Question

A car is designed to get its energy from a rotating flywheel with a radius of 1.50 m and a mass of 430 kg. Before a trip, the flywheel is attached to an electric motor, which brings the flywheel's rotational speed up to 5,200 rev/min.

Required:
a. Find the kinetic energy stored in the flywheel.
b. If the flywheel is to supply energy to the car as would a 15.0-hp motor, find the length of time the car could run before the flywheel would have to be brought back up to speed.

Answer 1

a

`KE = 7.17 *10^(7) \ J`

b

`t = 6411.09 \ s`

Step-by-step explanation:

From the question we are told that

The radius of the flywheel is
`r = 1.50 \ m`

The mass of the flywheel is
`m = 430 \ kg`

The rotational speed of the flywheel is
`w = 5,200 \ rev/min = 5200 * (2 \pi )/(60) =544.61 \ rad/sec`

The power supplied by the motor is
`P = 15.0 hp = 15 * 746 = 11190 \ W`

Generally the moment of inertia of the flywheel is mathematically represented as

`I = (1)/(2) mr^2`

substituting values

`I = (1)/(2) ( 430)(1.50)^2`

`I = 483.75 \ kgm^2`

The kinetic energy that is been stored is

`KE = (1)/(2) * I * w^2`

substituting values

`KE = (1)/(2) * 483.75 * (544.61)^2`

`KE = 7.17 *10^(7) \ J`

Generally power is mathematically represented as

`P = (KE)/(t)`

=>
`t = (KE)/(P)`

substituting the value

`t = (7.17 *10^(7))/(11190)`

`t = 6411.09 \ s`