Circular motion of a car and tires

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Homework Help Overview

The problem involves a car negotiating an unbanked circular turn at a specific speed, with a focus on the effects of reduced static friction due to a wet patch on the road. Participants are exploring how to determine the new speed required for the car to safely navigate the turn under these conditions.

Discussion Character

  • Exploratory, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • Participants are discussing the relationship between centripetal force and speed, questioning how to approach the problem without specific values for mass or radius. There are attempts to relate the forces involved and explore the implications of the reduced friction.

Discussion Status

Some participants have provided hints and guidance regarding the use of ratios to relate the forces and speeds, suggesting that the problem can be approached without needing to know certain variables. Multiple interpretations of the problem are being explored, particularly regarding the setup of equations and the significance of the friction reduction.

Contextual Notes

Participants note the absence of specific values for mass, radius, and the coefficient of friction, which are causing uncertainty in how to proceed with the calculations. There is an acknowledgment of the need to consider the effects of the wet patch on the maximum static frictional force.

xtrmk
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Homework Statement


A car is safely negotiating an unbanked circular turn at a speed of 21 m/s. The maximum static frictional force acts on the tires. Suddenly a wet patch in the road reduces the maximum static frictional force by a factor of three. If the car is to continue safely around the curve, to what speed must the driver slow the car?


Homework Equations





The Attempt at a Solution


Do I convert V to angular velocity and figure out the radius? Then ?_?
Do not know how to start, can someone help. Thanks
 
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Hint: How does the required centripetal force relate to the car's speed?
 
Doc Al said:
Hint: How does the required centripetal force relate to the car's speed?

Centripetal force = mv^2 / r ?
But I don't have an r or m. and what do I do without a given coefficient of friction?

(Sorry i just came back to class after a sick break)

(edit)
Am i starting it right?
Fc = friction = mv^2/r

u(mg) = mv^2/r?
 
xtrmk said:
Centripetal force = mv^2 / r ?
Right.
But I don't have an r or m. and what do I do without a given coefficient of friction?
You won't need any of those. Hint: Think ratios.
Am i starting it right?
Fc = friction = mv^2/r
Yes.
 
Doc Al said:
Right.

You won't need any of those. Hint: Think ratios.

Yes.

Could you look at this:

[u(mg)]/3 = mv^2 / r

I divide by 3 because it was reduced by the factor of 3 ?
I canceled out the masses and:

3.266u = 441/r

do I solve for the radius? Then consider a case 2 and plug it in?
 
As I said earlier, you don't need to know (or try to solve for) m, r, or mu, since they don't change. The only things that change are the force and the speed. Think ratios.

Try this:
F_1 = m v_1^2/r

F_2 = m v_2^2/r

You are given F_1/F_2 = 3; your job is to figure out v_1/v_2.
 

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