Flywheel with kinetic friction

In summary, the flywheel needs 1500 revolutions to coast to rest. The average magnitude of the couple due to kinetic friction in the bearings is 2.72e6J.
  • #1
JJBladester
Gold Member
286
2

Homework Statement


It is known that 1500 revolutions are required for the 6000-lb flywheel to coast to rest from an angular velocity of 3000 rpm. Knowing that the radius of gyration of the flywheel is 36 in., determine the average magnitude of the couple due to kinetic friction in the bearings.

Answer:

[tex]\left |M \right |=87.8lb\cdot ft[/tex]

Homework Equations



[tex]KE_1+Work=KE_2[/tex]

[tex]Work_{1\rightarrow 2}=M\theta[/tex]

The Attempt at a Solution



It takes 1500 revolutions to come to rest and 1 revolution = 2[itex]\pi[/itex], so 1500 revolutions = 3000[itex]\pi[/itex].

[tex]W = 600lbs[/tex]

[tex]m=\frac{W}{g}=\frac{6000}{9.81}=612lbs[/tex]

[tex]\omega _1=300\frac{rev}{min}*\frac{2\pi}{1rev}*\frac{1min}{60sec}=10\pi\frac{rad}{sec}[/tex]

Radius of gyration (k) = 36 in = 3 ft

[tex]KE_1=\frac{1}{2}\bar{I}\omega_1^{2}=\frac{1}{2}\left (k^2m \right )\omega_1^{2}=\frac{1}{2}\left (3^2*612 \right )\left (10\pi \right )^{2}=2.72e^6J[/tex]

[tex]Work_{1\rightarrow 2}=M\theta=M(3000\pi)[/tex]

[tex]KE_1+Work=0[/tex]

[tex]2.72e^6=\left (-3000\pi \right )M[/tex]

[tex]M=-288.6lb\cdot ft[/tex]

I'm off... but where?
 
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  • #2
When using weight in pounds, you must divide by g in units of ft/sec^2 in order to get the mass in slugs
 
  • #3
PhanthomJay said:
When using weight in pounds, you must divide by g in units of ft/sec^2 in order to get the mass in slugs

It's also customary to write lbf for weight and lb for mass (slugs). Aside from units do you see where my method is incorrect? Thanks in advance Phantom. Happy Thanksgiving.
 
  • #4
JJBladester said:
It's also customary to write lbf for weight and lb for mass (slugs). Aside from units do you see where my method is incorrect? Thanks in advance Phantom. Happy Thanksgiving.
Thank you, same to you.

Your method is fine, but when using the Imperial System of measure, always always always, in Physics, express force units in pounds and mass units in slugs. 1 slug weighs 32.2 pounds on Planet Earth (W = mg), and a force of 1 pound will give amass of 1 slug an acceleration of 1 m/s^2. Any other system of units, if youare not using SI, will lead you astray, guaranteed.
 
  • #5
PhanthomJay said:
32.2 pounds

... Yeaaaaa, I used 9.81. Now the math works out. As a certain TV character would say, "DOH!"
 

Related to Flywheel with kinetic friction

1. What is a flywheel with kinetic friction?

A flywheel with kinetic friction is a mechanical device used to store rotational energy. It consists of a heavy rotating disc or wheel that is connected to a shaft, which is then connected to a motor or other power source. The friction of the wheel against its bearings creates resistance, allowing the wheel to maintain its rotational speed and store energy.

2. How does a flywheel with kinetic friction work?

When a flywheel with kinetic friction is in motion, the friction between the wheel and its bearings creates a force that opposes the motion, slowing down the wheel. This resistance is what allows the wheel to store energy. When the wheel needs to release the stored energy, the motor or power source can be turned off, and the flywheel will continue to spin at a constant speed, releasing the stored energy as it slows down.

3. What are the benefits of using a flywheel with kinetic friction?

There are several benefits to using a flywheel with kinetic friction. It can store large amounts of energy in a relatively small space, making it a compact and efficient energy storage device. It also has a long lifespan and can be charged and discharged repeatedly without significant wear and tear. Additionally, the energy stored in a flywheel with kinetic friction is easily converted into other forms of energy, making it a versatile energy storage solution.

4. How is a flywheel with kinetic friction different from a regular flywheel?

A regular flywheel does not have the added element of kinetic friction. It relies solely on its inertia to store energy, whereas a flywheel with kinetic friction uses the forces of friction to store and release energy. This makes it more efficient and allows for a greater amount of energy to be stored in the same amount of space.

5. What are some practical applications of a flywheel with kinetic friction?

A flywheel with kinetic friction has several practical applications. It is commonly used in hybrid vehicles and electric trains to store energy during braking and release it during acceleration. It is also used in energy storage systems for renewable energy sources such as wind and solar power. Additionally, it can be used in industrial machinery to store energy and provide smooth and consistent power output.

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