Potential energy and conservation of energy

Chapter 6

Let us consider a book of mass m at an initial height yb above the ground, as shown in Figure, then the only force that does work on the book as it falls is the gravitational force exerted on the book . The work Wg done by the gravitational force as the brick undergoes a downward displacement d is

]1[.. ififg yymgjyyjmgdgmW

gifg UUUW

rFW appg .

In Equation 1, the work represents a transfer of energy into the system, and the system energy appears in a different form, which we have called gravitational potential energy. Thus, we can identify the quantity mgy as the gravitational potential energy Ug

Ug = mgy

Joule = N.m = kg.m2/s2

The unit of gravitational potential energy:

[Ug = ]Joule

Quick Quiz

calculate the work with a displacement having both vertical and horizontal components?

Quick Quiz: Choose the correct answer. The gravitational potential energyof a system

(a )is always positive )b( is always negative )c( can be negative or positive.

8.2 The Isolated System- Conservation of Mechanical

Energy

Let us now shift our focus to the work done on the book alone by the gravitational force .as the book falls back to its original height

the work done on the book is equal to the change in the kinetic energy of the book:

let us relate each side of this equation to the system of the and the Earth .

This equation is true for

conservation forces

conservation of mechanical energy

Elastic Potential Energy

Example 8.2 Ball in Free Fall

A ball of mass m is dropped from a height h above the ground, as shown in Figure

(A )Neglecting air resistance, determine the speed of the ball when it is at a height y above the ground.

(B )Determine the speed of the ball at y if at the instant of release it already has an initial upward speed vi at the initial altitude h.

Example 8.3 The Pendulum