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Chapter 6: Q6.3-32 PE (page 223)

Unreasonable Results (a) Calculate the minimum coefficient of friction needed for a car to negotiate an unbanked \({\bf{50}}.{\bf{0}}{\rm{ }}{\bf{m}}\) radius curve at\({\bf{30}}.{\bf{0}}{\rm{ }}{\bf{m}}/{\bf{s}}\). (b) What is unreasonable about the result? (c) Which premises are unreasonable or inconsistent?

Short Answer

Expert verified
  1. The minimum coefficient of the friction needed is \({{\rm{\mu }}_{\rm{s}}}{\rm{ = 1}}{\rm{.84}}\)
  2. \({{\rm{\mu }}_{\rm{s}}}\) has a value that is twice that of the regular value.
  3. Unbanking of the road and the value of velocity and radius is unreasonable.

Step by step solution

01

Definition of coefficient of friction

The coefficient of friction is defined as the ratio of frictional force to the normal reaction force. It is a scalar and dimensionless quantity with no units.

02

Calculating the minimum coefficient of friction

Radius of curve \({\rm{r = 50 m}}\)

Velocity of the car \({\rm{v = 30 m/s}}\)

The minimum coefficient of friction needed\({{\rm{\mu }}_{\rm{s}}}{\rm{ = ?}}\)

\({{\rm{\mu }}_{\rm{s}}}{\rm{ = }}{{\rm{v}}^{\rm{2}}}{\rm{/rg}}\)

Here, v is the velocity of the car, r is the radius of the curve and 碌s is the coefficient of the static friction.

The minimum coefficient of the friction needed is

\(\begin{aligned}{l}{{\rm{\mu }}_{\rm{s}}}{\rm{ = }}{{\rm{v}}^{\rm{2}}}{\rm{/rg}}\\{{\rm{\mu }}_{\rm{s}}}{\rm{ = 3}}{{\rm{0}}^{\rm{2}}}{\rm{/(50*9}}{\rm{.8)}}\\{{\rm{\mu }}_{\rm{s}}}{\rm{ = 900/490}}\\{{\rm{\mu }}_{\rm{s}}}{\rm{ = 1}}{\rm{.84}}\end{aligned}\)

03

Determining unreasonable about result

For concrete/asphalt roads, the coefficient of static friction reaches a maximum of \({\rm{0}}{\rm{.90}}\). The result that we have obtained for the minimum coefficient of the friction is which is almost twice the normal value. This is unreasonable in part (a).

04

Determining unreasonable or inconsistent

The statement 鈥榬oad is unbanked鈥� is unreasonable. Due to the opening of the road to the banks, the car will be disposed off. The velocity of the car should be less or the radius of the curve should be made greater.

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Most popular questions from this chapter

What is the ideal banking angle for a gentle turn of \(1.20{\rm{ km}}\) radius on a highway with a \(105{\rm{ km}}/{\rm{h}}\) speed limit (about \(65{\rm{ mi}}/{\rm{h}}\)), assuming everyone travels at the limit?

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