Question

A car is designed to get its energy from a rotating flywheel in the shape of a uniform, solid disk of radius 0.650 m and mass 600 kg. Before a trip, the flywheel is attached to an electric motor, which brings the flywheel's rotational speed up to 4.90 ✕ 10³ rev/min.

(a)

Find the kinetic energy stored in the flywheel (in J).

 __J

(b)

If the flywheel is to supply energy to the car as a 11.0 hp motor would, find the length of time in hours the car could run before the flywheel would have to be brought back up to speed.

__ h

Answer 1

Solution;

Given;

Radius,R=0.65m

Mass,M=600kg

Rotation,N=4.90×10³RPM

(a)

Kinetic energy is given by;

K.E=$\frac12×I×w^2$

$I$ is the moment of inertia given by;

$I=\frac12mR^2$

$I=\frac12×600×0.65^2$

$I=126.75kgm^2$

The angular velocity,w;

$w=\frac{2πN}{60}$ =$\frac{2×π×4.90×10^3}{60}$

$w=513.126rad/s$

Kinetic energy ;

$K.E=\frac 12×I×w^2$

$K.E=0.5×126.75×(513.126)^2$

$K.E=16686529.25J$

(b)

11hp=8202.7W

$t=\frac{16686529.25}{8202.7}=2034.27s$

Convert into hours;

$t=\frac{2034.27}{3600}=0.565hrs$

t=0.565 hours