Fraction of Kinetic Energy from Rotating Wheels in Moving Car

  • Thread starter Thread starter Ignitia
  • Start date Start date
  • Tags Tags
    Wheel
Click For Summary

Homework Help Overview

The discussion revolves around a problem involving the kinetic energy of a moving car and its wheels. The original poster presents a scenario where a 1000-kg car has four 10-kg wheels, and the objective is to determine the fraction of the total kinetic energy attributed to the rotation of the wheels. The problem includes considerations of the wheels' mass and their moment of inertia.

Discussion Character

  • Exploratory, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • Participants explore the calculation of kinetic energy for both the car and the wheels, questioning the assumptions about the wheels' shape (rings vs. cylinders) and the total kinetic energy of the car. There are attempts to derive the ratio of the kinetic energy of the wheels to the total kinetic energy, with various calculations presented.

Discussion Status

The discussion is active, with participants providing insights and calculations regarding the kinetic energy of the wheels and the car. Some participants express confusion about the calculations and the assumptions made, while others seek clarification on the definitions and relationships involved in the problem.

Contextual Notes

There is a lack of explicit information regarding the total kinetic energy of the car, which is noted as a constraint in the discussion. Participants are also grappling with the implications of the wheels' mass relative to the car's mass in their calculations.

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 Icomω2 + 1/2mv2

Inertia for Wheel:
I=1/2mv2

v=ωr
ω=v/r

The Attempt at a Solution


(Per wheel)
K=1/2 Icomω2 + 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?
 
Physics news on Phys.org
What is the total kinetic energy of the car?
 
Also, are the wheels assumed to be rings or cylinders?
 
  • Like
Likes   Reactions: Orodruin
Orodruin said:
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.

kuruman said:
Also, are the wheels assumed to be rings or cylinders?
Cylinders.
 
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?
 
Ignitia said:
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.
 
Well, car's is KE=1/2mv^2,
and [KE=3/4mv^2]x4 = 3mv^2

And that doesn't look right.
 
Of course it does not look right. Does the car have the same mass as a wheel?
 
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.
 
  • #10
Note that you were just asked about the rotational kinetic energy of the wheels. Not the total kinetic energy of the wheels.
 
  • #11
Late reply sorry. I got it now, thanks!
 

Similar threads

  • · Replies 7 ·
Replies
7
Views
1K
  • · Replies 3 ·
Replies
3
Views
2K
Replies
3
Views
2K
  • · Replies 4 ·
Replies
4
Views
2K
Replies
33
Views
11K
  • · Replies 7 ·
Replies
7
Views
5K
Replies
6
Views
1K
Replies
9
Views
3K
  • · Replies 25 ·
Replies
25
Views
3K
  • · Replies 6 ·
Replies
6
Views
2K