(11 %) Problem 8: A flywheel is a mechanical device used to store rotational kin
ID: 2035136 • Letter: #
Question
(11 %) Problem 8: A flywheel is a mechanical device used to store rotational kinetic energy for later use. Consider a flywheel in select part of a uniform solid cylinder rotating around its axis, with moment of inertia 1- 1/2 m?2 33% Part (a) If such a flywheel of radius r,-.2 m and mass m1-23 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 e &s.; 33%, Part (b) Consider a scenario in which the flywheel described in part (a) (ri-.2 m. mass m1-23 kg, Grade Summary Deductions Potential 0% 100% tanOJt( Submissions Attempts remaining: 10 ino coS cotan in cos0 atan)a cosh()tanhO cotanhO asin % per attempt) detailed view acotan sinh) 23 END Degrees ORadians BACKSPACE DELCLEAR Submit Hint I give up! Hints: 0% deduction per hint. Hints remaining: 3 Feedback: 0% deduction per feedback ? 33% Part (c) Return now to the flywheel of part (a), with mass mi, radius ri, 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 hereExplanation / Answer
a)
Angular velocity of the flywheel is
w = v/r = 35 m/s / 1.2 m
w = 29.17 rad/s
Rotational kinetic energy of flywheel is
K = 1/2(Iw^2)
K = 1/2(1/2mr^2)w^2
K = 1/4mr^2w^2
K = 1/4 x 23 kg x (1.2 m)^2 x (29.17 rad/s)^2
K = 7043.75 J
b)
from law of conservation of angular momentum
Li = Lf
I1w1 + I1w2 = (I1 + I2)w
w = (I1w1 + I1w2) / (I1 + I2)
w = [(1/2m1r1^2)w1 + (1/2m2r2^2)w2) / (1/2m1r1^2 + 1/2m2r2^2)
w = [(23*1.2^2*29.17 + (8*1.1^2*0) / (23*1.2^2 + 8*1.1^2)
w = 966.1104 / 42.8
w = 22.57 rad/s
Energy stored in first wheel is
K = 1/2I1w^2
K = 1/2*(1/2m1r1^2)w^2
K = 1/4 x 23 x (1.2)^2 x (22.57)^2
K = 4217.87 J
c)
Kinetic energy of car at it's top speed is
Kcar = 1/2mcar*Vcar^2
Rotational kinetic energy of flywheel is
Kfly = 1/2(1/2m1r1^2)w1^2
Kfly = 1/2(1/2m1r1^2)(v/r1)^2
Kfly = 1/4m1v^2
one thired kinetic enegy of car is equal to the kinetic energy of car
1/3Kfly = Kcar
1/3*( 1/4m1v^2) = 1/2mcar*Vcar^2
mcar = m1v^2 / 6Vcar^2
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.