In your job as a mechanical engineer you are designing a flywheel and clutch-pla
ID: 2304040 • Letter: I
Question
In your job as a mechanical engineer you are designing a flywheel and clutch-plate system like the one in (Figure 1). Disk A is made of a lighter material than disk B, and the moment of inertia of disk Aabout the shaft is one-third that of disk B. The moment of inertia of the shaft is negligible. With the clutch disconnected, A is brought up to an angular speed ?0; B is initially at rest. The accelerating torque is then removed from A, and A is coupled to B. (Ignore bearing friction.) The design specifications allow for a maximum of 3300 J of thermal energy to be developed when the connection is made.
What can be the maximum value of the original kinetic energy of disk A so as not to exceed the maximum allowed value of the thermal energy? Express your answer with the appropriate units.
to BEFORE Forces Fand -F are along the axis of rotation and thus exert no torque about this axis on either disk AFTER A+Explanation / Answer
Solution:
There are no external torques to the system, so angular momentum is conserved, so the final angular speed ? satisfies:
( IA + IB ) ? = IA ?o
It is given that IA = 1/3 IB, Therefore from above equation,
? = 1/4 ?o.
Now consider the kinetic energies before and after coupling.
Kafter = 1/2 (IA + IB) ?2 = IA ?2o / 8
Kbefore = 1/2 IA ?2o
Therefore the loss in kinetic energy is
Kbefore - Kafter = 3/8 IA ?2o.
This went into heat, and since we want that maximized to Qmax (3300J in this problem) we have
3/8 IA ?2o < Qmax
So
1/2 IA ?2o < 4/3 Qmax
So the maximum initial kinetic energy of A is 4*3300J/3
= 4400J
I hope you understood the problem, If yes rate me!! or else comment for a better solution.