# PHY 123 Lab 4 - Conservation of Energy

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

If you need the .pdf version of these instructions you can get them here.

## 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, (in this course we use $\delta$ to denote a change in a quantity and $\Delta$ to denote the uncertainty in a quantity),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. 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 on your worksheet.
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 2. From this measurement determine the distance d and its error according to expression (11) from Lab 1. Record all values on your worksheet.
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.
4. Attach a 20 gram mass (NOT more than 20 g!), 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 on your worksheet. 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. Get the computer ready for data taking: Double click the icon “Exp4_xv_t2”. A window with a spreadsheet on the left (having “Time, Distance, Velocity” columns) and an empty graph on the right with velocity and time axes comes up. On top is a window “Sensor Confirmation”. Click “Connect”, again “Connect”.
6. Enter your value for the distance d in Fig. 2 above from step 2) into the program: Click Data→User Parameters: the window “User Parameters” comes up and should show:
Name:Value:Units:Places:Increment:Editable:
PhotogateDistance1your value of d 41.0000

Click OK. You are ready to take data now. Click Experiment→Start Collection.

Hold the glider on the air track at the far end from the pulley with the photo gate ~ 3 cm in front of the first picket. Release the glider and hit the space bar (which stops the data taking) when the glider is ~ 10 pickets from the end at the pulley side. (You may want to practice this a few times.) After a good run you should have ~13 velocity-time pairs in the spreadsheet and a straight line velocity vs time graph. If you do not get a linear graph, repeat the measurement. If your final graph still has a kink at the beginning use only data after the kink. Copy the first 8 data points (rows which contain a velocity) from your spreadsheet into Table 1 on you worksheet. The first point you enter is your data point “1” in the analysis below. Don't skip any points after point “1”

## Analysis

Enter in the table below your value for $d$ and $\Delta d$, $m$ and $\Delta m$, $M$ and $\Delta M$ and then the 8 velocity and time values you wrote in your table. When you click submit the computer will produce a table and a graph from your values. To calculate the change in potential energy it works out $\delta h$ and then multiplies it by $mg$ to get $\delta PE$, the change in potential energy from the value at the first measurement point. The change in the height $\delta h$ in equation (4.2) is the same (in magnitude, not sign) as the distance traveled by the weight from the data point 1 to 2, 1 to 3, 1 to 4,… etc. Thus for data point 2, $\delta h =-(2-1)d$, for data point 3, $\delta h =-(3-1)d$ etc.

In the calculations of errors the error in the time is 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. There are a few exercises in the preparation assignment about how the errors in the various quantities are calculated from the errors in what we measured.

The computer calculates the Kinetic Energy at each velocity measurement by using equation (4.1). Following this a plot is made of $\delta PE$ vs $KE$. What do you expect the slope of this graph to be. Are your results consistent with this expectation?

A second plot of velocity vs time is also made. The slope of this graph is the acceleration. Check whether it matches the value you expect from equation (4.4).

Discuss your results with your TAs!

d= +/- m
m= +/- kg
M= +/- kg
Time and Velocity Values
t1 s   v1 m/s
t2 s   v2 m/s
t3 s   v3 m/s
t4 s   v4 m/s
t5 s   v5 m/s
t6 s   v6 m/s
t7 s   v7 m/s
t8 s   v8 m/s

phy123off/lab_4.txt · Last modified: 2010/08/03 17:06 by mdawber