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

Answer:

The speed of the car is 245.6 m/s.

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

$I= \dfrac{1}{2}mR^2$

Put the value into the formula

$I=\dfrac{1}{2}\times370\times(0.500)^2$

$I=46.25\ kgm^2$

We need to calculate the kinetic energy of the fly wheel

Using formula of kinetic energy

$K.E=\dfrac{1}{2}I\omega^2$..(I)

We need to calculate the kinetic energy of car

$K.E=\dfrac{1}{2}mv^2$....(II)

We need to calculate the speed of the car

From equation (I) and (II)

$\dfrac{1}{2}I\omega^2=\dfrac{1}{2}mv^2$

$v^2=\dfrac{I\omega^2}{m}$

Put the value into the formula

$v^2=\dfrac{46.25\times(230\times2\pi)^2}{1600}$

$v=\sqrt{60368.05}$

$v=245.6\ m/s$

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