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Elastic P.E. - work stored in a deformed spring
a) General Equation
PEs = Fx
F = Average Force needed to deform spring
x = distance deformed (stretch or compress)
Ideal Spring
St. Mary's H.S.
b) Hooke's Law - force needed to deform an ideal spring, a given amount is directly proportional to its displacement (deformation)
Graphic from Learning-Connections Clipart
Robert Hooke
Robert Hooke: Victim of Genius
'Newton's bitter rival'
Ex) Ideal Spring
|
F
(Force to Deform) (N) |
X
(distance deformed) (m) |
|
2.0 |
.30 |
| 4.0 | .60 |
|
6.0 |
.90 |
|
8.0 |
1.2 |
Hooke's Law
University of Colorado - PhET
slope = F/x
x = stretch
c) Spring Constant, Ideal Spring
-
quantifies stiffness
of
a spring
| K | = | F | (N) |
| X | (m) |
What is the spring constant of the spring that produced the data? above?
| F
(Force to Deform) (N) |
X
(distance deformed) (m) |
| 2 | .30 |
| 4 | .60 |
| 6 | .90 |
| 8 | 1.2 |
| k | = | 2.0 N |
| .30 m |
k = 6.7 N/m
Which is the stiffer spring?
Spring A is the stiffer spring.
More
force is required
for the same stretch
Ex) Plots and K
Pick any point on the line
| K | = | F | (N) |
| X | (m) |
| K | = | 20. N |
| .40 m |
K = 50. N/m
d) Elastic P.E. = area of triangle under F vs x graph
PEs = (½)basexheight
PEs = 6 Joules
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