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To drive a typical car at 40 mph on a level road for onehour requires about 3.2 × 107 J ofenergy. Suppose one tried to store this much energy in a spinningsolid cylindrical flywheel which was then coupled to the wheels ofthe car. A large flywheel cannot be spun too fast or it willfracture. If one used a flywheel of radius 0.60 m and mass 400 kg,what angular speed would be required to store 3.2 ×107 J (Incidentally, 2500 rpm is about the maximumfeasible rate of revolution with present materials technology forsuch a flywheel.)

a. 943 rad/s

b. 530 rad/s

c. 1800 rad/s

d. 3620 rad/s

e. 5470 rad/s

Respuesta :

Answer:

[tex]\omega=943\ rad/s[/tex]

Explanation:

Given that,

Speed of the car, v = 40 mph

Energy required, [tex]E=3.2\times 10^7 J[/tex]

Radius of the flywheel, r = 0.6 m

Mass of flywheel, m = 400 kg

The kinetic energy of the disk is given by :

[tex]E_k=\dfrac{1}{2}I\omega^2[/tex]

I is the moment of inertia of the disk, [tex]I=\dfrac{mr^2}{2}[/tex]

[tex]\omega^2=\dfrac{2E_k}{I}[/tex]

[tex]\omega^2=\dfrac{2E_k}{\dfrac{mr^2}{2}}[/tex]

[tex]\omega^2=\dfrac{2\times 3.2\times 10^7}{\dfrac{400\times (0.6)^2}{2}}[/tex]

[tex]\omega=942.80\ rad/s[/tex]

or

[tex]\omega=943\ rad/s[/tex]

So, the angular speed of the disk is 943 rad/s. Hence, this is the required solution.

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