# PHY 141 Lab 4 - Conservation of Energy

The purpose of this lab is to verify the conservation of mechanical energy experimentally

## Equipment

• air track (with picket fence)
• glider
• photo gate (mounted on top of the glider)
• interface box (photo gate – computer)
• computer

## Introduction

For an isolated system, the total energy must be conserved. In this experiment we will examine the law of the conservation of the total mechanical energy by observing the transfer of gravitational potential energy to kinetic energy, using a glider on an air track that is pulled by a falling mass. The apparatus is is called an air track because an air “cushion” reduces the friction. We consider the system, glider-mass, to be isolated from friction. The position of the glider as a function of time can be accurately recorded by means of a photo gate device.

In this experiment, the glider on the air track obtains kinetic energy due to the loss of potential energy experienced by the small falling mass m.

The kinetic energy of the mass plus glider system when it is moving with velocity v is given by

$\Large \frac{1}{2}(M+m)v^{2}$
(4.1)

The change in the potential energy $\Delta PE$ of the system,when the height $h$ of the small mass m changes by $\Delta h$ is given by

$\Large mg(\Delta h)$
(4.2)

Note that $\Delta h$ will be negative in this experiment, ie. the system's gravitational potential energy should be reduced as the mass falls. The principle of conservation of energy leads us to expect that this decrease in the system's potential energy should result in an equal and opposite increase in it's kinetic energy.

$\Large \Delta KE=-\Delta PE$
(4.3)

We can also use Newton's second law to calculate what we expect the acceleration of the this system to be and check that with our experiment as well.

$\Large F_{net}=mg=(M+m)a \Rightarrow a=\frac{m}{M+m}g$
(4.4)

## Experimental Procedure

A battery-powered photo gate is mounted on the glider. When activated with the small push button on the side of the glider, the photo gate turns on a bright light emitting diode (LED) whenever the picket fence over the air track blocks the photo gate. A light sensor at the end of the air track receives the LED signals and the timing program in the computer measures and records the times when the light beam of the photo gate is blocked. Of course you need to make sure the LED on the base of the glider is facing the receiver on the track.

A small mass is attached to the glider via a string on a level air track. When we drop the small mass, the change in height of the small mass can be measured, as well as the velocity of the glider-mass system. This will allow the computation of the sum of kinetic and potential energies before and after the mass falls and verify (or dismiss!) the law of the conservation of mechanical energy as a useful concept.

1. Your lab instructor has a list of the masses for all the gliders (on the back of the rear door of the lab). Get the number of your glider and obtain its mass, M, from your lab instructor. Assume a 1 gram error for this mass and record this mass and the error in your notebook.
2. We need to determine the distance d from one “picket” to the next and enter it into the computer later on. Measure 10d and estimate the absolute error for it.You might remember that we did the same thing in lab 3. From this measurement determine the distance d and its error. Record all values in your notebook.
3. Level the air track by carefully adjusting the single leveling screw at one end of the track. When the track is level, the glider should remain nearly stationary at any point on the track. Be sure to tighten the wing nut on the leveling screw when the track is level. The leveling of the track is very important, if the track is not level your results will be incorrect.
4. Attach a 10 gram mass, to the glider with a piece of string and rest the string on the pulley at the end of the air track so that the mass hangs over the edge of the table and can fall freely. Record the value of this mass and an assumed error of 0.2 grams. Make sure the string with the weight attached is long enough so that you can reach the far end from the pulley and can start the motion with the photo gate in front of the first “picket”. The string should not be too long. The weight should not hit the ground before the glider is ~ 10 pickets from the end on the pulley side.
5. Set the computer on “MOTION TIMER” mode. When you are ready to begin a run, push the small button on the side of the glider. (This will activate the photo gate for about one minute, after which it will turn itself off automatically to save the batteries.) Hold the glider in a position where the photo gate is not blocked (LED off). Push the “SET” button on the grey interface box, then push “ENTER” on the keyboard. After you let the glider go, data recording will start when the photo gate is first blocked. Push the “STOP” button on the interface box before the glider rebounds from the end of the air track or before the falling weight hits the floor, which ever comes first. Push “ENTER” on the keyboard and a table of times will appear on the screen. Make sure that you have enough data points, ~35 points (you must arrow down to see the end of your data). Do not use the values from this table, but instead use those from the table you see after you have followed the instructions for entering d below!!
6. Hit “ENTER” on the keyboard and choose “Graph Data”. Choose “Velocity vs. Time”, then choose “Other (specify the length)”. Enter your value for d, hit “ENTER” to bypass the “SELECT GRAPH STYLE” screen, hit ‘ENTER” twice to bypass the horizontal and vertical scaling. You should see a linear velocity vs. time graph. If you do not get a linear graph, repeat the measurement (step 4). Hit “ENTER” and select “Display Table of Values”, you should see the time values and calculated velocity values. Disregard the first data point and copy a selection of data points in to your lab notebook. You should get ~8 data points which should be spread out over your motion.
7. For each velocity value you also need a change in height $\Delta{h}$. You can define this as zero at the first data point you record and then use the distance traveled along the air track. For example if you first point is the 2nd point and your second point is the 5th point, then $\Delta h =-(5-2)d$

## Analysis

To calculate the potential energy for each point use equation (4.2). To calculate the kinetic energy use equation (4.1). You should also calculate the uncertainty in each quantity. In the calculations of uncertainty the error in the time may be neglected, because we assume the computer is pretty good at measuring time accurately, or at least much more accurately than we can measure a distance or a weight, and therefore the relative error in the time is much less than the relative error in either d,m or M.

Make plots using the plotting tool of Potential Energy vs Kinetic Energy and Velocity vs Time.

Find the slope of the PE vs KE plot and compare it to your expectation based on conservation of mechanical energy.

Use the slope of your graph of velocity vs time to find the acceleration of the system and then (once again!) obtain the value of the acceleration due to gravity.