   Chapter 4, Problem 50P

Chapter
Section
Textbook Problem

A car is traveling at 50.0 km/h on a flat highway. (a) If the coefficient of friction between road and tires on a rainy day is 0.100, what is the minimum distance in which the car will stop? (b) What is the stopping distance when the surface is dry and the coefficient of friction is 0.600?

(a)

To determine
The minimum stopping distance on a rainy day.

Explanation

Given Info: The co-efficient of friction on a rainy day ( μk ) is 0.100. The speed of the car is 50.0 km/h.

The normal force (N) equals the weight of the car.

N=mg (I)

• m is the mass of the car.
• g is the acceleration due to gravity.

The friction force ( Fk ) is equal and opposite to the horizontal force (F).

F=Fk (II)

Formula for friction force is,

Fk=μkN (III)

Formula for the horizontal force is,

F=ma

• m is the mass of the car.
• a is the acceleration.

From Equations (I), (II) and (III),

ma=μkmga=μkg

From Newton’s equation of motion, the stopping distance is,

s=v2u22a

• v is the final velocity.
• u is the initial velocity.
• a is the acceleration.

Substitute μkg for a in the above expression to get s.

s=u2v22μkg

Substitute 0 m/s for v, 50

(b)

To determine
The minimum stopping distance when the surface is dry.

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