Honors Physics

Work, Gravity and Potential Energy

Work Done by Gravity Consider a falling tennis ball. As the ball falls, gravity does positive work

on the ball. This is evident by the increase in Kinetic

Energy of the ball. The definition of work can be used to

calculate the magnitude of the work. The force is constant and the angle

between the force and motion is zero degrees.

Work done by Gravity We let the distance, s,

that it falls be the difference between initial and final heights.

This shows that the work done is dependent upon the change in vertical position only, not the actual path taken.

grav gravW F s

grav i fW mg h h

Going Up? Is the expression valid for an object

traveling upward? Yes! The final height is greater than the

initial height, yielding work to be a negative quantity.

The next question then is: Form where do we measure the height?

Reference Level The position of zero height, h = 0, is called

the reference level. The choice is arbitrary. We can put the

reference level wherever we like. You will see that a wise choice can simplify

many problems. The only condition is that all heights be

measured from the same reference level.

Gravitational Potential Energy Notice that the work done by gravity is the

difference between two like terms. This similar to the Work-Energy Theorem. In this case, each term is again a type of energy. Gravitational Potential Energy.

gravPE mgh

Gravitational Potential Energy This is the energy possessed by an object due to

its position. It is a result of the forces exerted between two

particles of the same system. We can show that there is energy by showing its

ability to do work. Demonstration: A massive object held above a

soda can. When the mass hits the can, it crushes the can,

thus doing work. It must have had energy!

Types of Forces All forces can be placed is one of two

classes: Conservative Nonconservative

Conservative forces are those for which the work they do is independent of the path taken.

Nonconservative forces are those for which the work done is path dependent.

Conservative Forces The work done by conservative forces is

independent of the path taken. A potential energy is associated with a

conservative force. The total work done around any closed

path is zero. To date, Gravity is the only conservative

force that we have discussed.

Nonconservative Forces The work done is path dependent. The transfer of energy by a

nonconservative force is not reversible, therefore there is no potential energy associated with such forces.

To date, all forces other than gravity have been nonconservative.

Work-Energy Theorem Revisited

2 21 12 2f iW mv mv

2 21 12 2nc grav f iW W mv mv 2 21 1

2 2nc f i gravW mv mv W

2 21 12 2nc f i f iW mv mv mgh mgh