Unit 6 Part 3 – Springs and
Energy
Section 10.3
Elastic Potential Energy
 The elastic potential energy is the energy that a spring
has by virtue of being stretched or compressed.
 For an ideal spring:
𝑼𝒔 =
𝟏
𝒌𝒙𝟐
𝟐
(on AP Equation Sheet)
 So the maximum elastic potential energy occurs when
the spring is at its maximum displacement.
 When the spring is unstretched/uncompressed (at
resting/equilibrium position) 𝑈𝑠 = 0.
Conservation of Energy
 Just as we have previously studied, in the case of an
ideal spring, energy is conserved.
Sample AP Problem
Period: is proportional
to
𝑚
𝑘
so the period will
be greater due to the
larger mass.
Max Kinetic Energy:
since it will be equal
to the maximum
potential energy,
which does NOT
depend on mass, it
will be the same!
Answer: D
Sample AP Problem 2
The block has no potential energy, but it will have
kinetic energy as it moves back and forth.
Without friction, the block/spring system would
maintain constant energy, but friction makes it
gradually lose energy.
Answer: D
Calculations with Energy
 If you know the original/maximum displacement of a
spring and the spring constant, you can find the
maximum elastic potential energy of the spring.
 If the spring is just released from rest, this potential
energy is equal to the total energy of the system.
 To find the kinetic energy at any point in the oscillation,
find the potential energy and subtract from the total
energy.
 Then you can use our “normal” kinetic energy formula
and solve for the speed.