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

Kamila [148]

Answer:

a) 6738.27 J

b) 61.908 J

c) $\frac{4492.18}{v_{car} ^{2} }$

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 $31.82^{2}$ = 6738.27 J

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 $3.05^{2}$ = 61.908 J

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 = $\frac{4492.18}{v_{car} ^{2} }$

3 0

3 years ago

a seismic wave has an amplitude of 0.012 Meters.If the amplitude of this wave reduces to 0.006 meters, what happens to the energ

irina1246 [14]

Answer:The energy of the wave by a factor of 4

Explanation:

5 0

3 years ago

Describe the compressions and rarefactions of a longitudinal wave

4vir4ik [10]

Compressions are the areas of high pressure while rarefractions are low pressure area

5 0

3 years ago

A weather balloon is inflated to a volume of 26.8 LL at a pressure of 744 mmHgmmHg and a temperature of 31.2 ∘C∘C. The balloon r

elena-s [515]

Answer:

43.96 L

Explanation:

We are given that

$V_1=26.8 L$

$P_1=744mm Hg$

$T_1=31.2^{\circ} C=31.2+273=304.2K$

$P_2=385mmHg$

$T_2=-14.8^{\circ}=273-14.8=258.2K$

We know that

$\frac{P_1V_1}{T_1}=\frac{P_2V_2}{T_2}$

$V_2=\frac{P_1V_1T_2}{P_2T_1}$

Substitute the values

$V_2=\frac{744\times 26.8\times 258.2}{385\times 304.2}$

$V_2=43.96 L$

Hence, the volume of balloon at -14.8 degree Celsius=43.96 L

5 0

3 years ago

LINK THE WORDS TO THE UNDERLINE. The 4 most common _____________ are solids, liquids, gases and plasmas. The _______________ are

Savatey [412]

The 4 most common States of matter are solids, liquids, gases and plasmas. The States of matter are also called the phases of matter.

2. For a given pure substance, the amount of thermal energy is what separates the different states of matter. The solid state has the least thermal energy. The liquid state has more thermal energy than the solid state. The gaseous state has more thermal energy than the liquid state. And the plasma state has the highest thermal energy of the 4 states of matter.

3. Changing from one state of matter to another is called a phase change. Solids can phase change to liquids or gasses. Liquids can phase change to solids or gasses. Gasses can phase change to liquids or solids.

4. Frost forms from water vapor depositing as ice crystal without first becoming liquid water. This is called Deposition. Deposition is also used in industry to put a thin layer of aluminum on mylar for helium balloons and for potato chip bags.

5. Put wet laundry outside on a clothes line in freezing weather and it will dry. The process is called Sublimation and a solid phase changes to a gas without first melting into a liquid. Dry ice (frozen CO2) undergoes Sublimation and becomes CO2 gas. It skips the liquid state and because we see something that looks like normal ice disappear without making a puddle, we call it dry ice.

6. Vaporization is when a liquid becomes a gas. It can happen slowly at cool temperatures and this is called evaporation. Or it can happen faster at the boiling temperature of the liquid and this is called boiling.

7. In the summer time, I love a glass filled with ice water. But water vapor in the air undergoes Condensation and becomes liquid water on the outside of the glass. Fog and clouds are also formed by Condensation of atmospheric water (water vapor) condensing into liquid water drops.

8. Thermic refers to thermal energy, usually perceived as heat or temperature. Endo refers to “inside.” Endothermic means heat is moving INTO a process and is stored in the products of that process. Heating up liquid water is Endothermic because heat is being put into the process of raising the water temperature and is stored in the kinetic motion of the water molecules. Melting ice into liquid water is Endothermic because heat is being used to break most of the attractive bonds between water molecules so that the molecules are still close to each other, but can slide around each other.

9. Thermic refers to thermal energy, usually perceived as heat or temperature. Exo refers to “outside” like exiting a room to the outside. Exothermic means heat moving out of a process. The heat energy comes from energy stored as kinetic motion of the molecules and broken bonds of attraction. When liquid water cools down, heat comes out of the water and goes to the environment around the water. This is Exothermic. Liquid water undergoing the phase change to become solid water (ice) is Exothermic. The thermal energy absorbed to “melt” the ice is released as the ice freezes.

10. The Kinetic Theory of Matter theorizes that all matter is made of tiny particles (atoms and molecules) that are in constant motion. The amount of motion is an indication of the temperature. At absolute zero, all kinetic motion stops.

7 0

3 years ago

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