Lab

1 PHY 241 Fall 2018

PHY 241 Lab 6- Law of Conservation of Energy

Introduction:

Last week we spent significant effort understanding the forces and

resulting acceleration of the cart in Figure 1 to the right. This week we

want to keep the same experimental setup and focus our attention on the

various Energies within this system. For example, because objects are

moving up and down, there must be Gravitational Potential Energy, GPE.

Also, a spring is involved, so there must be Spring Potential Energy, SPE,

as well. If we add ALL forms of energy involved in the system, we can also

define a Total Energy, TE,

𝑇𝐸 = 𝐺𝑃𝐸 + 𝑆𝑃𝐸 + ⋯ . (1)

The Total Energy is a very useful idea because the Law of Conservation of Energy promises us that the

Total energy will behave in a very specific, simple way. The Law of Conservation of Energy states:

“The total amount of energy in a system is a constant unless energy is transferred through the

system boundary through Work, Heat, Electrical Transmission, etc.”

This single statement gives us a series of concrete goals.

A. Calculate, 𝐺𝑃𝐸 and 𝑆𝑃𝐸 for each time step at which we collected data. B. Plot each form of Energy over multiple bounces of the cart. Also add 𝑇𝐸 to the graph below.

Does the behavior of the Total Energy agree with the Law of Conservation of energy stated

above?

spring

𝑚2

𝑋

𝑚𝑐𝑎𝑟𝑡 Pulley

Figure 1 H

0

0.2

0.4

0.6

0 0.2 0.4 0.6 0.8 1

E n

e rg

y (

j)

Time (s)

All Energies?

GPE SPE

2 PHY 241 Fall 2018

C. Plot 𝑇𝐸 over multiple bounces with the Energy axis “zoomed in” so you can evaluate the fluctuations in TE, similar to the “Is TE Constant?” graph below. Worry, ponder, and deliberate

whether the changes in TE are due to Random Uncertainty, or some unaccounted form of

Energy.

D. If possible describe the Energy Transfer involved during your data run both qualitatively and quantitatively.

Equipment: (same as last experiment)

CBR 2- connected directly to a computer using a USB cable

Spring

String with loop knots in each end

Set of Masses

Hook

Cart

Safety glasses

Paperclip

Pulley

2 m track

Bubble level

Computer with Logger Pro or Logger Lite and Excel.

Procedure:

1) The central goal/question for this lab is: How does the Total Energy of our system change as the cart bounces back and forth multiple times?

2) Take some time to familiarize yourself with the accompanying spreadsheet. You should notice that there is a region for Initial Values. An important part of this lab is figuring out

0 0.1 0.2 0.3 0.4 0.5

E n

e rg

y (

J)

Time (s)

Is TE Constant?

TE

3 PHY 241 Fall 2018

what measurements you need to take to supplement the CBR measurements in order to

calculate the energies required. Most likely, there are too many columns in the Initial

Values and the Data Table.

3) Arrange your equipment to match Figure 1. Figure 2 shows a fast and easy way to connect the different components. Make sure you place the CBR in a location where it can measure

either the cart or the hanging mass as it moves.

4) When entering equations in E through L columns make sure you use: a. absolute references ($X$1) when using Initial Value cells.

b. relative references (X1) when using Data Table cells.

c. Refer to your Prelab for hints to improve the accuracy of your calculations.

5) Before leaving the classroom, make sure you email the data out to the entire group and the Teaching Assistant. Please use the subject “Lab 6 data- Section ###, Group ###.”

6) Also clean up your work station and returning small equipment to the appropriate storage.

7) Researcher: Use formulae (and the Word Equation Editor) to explicitly describe how the position data from the CBR was transformed into Stretch and Height data of the spring and

hanging mass respectively.

8) Researcher: For each type of energy your group calculate in evaluating TE, provide a formula describing how your group calculated that energy.

For example, if you were to consider the work done by the friction inside the pulley you

might write:

“For each data time step, our group estimates that the friction inside the pulley does work

on the system and reduces the total energy by Δ𝐸𝑝𝑢𝑙𝑙𝑒𝑦 = −𝑚ℎ𝑎𝑛𝑔𝑖𝑛𝑔 ∙ 𝑎𝑓𝑟𝑖𝑐𝑡𝑖𝑜𝑛𝑝𝑢𝑙𝑙𝑒𝑦 ∙ Δ𝑥𝑐𝑎𝑟𝑡 , (2)

Where 𝑎𝑓𝑟𝑖𝑐𝑡𝑖𝑜𝑛𝑝𝑢𝑙𝑙𝑒𝑦 ≈ .1 𝑚

𝑠2 (as given in the lab manual) and Δ𝑥𝑐𝑎𝑟𝑡 is the distance the cart

traveled between adjacent data points.”

Notice that symbols are clearly labeled (using the “_” key in the Word Equation Editor to

add subscripts to symbols) and new values like 𝑎𝑓𝑟𝑖𝑐𝑡𝑖𝑜𝑛𝑝𝑢𝑙𝑙𝑒𝑦 get a bit of explanation.

paperclip

Figure 2

4 PHY 241 Fall 2018

9) DA: Creating the two graphs described in the introduction and make sure they are properly formatted, including captions.

10) DA: Determine and report the approximate magnitude of the Random Uncertainty in your Total Energy measurement (with proper rounding and units).

11) PI: Calculate the energy transferred into/out of the system based on your data (a graph is a good way to visualize this calculation). Is this consistent with the acceleration of friction

measurements you collected in Lab 3? Explain.

12) PI: Evaluate the Law of Conservation of Energy (as given in the intro of this lab manual) in light of your group’s data and analysis. Be as specific as possible in highlighting any

deficiencies you see in the Law or in your data.