Recall from Our Spring Lab that
the Spring Constant (k) was the
slope of the graph of Fs vs. x!
The Spring
constant or
“Stiffness Factor”
provides an
indication of
spring strength.
Bigger (steeper)
k, stronger
spring!
We Derived Hooke’s Law…
Where:
Fs = Force stretching
or compressing the
spring OR the
restoring force built
up within the spring.
x = the maximum
displacement from the
equilibrium position
(unstretched).
Hooke’s Law
• The amount of Force stretching or
compressing a spring is directly
proportional to the displacement
(change in length) of the spring from its
equilibrium position.
• The restoring force that builds up
internally in the spring equals the
applied force.
Elastic Potential Energy (PEs)!
When we did work to stretch the spring, Elastic PE was stored in
the spring as a result. An equation for this relationship can be
derived from the area of our graph:
Slope = spring constant
Fs
Area =
x
A = ½ bh = ½ Fsx = ½ kx(x) = ½ kx2
PEs = W (done on the spring) !
Elastic Potential Energy (PEs)!
PEs is energy stored in an elastic material, such as
a spring, due to an applied force causing a
displacement/deformation of the material (work).
Equations:
Hooke’s Law!
Fs = force compressing
PEs = Potential
Energy of a
compressed or
stretched spring
or stretching the spring
K = the spring constant
in N/m
Add to reference tables:
X = the displacement
WS = ½ Fsx = PES
of the spring from the
equilibrium (rest)
position
PES = ½ kx2 ?
- But we don’t know k!
It’s easiest to use the work equation from the lab:
WS = PES = ½ Fsx
= ½ (10N)(.2m) = 1.0 J
PES = ½ kx2
Calculate k with Hooke’s law:
k = FS = 10 N
x
.2m
= 50N/m
- or we can find k!
Thus, PEs can be found:
PES = ½ kx2
= ½ (50N/m)(.2m)2
= 1.0 N·m = 1.0 J