Question

A 1030 kg car has four 12.0 kg wheels. When the car is moving, what fraction of the total kinetic energy of the car is due to rotation of the wheels about their axles

Answer 1

The required fraction is 0.023.

Step-by-step explanation:

Given that

Mass of a car, m = 1030 kg

Mass of 4 wheels = 12 kg

We need to find the fraction of the total kinetic energy of the car is due to rotation of the wheels about their axles.

The rotational kinetic energy due to four wheel is

`=4* (1)/(2)I\omega^2\\\\=4* (1)/(2)* (1)/(2)mR^2((v)/(R))^2\\\\=mv^2`

Linear kinetic Energy of the car is:

`=(1)/(2)mv^2\\\\=(1)/(2)* Mv^2`

Fraction,

`f=(mv^2)/((1)/(2)Mv^2)\\\\f=(m)/((1)/(2)M)\\\\f=(12)/((1)/(2)* 1030)\\\\=0.023`

So, the required fraction is 0.023.