   Chapter 4, Problem 30P

Chapter
Section
Textbook Problem

Suppose the coefficient of static friction between a quarter and the back wall of a rocket car is 0.330. At what minimum rate would the car have to accelerate so that a quarter placed on the back wall would remain in place?

To determine
The minimum acceleration of the car.

Explanation

Given info: The co-efficient of static friction ( μs ) is 0.330.

The free body diagram is given below.

From the above diagram,

N=ma (I)

Fs=mg (II)

• m is the mass of the car
• g is the acceleration due to gravity
• a is the acceleration
• N is the normal force
• Fs is the force of static friction

The condition for minimum acceleration is,

FsμsN

On re-arranging,

FsNμs

Divide equation (II) by equation (I).

FsN=ga                                                (III)

For the acceleration to be minimum,

FsN=μs (IV)

Equate equations (III) and (IV) to get minimum acceleration ( amin )

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