6.2. Energy http://www.ck12.org
FIGURE 6.13
The change in as measured from an ob-
ject’s center of mass.Answer:True. Gravity acts in the opposite direction of the motion of the object and therefore does negative work
on the object.
1c. True or False: Gravity does positive work on the object inFigure6.13 if the object is released from the heighth.
Answer:True. In this case the force of gravity is in the same direction as the motion of the object.
Potential Energy and Springs
The spring is a useful and ubiquitous invention that is often overlooked. There are spring-loaded screen doors and
toys and a host of other devices that hide the springs away so we are privy only to their “magical” movements. In a
“clockwork universe,” springs may not be kings, but you’d be hard pressed to find many other things so important!
But it is more than just the mechanical workings of springs that are important to physicists. As we will see in later
chapters, the spring behavior has rich analogies in many other branches of physics.
A force must be applied in order to stretch or compress a spring. Work therefore must be done on the spring. The
work done on the spring is stored in the form of potential energy in the spring. In order to find the work done on
the spring, we calculate the product of the applied force and the distance the spring moved. But the force applied to
a spring isnotconstant; it does not, for example, take the same force to stretch a spring 5 cm as it does to stretch
it 10 cm. Fortunately, the relationship between the force and the distance a spring is stretched is a simple one.
Robert Hooke (1635, 1703) discovered that the force is directly proportional to the distance the spring is stretched
(or compressed). In other words, it takes twice the force to stretch the spring twice the distance, three times the force
to stretch it three times the distance, and so on. Mathematically, we haveF=kx, whereFis the applied force,k, is
thespring constantwith units N/m andxis the distance the spring is stretched.
Illustrative Example
A plot of the applied force,Fvs.x, the distance the spring is stretched, is shown inFigure6.15.