6.11 - Work and gravitational potential energy
Potential energy is the energy of a system due to forces between the particles or
objects that make up the system. It can be related to the amount of work done on a
system by an external force. We will use gravitational force and gravitational potential
energy as an example of this general principle. Our discussion applies to what are
called conservative forces, a type of force we will later discuss in more detail.
The system we consider consists of two objects, the bucket and the Earth, illustrated to
the right. The painter applies an external force to this system (via a rope) when she
raises or lowers the bucket. The bucket starts at rest on the ground, and she raises it up
and places it on the scaffolding. That means the work she does as she moves the
bucket from its initial to its final position changes only its gravitational PE. The system’s
kinetic energy is zero at the beginning and the end of this process.
As she raises the bucket, the painter does work on it. She pulls the bucket up against
the force of gravity, which is equal in magnitude to the bucket’s weight, mg. She pulls in
the direction of the bucket’s displacement, ǻh. The work equals the force multiplied by
the displacement: mgǻh. The paint bucket’s change in gravitational potential energy
also equals mgǻh. The analysis lets us reach an important conclusion: The work done
on the system, against gravity, equals the system’s increase in gravitational potential
energy.
Earlier, we stated the work-kinetic energy theorem: The net work done on a particle
equals its change in kinetic energy. Here, where there is no change in kinetic energy,
we state that the work done on a system equals its change in potential energy.
Are we confused? No. Work performed on a system can change its mechanical energy,
which consists of its kinetic energy and its potential energy. Either or both of these
forms of energy can change when work is applied to the system.
As the painter does work against the force of gravity, the force of gravity itself is also
doing work. The work done by gravity is the negative of the work done by the painter.
This means the work done by gravity is also the negative of the change in potential
energy, as seen in Equation 2.
Imagine that the painter drops the bucket from the scaffolding. Only the force of gravity
does work on the bucket as it falls. The system has more potential energy when the
bucket is at the top of the scaffolding than when it is at the bottom, so the work done by
gravity has lowered the system’s PE: the change in PE due to the work done by gravity
is negative.Work and potential energy
Work equals change in energy
Work done against gravity
W = ǻPE
W = work done against gravity
PE = potential energy of system
Work done by gravity
W = íǻPE
W = work done by gravity
PE = potential energy of system
(^132) Copyright 2007 Kinetic Books Co. Chapter 06