1. Sect. 7.6: Potential Energy

2. above Earth m has the potential to do work = mgy when it falls
Potential Energy (U or PE)  Energy associated with position or configuration of a mass.
Potential work done!
Gravitational Potential Energy
Ug  mgy, y = distance
above Earth m has the
potential to do work
= mgy when it falls
(W = Fy, F = mg)

3. Ug = mg(y2 - y1) Gravitational PE
Consider a problem in which the height of a mass above the Earth changes from y1 to y2:
Change in Gravitational PE is:
Ug = mg(y2 - y1)
Work done on the mass: W = Ug
y = distance above Earth. Where we choose y = 0 is arbitrary, since we take the difference in 2 y’s in Ug

4. Ug ≡ mgy
= (Ug)2 - (Ug)1
= ΔUg

5. Example Ug
Also do Example 7.8!
ΔUg = mg(y2 – y1)
y = 0 

6. There are other types of PE besides gravitational.
Consider again an ideal spring:
Characterized by a spring
constant k. A measure of
how “stiff” the spring is.
Hooke’s
“Law”
restoring
force
Fs = -kx
(Fs >0, x <0; Fs <0, x >0)
Work done by person: W = (½)kx2  Ue
(Elastic PE)

7. Elastic PE Ue

8. Elastic PE
Figure 7.16: (a) An undeformed spring on a frictionless, horizontal surface. (b) A block of mass m is pushed against the spring, compressing it a distance x. Elastic potential energy is stored in the spring–block system. (c) When the block is released from rest, the elastic potential energy is transformed to kinetic energy of the block. Energy bar charts on the right of each part of the figure help keep track of the energy in the system.

9. The PE belongs to the system, not to individual objects
In a problem in which compression or stretching distance of spring changes from x1 to x2.
The change in PE is:
Ue = (½)k(x2)2 - (½)k(x1)2
The work done: W = Ue
The PE belongs to the system, not to individual objects