Investigating the Impulse-Momentum
Relation
As we have seen, the impulse delivered
to a body during an interaction is equivalent to the change in momentum of the
body. We also saw that impulse can be thought of as the area under the Force-Time
graph for the force that acts during the interaction. In this investigation
we will test the impulse-momentum relation.
Procedure
- Drop a small mass (50 g or 100g
) into a sand filled cup resting on a wooden plate which is attached to a
force (strain) gauge. The gauge is attached to a Logger Pro interface. (Get the lab set-up file here.) Using a
high sampling rate (1000 samples per second) it is possible to record the
force exerted on the gauge as the mass comes to rest. We will look at the
details on how to set up the interface in class. Each group should repeat this 5 times to get enough data.
- If you know the velocity of the
mass before hitting the cup you can easily determine the momentum of the body
prior to interacting with the cup and sand mixture. From this you can determine
the change in momentum and hence impulse that the cup/sand exerted on the
mass.
- The velocity of the mass can be
determined if you know the distance through which the mass falls. It is very
easy to show that the magnitude of the velocity is given by the formula:
In this formula v
= the velocity after falling a distance h, 'g' is the local acceleration of
gravity. In this experiment you should measure the drop distance 'h' to within
the nearest 0.5 cm and try to measure from the center of mass of the object.
A good drop height would be about 20 cm. A simple length of pvc tubing will help you "aim" so that the mass will land in the centre of the cup. Adjust the tubing so that the top of the tube is the desired height above the sand. Make sure you record this height
- When ready, drop the
mass and collect Force-Time data with the interface. You may need to do this
several times before getting a good run. Be sure to either save the data (use
file->save or export the data file->export) so that you can refer to
it again if necessary. Make sure that you know where the files are being saved (likely your documents folder) and give the files useful names (drop1.txt or something like that)
Analysis - What to
Do with the Data
- Reset the zero point on your data. This means you will need to mathematically move the force measurements up so that the rest position of the Force-time graph reads zero N. Take a look at the following graph to see what I mean. Make sure to discuss within your group the best way to determine the offset you need and also be sure to tell me how you did it! This is easiest to do in Excel so just cut&paste the data from LoggerPro into Excel - process it and then take it back into LoggerPro for analysis.
- LoggerPro software has area finding
tools built in. In class we will look at some sample data, how to move it back and forth between LoggerPro and Excel and how to measure
the area for this data set.
- Prepare a summary table in which you state the area measured for each run. Include in your table an average of the 5 runs as well as a measure of the standard deviation of the 5 areas. This will be used as the error (+ or -) for your measurement of the impulse. Note - you should not use the entire graph to determine the area - explain what part of the graph is relevant and what part you "ignored" in your area measurements.
- Discuss how well your experiment
illustrates the impulse-momentum relation. (Note - It is difficult to get
much better than about a 10% precision in this experiment. Be sure to indicate
how closely the measured impulse matched the change in momentum for the mass.)
Additional Questions
- What was the maximum force exerted
on the mass during the interaction with the sand?
- Why does the Force-Time graph
"oscillate" for a brief period of time after the original interaction?
- Why did we use sand?
- How would you expect the graph
to change if you did not use sand but dropped the mass directly onto the wooden
platform? You may want to do this to corroborate your answer.
- What was the average
force exerted on the mass as it came to rest? Explain how you
determined "average".
What to Hand In
Each group should hand in a complete report which includes an impulse
graph or graphs, table that summarizes your data and sample calculations showing that the impulse-momentum relation has
been verified (estimate how precisely you were able to do this). Make sure that all graphs and tables are numbered and properly labeled. Be sure to
answer all of the additional questions as well.
Some Common Errors to Avoid...
Here are some of the more common errors that I see and ones to avoid:
- Too many significant digits shown! A really common mistake is to not think about how many decimal points or significant digits to use. If in doubt ask. Correct use of "Sig digs" really involves using common sense.
- Don't just hit the print button on EXCEL and spit out tables. Although Excel produces very good graphs it is not nearly as good at producing attractive and readable tables. I will be brutal with this! Take the time to format tables carefully. Also - embed graphs and tables within the report. Don't tack them at the back.
- Label all tables and graphs (Figure 1, Figure 2, Table 1, etc) and don't include a graph or table if you never mention it in the body of the report.
- Each graph or table should have a brief caption saying what it is.
- Don't leave off the units from either tables or graphs - this is almost a capital offence!
- Your lab report should have a cover page identifying the group, lab title, date etc.
- Use a standard report structure: Introduction, Observations (Data), Analysis and Conclusions. Each of these should be in a separate section of the report and you could share the writing within the group. Be sure that the final report uses a consistent font and size and conforms to rules of correct report writing.
- Make sure to cite all sources used. If you used another group's data be sure to acknowledge this.
- Final copy should be printed (not e-mailed) but I can look at preliminary copies via e-mail if you have questions about style, graphs etc.
Date Due:
Next lab period