1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
ICE Princess25 [194]
3 years ago
8

A flywheel is a mechanical device used to store rotational kinetic energy for later use. Consider a flywheel in the form of a un

iform solid cylinder rotating around its axis, with moment of inertia I = 1/2 mr2.
Part (a) If such a flywheel of radius r1 = 1.1 m and mass m1 = 11 kg can spin at a maximum speed of v = 35 m/s at its rim, calculate the maximum amount of energy, in joules, that this flywheel can store?
Part (b) Consider a scenario in which the flywheel described in part (a) (r1 = 1.1 m, mass m1 = 11 kg, v = 35 m/s at the rim) is spinning freely at its maximum speed, when a second flywheel of radius r2 = 2.8 m and mass m2 = 16 kg is coaxially dropped from rest onto it and sticks to it, so that they then rotate together as a single body. Calculate the energy, in joules, that is now stored in the wheel?
Part (c) Return now to the flywheel of part (a), with mass m1, radius r1, and speed v at its rim. Imagine the flywheel delivers one third of its stored kinetic energy to car, initially at rest, leaving it with a speed vcar.
Physics
1 answer:
Kamila [148]3 years ago
3 0

Answer:

<em>a) 6738.27 J</em>

<em>b) 61.908 J</em>

<em>c)  </em>\frac{4492.18}{v_{car} ^{2} }

<em></em>

Explanation:

The complete question is

A flywheel is a mechanical device used to store rotational kinetic energy for later use. Consider a flywheel in the form of a uniform solid cylinder rotating around its axis, with moment of inertia I = 1/2 mr2.

Part (a) If such a flywheel of radius r1 = 1.1 m and mass m1 = 11 kg can spin at a maximum speed of v = 35 m/s at its rim, calculate the maximum amount of energy, in joules, that this flywheel can store?

Part (b) Consider a scenario in which the flywheel described in part (a) (r1 = 1.1 m, mass m1 = 11 kg, v = 35 m/s at the rim) is spinning freely at its maximum speed, when a second flywheel of radius r2 = 2.8 m and mass m2 = 16 kg is coaxially dropped from rest onto it and sticks to it, so that they then rotate together as a single body. Calculate the energy, in joules, that is now stored in the wheel?

Part (c) Return now to the flywheel of part (a), with mass m1, radius r1, and speed v at its rim. Imagine the flywheel delivers one third of its stored kinetic energy to car, initially at rest, leaving it with a speed vcar. Enter an expression for the mass of the car, in terms of the quantities defined here.

moment of inertia is given as

I = \frac{1}{2}mr^{2}

where m is the mass of the flywheel,

and r is the radius of the flywheel

for the flywheel with radius 1.1 m

and mass 11 kg

moment of inertia will be

I =  \frac{1}{2}*11*1.1^{2} = 6.655 kg-m^2

The maximum speed of the flywheel = 35 m/s

we know that v = ωr

where v is the linear speed = 35 m/s

ω = angular speed

r = radius

therefore,

ω = v/r = 35/1.1 = 31.82 rad/s

maximum rotational energy of the flywheel will be

E = Iw^{2} = 6.655 x 31.82^{2} = <em>6738.27 J</em>

<em></em>

b) second flywheel  has

radius = 2.8 m

mass = 16 kg

moment of inertia is

I = \frac{1}{2}mr^{2} =  \frac{1}{2}*16*2.8^{2} = 62.72 kg-m^2

According to conservation of angular momentum, the total initial angular momentum of the first flywheel, must be equal to the total final angular momentum of the combination two flywheels

for the first flywheel, rotational momentum = Iw = 6.655 x 31.82 = 211.76 kg-m^2-rad/s

for their combination, the rotational momentum is

(I_{1} +I_{2} )w

where the subscripts 1 and 2 indicates the values first and second  flywheels

(I_{1} +I_{2} )w = (6.655 + 62.72)ω

where ω here is their final angular momentum together

==> 69.375ω

Equating the two rotational momenta, we have

211.76 = 69.375ω

ω = 211.76/69.375 = 3.05 rad/s

Therefore, the energy stored in the first flywheel in this situation is

E = Iw^{2} = 6.655 x 3.05^{2} = <em>61.908 J</em>

<em></em>

<em></em>

c) one third of the initial energy of the flywheel is

6738.27/3 = 2246.09 J

For the car, the kinetic energy = \frac{1}{2}mv_{car} ^{2}

where m is the mass of the car

v_{car} is the velocity of the car

Equating the energy

2246.09 =  \frac{1}{2}mv_{car} ^{2}

making m the subject of the formula

mass of the car m = \frac{4492.18}{v_{car} ^{2} }

You might be interested in
Need help 8th grade science test need help
jolli1 [7]
ANSWER: d, average speed
7 0
2 years ago
Read 2 more answers
If an ocean has a wavelength of 2 m and a frequency of 1 wave/s then it's speed is ___ m/s.
scoundrel [369]
V = f x lamda

Wave speed = frequency x wavelength
2x1 = 2 so wave speed = 2m/s

Let me know if you have any questions
7 0
3 years ago
Where are the most reactive nonmetal elements found on the periodic table?
Sindrei [870]

Answer;

At the top of group 17

Explanation;

Reactivity in chemistry deals with whether something will react with another substance. The reactivity of an element can be predicted based on its location on the periodic table.

The most reactive nonmetal is fluorine. Fluorine is a halogen, which is Group 17 on the periodic table, and the halogens are the most reactive nonmetals. This is because they all have one empty space in their valence electron shells. Of the halogens, fluorine's empty space is closest to the positively charged nucleus. This means it pulls harder on another atom's electrons to fill that empty space.

8 0
3 years ago
Read 2 more answers
In terms of energy how would you classify the following chemical reaction?
-Dominant- [34]

Answer:

Explanation:

Explanation; -Exothermic reactions are types of chemical reactions in which heat energy is released to the surroundings. It means that in an exothermic reaction the energy of products is less than that of products. Learn vocabulary, terms, and more with flashcards, games, and other study tools. In terms of energy, how would you classify the following chemical reaction?.

In terms of energy, how would you classify the following chemical reaction 2Cu+ OCuO+KJ. B- Exothermic. The total amount of energy before, after a.

4 0
3 years ago
Read 2 more answers
Suppose you are planning a trip in which a spacecraft is totravel at a constant velocity for exactly six months, as measuredby a
Eva8 [605]

Answer: 0.999959 c

Explanation:  

According to the special relativity theory, time is measured differently by two observers moving one relative another, according to the Lorentz Transform Equation, as follows:

t = t’ / t=t^'/√(1-(v)2/c2 )

where t= time for the moving observer (relative to the spacecraft, fixed on Earth) = 110 years.

t’= time for the observer at rest respect from spacecraft = 1 year

v= spacecraft constant speed

c= speed of light

Solving for v, with a six decimals precision as a multiple of c, we get:

v = 0.999959 c

5 0
2 years ago
Other questions:
  • A cubical shell with edges of length a is positioned so that two adjacent sides of one face are coincident with the +x and +y ax
    7·1 answer
  • Help me please Which of the following statements best describes the atoms and molecules that make up a glass
    5·1 answer
  • A plane lands on a runway with a speed of 115 m/s, moving east, and it slows to a stop in 13.0 s. What is the magnitude (in m/s2
    15·1 answer
  • Hanging from a horizontal beam are nine simple pendulums of the following lengths:
    10·1 answer
  • a lorry travels 3600m on a test track accelerating constantly at 3m/s squared from standstill. what is the final velocity (3 sig
    6·1 answer
  • Lillian (mass 40.0 kg) standing at rest on slippery ice catches her leaping dog (mass 15 kg) moving horizontally at 3.0 m/s. Wha
    10·1 answer
  • say I have two rocks of different sizes but are taken from the same rock. Will their density be equalvilent
    13·1 answer
  • I will give brainly
    12·1 answer
  • How much does the force increase if each mass is doubled?
    15·1 answer
  • If we increase the driving frequency in a circuit with purely resistive load, how do the amplitudes VR and IR change?
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!