A car is designed to get its energy from a rotating flywheel (solid disk) with a

Question

A car is designed to get its energy from a rotating flywheel (solid disk) with a radius of 1.50 m and a mass of 575 kg. Before a trip, the flywheel is attached to an electric motor, which brings the flywheel's rotational speed up to 4,500 rev/min. (a) Find the kinetic energy stored in the flywheel.
1 ___________J

(b) If the flywheel is to supply energy to the car as a 10.0-hp motor would, find the length of time the car could run before the flywheel would have to be brought back up to speed.
___________h (a) Find the kinetic energy stored in the flywheel.
1 ___________J

(b) If the flywheel is to supply energy to the car as a 10.0-hp motor would, find the length of time the car could run before the flywheel would have to be brought back up to speed.
___________h

Explanation / Answer

adius of the fly wheel R = 1.5 m mass of the fly wheel M = 575 kg rotational speed of the fly wheel ω = 4500 rev/min = (4500)(2π/60) rad/s = 471 rad/s a) kinetic energy stored in the fly wheel is K.E = 1/2 Iω2 .............. (1) here , moment of inertia of the fly wheel I = (1/2) MR2 = (1/2) (575 kg)(1.5 m)2 =646.875kg.m2 substitute the given data in eq (1) , we get K.E = (1/2)(646.875kg.m2)(471 rad/s)2 = 71751698.4375 J = 0.71*108 J b) power P = 10 hp = 746*10 W = 7460 W power P = energy/time therefore , time t = energy/power = 71751698.4375 J / 7460W = 9618.190139075067 s = (9618.190139075067 s)(1 h/ 3600 s) ˜ 2.671719483076408 h
substitute the given data in eq (1) , we get K.E = (1/2)(646.875kg.m2)(471 rad/s)2 = 71751698.4375 J = 0.71*108 J b) power P = 10 hp = 746*10 W = 7460 W power P = energy/time therefore , time t = energy/power = 71751698.4375 J / 7460W = 9618.190139075067 s = (9618.190139075067 s)(1 h/ 3600 s) ˜ 2.671719483076408 h
= 71751698.4375 J = 0.71*108 J b) power P = 10 hp = 746*10 W = 7460 W power P = energy/time therefore , time t = energy/power = 71751698.4375 J / 7460W = 9618.190139075067 s = (9618.190139075067 s)(1 h/ 3600 s) ˜ 2.671719483076408 h

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