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Springs and Hooke’s Law
Physics 11
Springs
A mass-spring system is given below.
As mass is added to the end of the
spring, how would you expect the
spring to stretch?
Springs
Fspring
x
Fg  1m g
x
Fg  2m g
x
x
Fg  3m g
Fg  mg
 Fg  Fspring
Springs
 2 times the mass results in a 2 times of
the displacement from the equilibrium
point…
 3 time the mass… 3 times the
displacement…
 Fg  Fspring
Fspring  kx
 mg  kx
 2m g  k 2 x 
What kind of energy is this?
 Potential Energy
 Elastic Potential Energy to be exact!
What else besides springs has
elastic potential energy?
 Diving boards
 Bows (bow and arrows)
 Bungee cord
Hooke’s Law
Fspring  kx
Fspring: Applied force
X : displacement of the spring from the
equilibrium position (units: m)
K: the spring constant (units: N/m)
Hooke’s Law
 the restoring force is
opposite the applied
force. (negative sign)
 Gravity applied in the
negative direction, the
restoring force is in the
positive direction
Fspring  kx
Example
 An archery bow requires a force of
133N to hold an arrow at “full draw”
(pulled back 71cm). Assuming that
the bow obeys Hooke’s Law, what is
its spring constant?




F = kx
133 = k(0.71)
k = 133/0.71
k = 187.32 N/m  190 N/m
Restoring Force
 The restoring force is the force that is
needed to put the spring back to
equilibrium.
 Example: If you stretch a spring by
0.5m and you had to use 150N of
force, the restoring force is -150N.
Practice Problems
 Textbook
 Page 258
 35-37
Elastic Potential Energy of a Spring
 Formula: Ee = ½ kx2
 Units: Joules (J)
Example:
 A spring with spring constant 75 N/m
is resting on a table.
 A) If the spring is compressed a
distance of 28cm, what is the
increase in its potential energy?
 B) What force must be applied to
hold the spring in this position?
Answer:






A) Ee = ½ kx2
Ee = ½ (75)(0.28)2
Ee = 2.9 J
B) F = kx
F= 75(0.28)
F = 21 N
Practice Problems
 Page 261, questions 38, 39, 40
 Page 261 (Section Review)
 1, 2, 3, 4, 7
Conservation of Energy with a
Spring
 Ex. 1: A 4.0 kg block slides across a
frictionless table with a velocity of
5.0m/s into a spring with a stiffness
of 2500 N/m. How far does the
spring compress?
Answer
 X = 0.20m
Example 2:
 A 70. kg person bungee jumps off a
50.m bridge with his ankles attached
to a 15m long bungee cord. Assume
the person stops at the edge of the
water and he is 2.0m tall, what is the
force constant of the bungee cord?
 Answer: 64 N/m
 Conservation of Energy Worksheet
Practice Problems
 Textbook
 Page 261
 38-40
 Section review (p 261)
 1-10