Fraction of Kinetic Energy from Rotating Wheels in Moving Car

[Ignitia]

Homework Statement

A 1000-kg car has four 10-kg wheels. When the car is moving, what fraction of its total kinetic energy is due to rotation of the wheels about their axles? Assume that the wheels the same mass and size.

Homework Equations

Rolling Wheel:
K=1/2 I_comω² + 1/2mv²

Inertia for Wheel:
I=1/2mv²

v=ωr
ω=v/r

The Attempt at a Solution

(Per wheel)
K=1/2 I_comω² + 1/2mv²
K=1/2 [1/2mv²*vSUP]2[/SUP]/r² + mv²]
K=1/2 [1/2mv² + mv²]
K=1/2 [3/2mv²]
K=3/4 mv²]

The book states the answer to be 0.020
How?

 

[Orodruin]

What is the total kinetic energy of the car?

 

[kuruman]

Also, are the wheels assumed to be rings or cylinders?

 

[Ignitia]

What is the total kinetic energy of the car?

It's not given. Although that'd be KE = 1/2mv^2, whatever the velocity is.

Also, are the wheels assumed to be rings or cylinders?

Cylinders.

 

[kuruman]

Well, you need the ratio of the kinetic energy of the four wheels about their center of mass to the kinetic energy of (the car's center of mass + the kinetic energy of the four wheels about their center of mass). Do you think you can find this ratio?

 

[Orodruin]

It's not given.

Of course not, but your problem asks you to find the ratio of the rotational energy of the wheels and the total kinetic energy. The car’s kinetic energy is clearly included in that so you better find it.

 

[Ignitia]

Well, car's is KE=1/2mv^2,
and [KE=3/4mv^2]x4 = 3mv^2

And that doesn't look right.

 

[Orodruin]

Of course it does not look right. Does the car have the same mass as a wheel?

 

[Ignitia]

Well, this shows I'm half asleep.

4*[3/4(10v^2)]/1/2*(960v^2) = 4*[3/4(10)]/1/2*(960) = 4*7.5/.5*960 = 1/16 = .06

It's still not correct though.

 

[Orodruin]

Note that you were just asked about the rotational kinetic energy of the wheels. Not the total kinetic energy of the wheels.

 

[Ignitia]

Late reply sorry. I got it now, thanks!