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)

• Elastic Potential Energy (EPE)(k=spring constant

x=distance stretched)

• Kinetic Energy (KE)(m=mass v= velocity)

• Heat Energy (Friction can turn KE into heat energy, for example)

hgmGPE

2

2

1xkEPE

2

2

1vmKE

Your choice where that is – be smart about it!

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 = - k x

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.

m mg x mg

x

slope = k

measured measuredcalculated

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

masshangingofheightofchange

length spring theof change

masshangingofmass

changeEnergy%

x

m

xgm

EE

h

h

initialfinal

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….