### Energy is “conserved”

```Physics 2015: Mechanical Energy Conservation
Purpose
Study energy conservation by looking at the relationship
between three different types of energy:

Gravitational potential energy (GPE)

Elastic potential energy (EPE)

Kinetic energy (KE)
Physics 2015: Mechanical Energy Conservation
Energy is “conserved” if we can add up all of the
different types of energy present in a closed
system and see that the total sum remains
constant.
 A “closed system” is one where no energy is added to or
taken away from the system (in our case, a system with
negligible friction)
 The types of energy will change depending on the setup.
Ours were listed on the previous slide.
Physics 2015: Mechanical Energy Conservation
Different Energy Types
• Gravitational Potential Energy (GPE)
(relative to a vertical level where h=0)
GPE  m g h
Your choice where that is – be smart about it!
• Elastic Potential Energy (EPE)
(k=spring constant
x=distance stretched)
• Kinetic Energy (KE)
(m=mass
v= velocity)
1
EPE 
k x2
2
1
2
KE 
mv
2
• Heat Energy (Friction can turn KE into heat energy, for example)
Physics 2015: Mechanical Energy Conservation
Our Setup in the Lab
photogate
Note as the system is released, the quantity
GPE+EPE+KE should stay the same. We will be able to
measure all three energies (and thus their sum) at two
different points of the cart’s travel and compare.
Physics 2015: Mechanical Energy Conservation
Activity I - Find the spring constant k
Hook’s law:



F=-kx
Attach different masses.
Measure the change of length of the spring compared to it’s un-stretched
length.
You can plot your data in Excel and use linear regression to find the slope k.
measured
m
calculated
measured
mg
x
mg
slope = k
x
Physics 2015: Mechanical Energy Conservation
Activity II - Conserving Energy.
photogate
 Decide where you want to make your GPE=0. A good choice
will make your calculations a lot easier.
 Measure all masses (including the mass of the cart).
 Set photogate such that the cart will pass through it (to measure
it’s velocity) as the hanging mass accelerates the cart to the left.
Physics 2015: Mechanical Energy Conservation
Hints
% Energy change 
E final  Einitial
mh g x 
mh  mass of hanging mass
x  changeof thespring length
 change of height of hanging mass
If you do find an energy change, ask whether your “system” was
totally “closed”.
Was some form of energy not accounted for?
Physics 2015: Mechanical Energy Conservation
Correction
There is a mistake in the lab manual on page 75: In the paragraph
at the top of the page it says:
“…create a scatter plot with Excel that graphs position on the
vertical axis and Force on the horizontal axis….”
It should be the other way around: You need to plot Force on the
vertical axis and position on the horizontal axis.
Please correct that in your manual now before you forget….
```