Question

A futuristic design for a car is to have a large solid disk-shaped flywheel within the car storing kinetic energy. The uniform flywheel has mass 370 kg with a radius of 0.500 m and can rotate up to 230 rev/s. Assuming 1/3 of the stored kinetic energy could be transferred to the linear velocity of the 1600 kg car, find the maximum attainable speed of the car.

Answer 1

The speed of the car is 245.6 m/s.

Step-by-step explanation:

Given that,

Mass of flywheel = 370 kg

Radius = 0.500 m

Angular velocity = 230 rev/s

Mass of car = 1600 kg

We need to calculate the moment of inertia of the disk

Using formula of moment of inertia

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

Put the value into the formula

`I=(1)/(2)*370*(0.500)^2`

`I=46.25\ kgm^2`

We need to calculate the kinetic energy of the fly wheel

Using formula of kinetic energy

`K.E=(1)/(2)I\omega^2`..(I)

We need to calculate the kinetic energy of car

`K.E=(1)/(2)mv^2`....(II)

We need to calculate the speed of the car

From equation (I) and (II)

`(1)/(2)I\omega^2=(1)/(2)mv^2`

`v^2=(I\omega^2)/(m)`

Put the value into the formula

`v^2=(46.25*(230*2\pi)^2)/(1600)`

`v=√(60368.05)`

`v=245.6\ m/s`

Hence, The speed of the car is 245.6 m/s.