042 Laboratory Four: Marble mass, velocity, and momentum

Introduction

This laboratory explores the concepts of momentum

Questions

Existing theory asserts that momentum is conserved. At first you will qualitatively explore the conservation of momentum. Then you will make some quantitative measurements of momentum for marbles inbound and outbound from a collision.

In physics:

Equipment

I. Qualitative exploration

Five marbles sit touching each other on the flat portion of a marble track. The marble track is made using rulers. One or more marbles are released from an elevated end of the track and allowed to collide with the five stationary marbles.

Marbles on ruler track rulers marbles wood block

  1. Release one marble into the group of five. How many marbles are ejected?
  2. Release two marbles into the group of five. How many marbles are ejected from the group?
  3. Repeat for three, four, five... marbles.
  4. How is the number of marbles in related to the number of marbles out?
  5. If zero marbles are sent in, how many marbles come out?
Marbles inMarbles out

As you work on the above questions, experiment. Play with the marbles. How to the marbles know what to do? How does a marble know whether to go or to stay? How do the marbles count? Just how smart is a marble? Play gently - marbles can and do break - but do play.

II. Quantitative explorations of a single marble inbound

Said "mathematically," the momentum before is equal to the sum of the momentums after is written:

Pbefore = Pafter
minbound × vbefore = moutbound × vafter
where m is the mass of the marble, v is the speed of the marble.

  1. Find the masses of both the inbound and outbound marbles.
  2. Following guidance in class, measure the distance and time for the inbound and outbound marbles. Use the table to calculate the inbound and outbound momentum. Repeat for different inbound speeds.
  3. After obtaining five pairs of momentum in and momentum out, prepare a graph of the data. Consider whether zero cm/s in is also zero cm/s out and whether this is a possible data point.

Data tables

mass inbound marble × velocity inbound = momentum in [x] mass outbound marble × velocity out = momentum out [y]
mass m (g) × distance (cm) ÷ time (s) = momentum (g cm/s) mass (g) × distance (cm) ÷ time (s) = momentum (g cm/s)
× ÷ = × ÷ =
× ÷ = × ÷ =
× ÷ = × ÷ =
× ÷ = × ÷ =
× ÷ = × ÷ =

Transfer the momentum results to the following table. The following is the data to be graphed.

momentum in p (g cm/s) [x]momentum out p (g cm/s) [y]
00

Graph

Make an xy scattergraph with the momentum in on the x-axis, momentum out on the y-axis

Analysis [a]

[Notes from the field for instructors: In this laboratory we explore conservation of linear momentum. Another momentum that is conserved is angular momentum. Angular momentum is the momentum of spinning. Spinning objects tend to continue to spin. Objects that are not spinning tend to remain at rest– to not spin. Think of a child's toy top. In the experiments above we considered only linear momentum, but the marbles are spinning as they move on the track. In part two a spinning m1 duck hits a non-spinning m2 duck. The m1 duck loses speed and thus spin, the m2 duck goes from not spinning (sitting still on the track) to spinning very quickly. These changes in spin momentum are related to why linear momentum is consistently "lost" in these collisions.

Where linear momentum is p = mv, the angular momentum L = Iω where I = 0.4mr² and ω = v/r. Thus the angular momentum of a marble is L = 0.4mrv. One cannot just add all the momentums and hope for the best: the units are different. Ultimately one has to retreat to an energy position noting that the potential energy must appear as both linear and rotational kinetic energy in both of the marbles post-collision, along with losses to friction, sound, and any heat produced in the collision.

The thought occurred as to what to try to reduce the impact of external torque exerted by the track. One idea was to lubricate the ruler track with some form of greaseless lubricant such as WD-40®.

WD40 was tried. The first complication is the tape no longer holds the tracks in place. This problem proved rather insurmountable. In addition, WD40 wound up everywhere - on hands, table tops, soaked into paper that slid into the WD40. Would need a greaseless lubricant. Even, the loss of taping ability would remain fatal.

Why not simply use pucks on an air table? Two key reasons. The puck and air table are unfamiliar to students - this raises the probability that the students will, in their own minds, see the whole thing as magic. Another mysterious thing in the modern world. Secondly, the lab should be as reproducible as possible by any teacher in the nation. Part one requires nothing more than what an instructor on an atoll might be able to get their hands on. Part two adds only one unlikely element - a stop watch.

Marbles on a track are very complex!]