Energy lost from a Flywheel to the Environment

[Poch]

1. A Flywheel (A) mass 100kg and radius of gyration 1200mm rotates 150rpm clockwise. The knetic energy of this flywheel is to be reduced 20% by impacting a second flywheel B rotating at 80 rpm in opposite direction, such that they have the same clockwise angular velocity after inpact. A) calclate mass of flywheel B if its radius of gyration is 800mm, B. calculate energey lost to the surroundings, C. is the impact elastic, give reasons



2. KE = 0.5 x I x W^2, I = M x K^2,



3. K = 1.2m
W = 150 rpm = 15.7 r/s
M = 100kg
I = MxK^2, I = 100 x 1.2^2 , I = 144

Flywheel A
KE = 0.5 x I x W^2
=0.5 x 144 x 15.7^2
= 17747.28 = 17.75J

-20% = 17.75 = 14.2 J

Energy lost = 3.55J, this is acquired by Flywheel B
Flywheel B 80rpm = 8.4 r/s
KE = 0.5 IW^2
I = KE x 2 / w^2
I = 3550 x 2 / 8.4^2
= 100.62 Kgm^2

Mass, I = M x K^2
M = I / K^2 = 100.62 / 0.8^2
=157.2kg

(Check – I = K^2M, 0.8^2 x 157.2 = 100.6)

B). Energy lost to the surroundings

Kinetic Energy before impact 17.75J – Kinetic Energy after impact 14.2J

17.75 – 14.2 = 3.55J

C). No it is inelastic as energy is given up and the 2 bodies move in the same direction at the same speed.

 

[Chi Meson]

Do you have a question for us? Well, anyway, here's an observation:

Are you really using "K" for radius? How bizarre!

Moment of inertia for a solid disk is not I=mr^2