   Chapter 5.6, Problem 5.8QQ

Chapter
Section
Textbook Problem

A book of mass in is projected with a speed v across a horizontal surface. The book slides until it stops due to the friction force between the book and the surface. The surface is now tilted 30°, and the book is projected up the surface with the same initial speed v. When the book has come to rest, how does the decrease in mechanical energy of the book-Earth system compare with that when the book slid over the horizontal surface? (a) It’s the same. (b) It’s larger on the tilted surface. (c) It’s smaller on the tilted surface. (d) More information is needed.

To determine

how the decrease in mechanical energy in both the cases are related.

Explanation

The change in mechanical energy of the system is equal to the work done on a system by all nonconservative forces.

Wnc=ΔE

The decrease in mechanical energy of the system is given by,

fk(Δx)

• fk is the kinetic friction force
• Δx is the displacement

When the book is in the tilted surface, the kinetic friction force is having a smaller value compared to the book in the horizontal surface because the normal force is smaller in tilted surface compared to horizontal surface.

In a tilted surface when the book is moving up, the gravitational pull is opposite to the direction of motion of the book. Hence, the displacement of book will be less than the displacement of book when it is moving in a horizontal surface.

Therefore, the decrease in mechanical energy of the system has a smaller value in tilted surface than a horizontal surface

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