Equate Kinetic Friction to Rotational Energy?

[Gear Head]

Homework Statement

So a car owner wants to change his current tires and rims to a wider set of tires and rims for increased handling ability. However, the owner does not want to lose any acceleration performance due to the increased friction of having wider tires. To combat this, the owner wants to know how much weight loss is necessary to overcome the increased frictional forces and maintain his current acceleration abilities. Assume a uniform weight distribution for the wheels.

All variables are held constant except:
New wheel width
New wheel weight

Given:
Coefficient of friction is 0.7
Stock wheel width is 6in. or 15.24cm
Stock wheel mass is 20lbs

Create an equation that compares wheel friction at a given width to wheel weight.

Homework Equations

I think I should use:
Kinetic energy = 1/2 Mv^2 where M is mass and v is velocity
Frictional force = coeff. of friction * F(n) where F(n) is the normal force.
Normal force = mass * gravity

The Attempt at a Solution

I[/B] am having a tough time with this one. I assume that if I can set the friction equation equal to the rotational equation, then I can use that same formula for the new wheel and the old wheel and can compare the forces easily. I just can't figure out how to set the equation up.

 

[haruspex]

I'm not sure whether this question is deliberately misleading or just wrong-headed.
Some questions to consider:
- what would the performance be if you were to eliminate tyre to road friction completely?
- In the equation you quote for frictional force, what role does area of contact play?
- Is road grip merely down to friction?
- what slows cars down?

Edit: I should break the last item into two parts:

- what reduces a vehicle's top speed?
- what reduces a vehicle's acceleration?
(and which of those is relevant for 'performance'?)

 

[Stephen Tashi]

Create an equation that compares wheel friction at a given width to wheel weight.

Is that the statement of the problem?

Or does the problem say you must calculate something to "maintain his current acceleration abilities"?

 

[CWatters]

The problem statement doesn't make a lot of sense to me at all.

the owner does not want to lose any acceleration performance due to the increased friction of having wider tires.

Increasing friction between the tyre and ground usually improves acceleration - so presumably he is worried about increased rolling resistance?

 

[CWatters]

Oh I think I see. The problem assumes that the wheels must slip in order that the engine achieve optimum power output. Therefore increasing friction must be compensated for by reducing the moment of inertia of the wheels so they spin up just as fast. Gosh the problem statement assumes you know a lot about drag racing.

 

[Bystander]

wider set of tires and rims for increased handling

Okay ----

does not want to lose any acceleration performance due to the increased friction of having wider tires.

If he's accelerating through any turn sharp enough to notice friction from the steered/steering action, there's more going on than is easily calculated.

Create an equation that compares wheel friction at a given width to wheel weight.

Since there's no turn radius specified, take a straight line drive, and there's no difference other than from toe-in and camber which are also not specified.