Chapter 5, Problem 99A

(a)

To determine

The angle of the inclined plane at which the two vector components of weight would be equal.

Explanation of Solution

Introduction:

If a book is kept on an inclined plane, its weight acts vertically downwards and a normal reaction force would act upwards.

The weight can be resolved into two vector components: $w\sin \theta$ parallel to the inclined plane and $w\cos \theta$ perpendicular to the inclined plane.

The two components would be equal when $\sin \theta =\cos \theta$ which is possible for angle $\theta =45°$ of the inclined plane.

Conclusion:

Thus, at $\theta =45°$ , the two components would be equal.

(b)

To determine

The angle of the inclined plane at which the parallel component of weight would be equal to zero.

Explanation of Solution

Introduction:

If a book is kept on an inclined plane, its weight acts vertically downwards and a normal reaction force would act upwards.

The weight can be resolved into two vector components: $w\sin \theta$ parallel to the inclined plane and $w\cos \theta$ perpendicular to the inclined plane.

The parallel component of the weight is $w\sin \theta$ .

It would be zero when $\sin \theta =0$ which is possible for $\theta =0°$ i.e. when there is no inclined plane.

Conclusion:

Thus, at $\theta =0°$ , the parallel component would be equal to zero.