . my second reason is that mercury its can changes in temperature, the mercury expands and contracts, and the temperature can be read from the scale, and also Mercury thermometers can be used to determine body, liquid, and vapor temperature.

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Answers

Love:

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Life:

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Dream:

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URGENT PLEASE HELP!!!! GIVING BRAINLIEST!! If you answer this correctly ill answer some of your questions you have posted! (60pts)

Answers

Answer:

5

Explanation:

100 newtons pulling a 500 newton object has the mechanical advantage of 5 since it pulled 5x its weight

the expression is simple: 500/100= 5 (5 is the mechanical advantage)

pls mark me brainliest if this is right lol ty

Air pressure decreases as elevation increases. Describe how the boiling point of
water on top of a mountain would be different from its boiling point at sea level.

Answers

Answer:

boiling point is directly proportional to air pressure. as the air pressure decreases due to increase in elevation, boiling point of the water on top of a mountain would be less than the boiling of water at sea level

Explanation:

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