Answer to Question #85243 in Mechanics | Relativity for Beast

Question

The car has 4 tires. Each tire has a mass of 25 kg and a diameter of 75 cm. The total weight of the car is 1200 kg and moves at 120 km / h. How much of the total rotational energy of the tires is the energy of the car? Tires can be treated as a flat circle.

Answer 1

m=25 kg

D=75 cm=0.75 m

M=1200 kg

ϑ=120 km/h

〖KE〗_R/〖KE〗_Tot -?

Solution.

Total kinetic energy of the car equals to the sum of translational kinetic energy of the car and rotational energy of the tires:

〖KE〗_Tot=〖KE〗_T+〖KE〗_R (1)

Translational kinetic energy of the car:

〖KE〗_T=(Mϑ^2)/2=(1200∙〖120〗^2)/2=8640000 (J)

Rotational energy of the tires:

〖KE〗_R=4(1/2 Iω^2 )=2Iω^2 (2)

Moment of inertia of the tire:

I=1/2 mR^2 (3)

Angular velocity:

ω=ϑ/R (4)

Let’s substitute (3) and (4) into (2):

〖KE〗_R=mR^2 (ϑ/R)^2=mϑ^2=25∙〖120〗^2=360000 (J)

Than:

〖KE〗_Tot=8640000+360000=9000000 (J)

〖KE〗_R/〖KE〗_Tot =360000/9000000=0.04=4%

Answer: 〖KE〗_R/〖KE〗_Tot =0.04=4%