# Conservation of Energy

#### Purpose

To check whether the Total Mechanical Energy is conserved for an object sliding down an air track.

#### Objectives

• To learn how to organize data in spreadsheet.
• To learn how to use built-in functions in spreadsheets for data calculations
• To learn how to use instrumental precision for limiting of how many digits to keep in data recording.
• To learn how to calculate the propagation of the uncertainty of measurements.

#### Equipment

• Air pump and air track with a glider
• Pasco Mechanical Kit
• Two photogates to connect to Pasco 850 Interface
• Ruler or calipers

#### Theory

The total mechanical energy of a system is equal to the sum of the kinetic energy of all parts plus the potential energy. For a single object with mass m moving at speed v at location h meters above the ground, the total energy is given by:

$E = \frac{1}{2}mv^2+mgh$

Here g = 9.8 m/s2 is the acceleration due to gravity.

#### Setup

In this lab, we will use a glider along an inclined air track. Below is a detailed experimental setup.

###### Experimental Setup

Things to watch:

• The photogate must blink each time a black tape portion goes through
• Watch out for friction. You should set the air pump at level 3. if you suspect friction is present along the track, you might have to increase the level of the air pump to 5 or max.

#### Activity. Determine the total Mechanical Energy of the glider at two locations

• Measure the height of the track at the location of the two photogates, and calculate its potential energy
• Run the experiment, and get the velocity of the glider at the two photogates. Calculate its kinetic energy.

#### Data and Results

• Use the spreadsheet built-in functions to calculate the potential and kinetic energy at both photogates
• Determine the total mechanical energy at both photogates.

Question: What is the percent difference between the two values?

Question: Is the Total Mechanical Energy conserved?

#### Analysis and Assignments

If you have a large difference between the values for the Total Mechanical Energy at the top photogate and the bottom photogate work on A1.

If the values at the top and bottom agree to within 5% or less, work on A2.

A1. (Only if you have large discrepancy between the measured and calculated values for the acceleration). Check whether any of the following factors can be accountable for the discrepancy:

• Photogate. Let the glider through each photogate and make sure the photogates blinks properly. There should be a solid blink during the glider’s passing through a photogate.
• Presence of friction. Increase the Air Pump level to 5 or higher and re-run the experiment.

Question: Which of the above factors led to significantly improved results?

A2. (Only if you have agreement within 5%). How does the uncertainty of you measurements affect the values for the Kinetic and Potential Energy?

Determine the absolute and relative uncertainty of each of your measurements: Δm, Δv, Δh.

Absolute uncertainty comes from the instruments – what is the smallest value that you can measure with that instrument.

Relative uncertainty is the fraction in percents of the absolute uncertainty to the value of your measurement.

Calculate the relative uncertainty of your measurements, and that of the final result:

$\frac{\Delta m}{m} = ...$

$\frac{\Delta v}{v} = ...$

$\frac{\Delta h}{h} = ...$

$\frac{\Delta KE}{KE} =\frac{\Delta m}{m} + 2 \frac{\Delta v}{v}$

$\frac{\Delta PE}{PE} =\frac{\Delta m}{m} +\frac{\Delta g}{g}+ \frac{\Delta h}{h}$