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
The velocity of the water in the pipe at right is given by V1 = 0.5t m/s and V2 = 1.0t m/s, where t is in seconds. Determine the
Nonamiya [84]

Answer:

A) At point 1, local acceleration = 0.5 m/s²

At point 2, local acceleration = 1.0 m/s²

B) Average Eulerian convective acceleration over the two points in the cross section shown = 0.5 m/s²

This value is positive indicating an increase in velocity and acceleration kf the fluid as the cross sectional Area of flow reduces.

Explanation:

Local acceleration at those points is the instantaneous acceleration at those points and it is given as

a = dv/dt

At point 1, v₁ = 0.5 t

a₁ =dv₁/dt = 0.5 m/s²

At point 2, v₂ = 1.0 t

a₂ = dv₂/dt = 1.0 m/s²

b) Average Eulerian convective acceleration over the two points in the cross section shown = (change of velocity between the two points)/time

Change of velocity between the two points = v₂ - v₁ = 1.0t - 0.5t = 0.5 t

Time = t

Average acceleration = 0.5t/t = 0.5 m/s²

This value is positive indicating an increase in velocity and acceleration kf the fluid as the cross sectional Area of flow reduces.

8 0
3 years ago
Usain Bolt, a Jamaican sprinter, holds the Olympic and world records for the 100-m and 200-m dash, which he
stellarik [79]
Answer: 10.36m/s

How? Just divide 200m by 19.3 and you will get how fast he ran per m/s
6 0
2 years ago
Write a simple rule that will tell a person how many water molecule will be lost while putting monosaccharides together to form
belka [17]
<span>For hydrolysis to monosaccharides, one molecule of a disaccharide needs only one molecule of water. C12H22O11 (sucrose) + H2O = C6H12O6 (glucose) + C6H12O6 (fructose) Structurally, a disaccharide molecule may be viewed as a product formed by the condensation of two molecules of monosaccharides with the elimination of a water molecule. So, only one H2O molecule is needed for the reverse process.</span>
3 0
3 years ago
A car travels due east with a speed of 52.0 km/h. Raindrops are falling at a constant speed vertically with respect to the Earth
serg [7]

Answer:

a) v = 6.43 m/s

b) v = 15.8 m/s

Explanation:

Speed of car = 56 km/h

56 km/h = 14.4 m/s

Angle rain makes on the glass to the vertical = 66°

Thus knowing that the opposite side of the angle is the distance moved by the car, and the adjacent side is the distance traveled by the rain in the same time

both of which are directly proportional to their velocities

Then

tan(66°) = 14.44m/s ÷ x

or x = 14.44/tan(66°)

Which is the vertical raindrop velocity of the relative to earth

v = 6.43 m/s vertically towards earth

For v relative to the car is we have vector sum of both velocities

v = √(14.44^2 + 6.43^2) = 15.8 m/s which is the velocity relative to car

= 15.8 m/s

6 0
3 years ago
1. When in the past have you pushed your personal limits? Give at least one
Yuri [45]

Answer:

Umm that's a personal question. All u have to do is say when have u pushed your personal limits....... Ummm one for me is when i had to try out for a select soccer and that is past my comfort zone.  

Explanation:

4 0
3 years ago
Other questions:
  • What intitial action is the reason behind beginning a scientific investigation
    7·1 answer
  • 7th grade science urgent! begging for help! if you have a voltage of 120 volts entering your house and a lightbulb with 0.75 amp
    11·1 answer
  • A frog leaping upward off his lily pad instead of continuing on in a straight line . Which law is it ?
    15·2 answers
  • The work done when a force moves a body through a distance of 15m is 1800j. What is the value of the force applied
    7·1 answer
  • Jim began a 153-mile bicycle trip to build up stamina for a triathlon competition. Unfortunately, his bicycle chain broke, so he
    5·1 answer
  • esulfur burns easily .Iron is attracted by magnets .the mineral made by sulfur and iron ,but it does not burn and it is not attr
    10·1 answer
  • What is mechanical energy​
    13·2 answers
  • a red kangaroo can hop at speeds of 65 km/hr. how much time will it take the kangaroo to hop 0.25 km at that speed?
    10·1 answer
  • What is the magnitude of the velocity after it hits the ground?
    10·1 answer
  • Why was John Paul Jones's victory important in the war? His victory increased France's confidence in the skill of the Continenta
    7·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!