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Energy Conservation
Introduction As an object slides down a frictionless surface its Total Mechanical Energy ( ET ) remains constant even though its potential and kinetic energies change. The purpose of this lab is to test the validity of the Conservation of Total Mechanical Energy.
Equipment Air Track Computer with Logger Pro Ring stand, Miniature Glider Vernier Photogate Meter Stick Air Supply Vernier Lab Pro Scale, Digital Table Jack Air Track Accessory Kit
Theory The Total Mechanical Energy of an object remains constant in the absence of non- conservative forces. This is called the Conservation of Total Mechanical Energy or sometimes, just Energy Conservation for short. This is a fundamental tenet of science and has extremely broad applications in all technical fields. The two types of energy that will be under consideration in this laboratory experiment are the potential energy PE and the kinetic energy KE. The object in this case will be a glider on an air track system. There are two forces at work in this experiment – gravity and friction. The frictional forces have been minimized by the use of the air track system and will therefore be neglected in our analysis. Gravity exerts a force on the glider and will contribute a gravitational potential
energy ( GPE ) to the Total Mechanical Energy ( ET ). The normal force of the track pushing back on the glider is perpendicular to the direction of the glider motion and so will produce no work and will not affect ET. Therefore, in this experiment the Total Mechanical Energy consists only of the Kinetic Energy ( KE ) and the Gravitational Potential Energy ( GPE ). Since there are no non-conservative forces acting on the glider its Total Mechanical Energy is conserved.
Terminology Gravitational Potential Energy: GPE = mgy Kinetic Energy: KE = ½ mv^2 Total Mechanical Energy: ET = KE + GPE = ½ mv^2 + mgy
General Procedure As the glider accelerates down the sloped air track you will make measurements of the glider’s GPE and KE for five different locations along the air-track. These five locations should be located at displacements of 0 cm, 30 cm, 60 cm, 90 cm, and 120 cm along the length of the track relative to your launching point. The glider GPE can be calculated if we know its vertical height from the reference level of zero gravitational potential energy. We will choose the zero reference level to be the height of the fifth (bottom) measurement position from the surface of the table. We will first measure the heights of each of the measurement positions relative to the surface of the table and record these in the first column of your Data Table. Then subtract off the height that you measured for the fifth (bottom) position ( y 5 ) from all five of the measured height values. Record these results in the second column of your Data Table. These vertical heights are relative measurements so you can make your measurements from the surface of the table to the bottom of the scale along the side of the air track. The glider will always maintain its constant vertical spatial relationship to this scale throughout all the experimental runs. Hence, you don’t need to locate the glider at each measurement position and measure the vertical height to some part of the glider itself.
- Measure the mass of your glider using the available scale and record the value in your Data Table.
- Place the jack under the single leg of the air track. The jack should be almost fully compressed. Set up the air-track with an inclination roughly similar to that shown in Figure 1.
- The displacement intervals along the air track are relative and will not agree with the scale values on the track itself. You can’t work from the actual end of the track where the “0” is located and the air track legs can get in the way of the ring stand holding the photogate. Therefore, on the side of the track that has the scale oriented with the zero end up, select measurement points 50.0, 80.0, 110.0, 140.0 and 170.0. These will satisfy the 30.0 cm interval requirements and avoid the end of the track and track leg problems. In the end these are simply reference points and their values do not enter into any calculations.
- The vertical height measurements are denoted by the variable yi. The measurements should be made at positions located at intervals of 0, 30, 60, 90 and 120 cm along the air track from your initial launching location. We will designate the height y 5 as the zero reference level of GPE. The difference in heights relative to this zero level will be designated by the variable y’ defined as y’i = yi – y 5.
0 30 cm 60 cm 90 cm
~120 cm y 1 y 2 y 3 y 4 y 5
Figure 1. Air-track, glider, and photogate arrangement. Measure the y -values from the tabletop surface to the scale along the air track.
- Measure y 1 through y 5 , as shown in Figure 1, to three significant figures. Calculate the y’i values and record them in your Data Table.
- Place the photogate at the 30.0 cm location along the air track. This will allow you to measure the velocity at y 2. Special Alignment Instructions – Align the pin on the side of the glider with the track scale. For the y 2 location you are 30.0 cm from your launching location and the track scale should read 80.0 cm. With the glider held at this location your lab partner should position the photogate so that the beam path is perpendicular to the path of the glider. The photogate should also be rotated slightly about its mounting axis so that its body is perpendicular to the plane of the air track. The flag should not strike anything as the glider travels down the air track. After taking data at this point this alignment procedure will be repeated at each of the other three positions
- Turn on the air supply to the air track and then turn up the air volume until the glider floats on a cushion of air. Let the glider accelerate from its rest position at Displacement = 0.0. ALL DATA WILL BE TAKEN WITH THE GLIDER RELEASED FROM THIS SAME LOCATION. Record the velocity measured, when the glider passes through the photogate, in the Data Table below. Repeat this velocity measurement two more times for a total of three velocity measurements at this photogate position.
- Repeat these velocity measurements with the photogate positioned at y 3 , y 4 , and y 5 and record the values in the Data Table below.
- Calculate the average velocity for each measurement location and record the results in the last column of the table below AND in the 5th^ column of the second Data Table
After completely filling in this entire Data Table you are ready to make your graph. The vertical scale will be energy in joules and the horizontal scale will be the Displacement position in centimeters. (it need not be in SI units since it only marks a location). Draw best-fit lines for each quantity, GPE , KE , and ET for your graph. You only need to do the line statistics, (ie. LINEST - equation, slope uncertainty and correlation coefficient) for the ET best-fit line.
Questions (Questions should be answered in your Formal Lab Report)
- The most sensitive measurement in this lab is that of the flag length, what would happen to the values of the velocities if you used a value of the length that was too large? How would this affect the kinetic energy values? What would this do to the value of the Total Mechanical Energy ( ET )?
- In this lab we neglected friction. If friction was present what would it do to the values of the velocities? How would this affect the kinetic energy values? What would this do to the value of the Total Mechanical Energy ( ET )?
- Is the best-fit line for the total energy E horizontal? In other words, is the slope of your best-fit line to your ET data zero within experimental error? Theoretically, should the best-fit line for ET be horizontal? Explain why or why not.
- Within reasonable limits of experimental uncertainty were you able to show conservation of energy for the glider on the air track? In other words, does the interval determined by the value of the slope of your Et line +/- its uncertainty contain the value zero?
