# PHY 123 Lab 5 - Momentum

The purpose of this lab is to demonstrate conservation of momentum in collisions of objects and compare elastic and inelastic collisions.

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

## Equipment

• air track
• computer
• small glider
• big glider
• interface box
• 2 photo gates

## Introduction

Conservation laws are very powerful tools in understanding physical phenomena. What takes place in collisions of objects is governed by momentum conservation. The experiment will use an air track to study collisions in one dimension and demonstrate that momentum is really conserved in these relatively simple processes. (They are simple because no external forces act in the horizontal direction since there is no appreciable friction.)

You will measure the velocity of each glider, before and after the collision, by measuring the amount of time that a metal tab on top of the glider blocks a photogate.

Measure the width, $w_{s}$, the width of the metal piece on the small glider and obtain the mass, $m_{s}$, of the small glider with the scale at the front of the room. Record your values on your worksheet. Repeat the two measurements for the big glider. Its mass exceeds the 200g capacity of the scale, so you have to put a 200g mass on the opposite pan – be sure to add 200g to the reading for the big glider. Assume that each width has an absolute error of 2 mm and each mass has an absolute error of 1 g.

## Elastic Collision-sliding small glider into big glider

In this part of the lab, there will be an elastic collision between a moving small glider and a stationary big glider.

For the first collision, you will collide the small glider with the big glider, which is at rest (the target). Turn on the air track and make sure that it is level. If you release a glider at rest in the area between the two photo-gates, it should not move. Set the gliders with the non-velcro ends of each glider, the ends with the springs, facing each other. Make sure the spring is rigidly attached to the cart. If it is not, get help from your instructor. Place the big glider in between the photo gates, not far from the second (downstream) photo gate and gently (you want to avoid an up-down wobble of the glider which will cause friction) launch the small glider toward the resting big glider. Observe the directions that the two gliders take after the collision, and enter your observations on your worksheet.

Turn on the computer and double click the icon “Exp5_t1_t2”. (If you can't find it on the desktop or in “New Folder” download it here (Right Click and Save to desktop))A window with a spreadsheet on the left (having “Time, Status 1, Status 2 columns) comes up. On top is a window “Sensor Confirmation”, where you may have to click “Connect” twice (two sensors)

You are ready for data taking now.

Position the small incident glider upstream of gate #1 and the big target glider close and upstream of gate #2. Make sure your incident glider goes into gate #1 (Time 1 in the table below.) Click the green “Collect” icon and launch the small glider. Make sure that you stop the computer before any of the two gliders hits the end of the track and bounces back. After the collision, you should see something like this table.

TimeState 1State 2
1.64711
1.78730
2.0445 1
2.2690 0
2.46981
3.37530

In the above $t_{i}$ the time the incident glider takes to pass through the photogate before the collision is 1.7873-1.6471 = 0.1402 s. Likewise, $t_{i}’$ for the large glider would be 2.2690-2.0445, and $t_{i}’$ for the small glider would be 3.3753-2.4698. Of course, you will fill in the data from your own measurement. Note that unprimed variables are before the collision, and primed variables are after. Fill in the time values on Table 1 of your worksheet.

## Elastic Collision-sliding big glider into small glider

This part is exactly the same as the previous part of your lab except that you will slide the big glider into the small glider that is at rest. Again, start the data collection and gently launch the big glider. Make sure your incident glider goes into gate #1. Fill your times into Table 2 on your worksheet.

## Inelastic Collision-sliding big glider into small glider

In this part, you will observe a perfectly inelastic collision between a moving big glider and a stationary small glider. Perfectly inelastic means that the objects stick together after the collision, which is accomplished by a piece of Velcro on each glide. For this collision, you collide the big glider into the small glider. Now, make sure that the velcro ends of each glider are facing each other. Launch the big glider and observe. Make sure your incident glider goes into gate #1. For this experiment, you only record two time intervals: the big glider in gate #1 before the collision, and the small glider in gate #2 after the collision. Record the times in Table 3 on your worksheet.

## Analysis

The velocity $v$ of the gliders before and after the collision by using the formula below:

$\Large v=\frac{w}{t}$
(5.1)

The error in $t$ may be neglected, and we can assume that the relative error of $w$ is equal to the relative error of $v$ to calculate the absolute error of $v$ according to expression (1.4) in Lab 1.

The momentum of each object is given by

$\Large p=mv$
(5.2)

The kinetic energy of each object is given by

$\Large KE=\frac{1}{2}mv^{2}$
(5.3)

The tool below will calculate the velocities, momentum and kinetic energies of the objects before and after the 3 collisions. You should then verify whether momentum and/or kinetic energy is conserved in each collision. Bear in mind that what you need to decide is whether the total momentum or total kinetic energy is the same before or after the collision within experimental error. This means that the values do not need to be exactly the same, but there should be overlap of the ranges around the values when you take in to account the experimental uncertainty. Discuss your results with your TA!

Fill in the widths and masses and their uncertainties in the appropriate boxes below:
ws= +/- m
wb= +/- m
ms= +/- kg
mb= +/- kg

Copy the results from your 3 experiments in to the tables below:
Table 1. Elastic Collision sliding small glider into big glider:
Glider
ti[s]
t'i[s]
Small
Big

Table 2. Elastic collision sliding big glider into small glider
Glider
ti[s]
t'i[s]
Small
Big

Table 3. Inelastic collision sliding big glider into small glider with velcro
ti[s]
t'i[s]
Pre-collision
Post-collision 