The Impulse-Momentum Theorem
 
Part II, Experiment
 
•  Open the Logger Pro file and the worksheet for today.  The switch on the force plate should be on the lower range setting, -200/+850 N.  Choose a ball that you can drop onto the force plate and record at least five distinct bounces on the F(t) graph.  Measure its mass.  If you need to put something on the mass balance to keep the ball from rolling off, make sure to subtract its mass.  Record the mass of the ball on the worksheet.  Also type a short description of the ball.

•  Place the ball on the force plate and zero the force using the Zero function on the upper Logger Pro toolbar. Then raise the ball above the plate by about one meter and drop it while acquiring data.  Record the times of the first five consecutive bounces in the table in the appropriate boxes of the worksheet. 

•  Zoom into the data for the second bounce.  You’ll see a collection of peaks.  The entire first peak plus the first half of the first valley is a good measure of the impulse of the impact.  Use the Integral function to obtain the impulse Jy2 of the impact and record it in the Jy2 box.  Repeat the integration for the third and fourth bounces and record Jy3 and Jy4.

•  Zoom back out to where your graph shows the five bounces plus the data boxes for the integrations for the second, third, and fourth bounces.  Copy and paste this graph into your worksheet, ensuring that the data boxes are readable.  You might need to decrease the size of the graph, such that the data boxes consume a larger portion of it. 

•  Calculate the parameters associated with the green boxes of the table in the worksheet:  the ball’s speed vi,i-1, its change in y-momentum pyi, and the ratio of the change in y-momentum to the integral of force over time pyi/Jyi.  Then find the average, sample standard deviation (defined in Part II of the friction experiment), and fractional uncertainty (sample standard deviation divided by the average).   Your fractional uncertainty should be less than 0.100. 

•  Check that you filled in all of the square brackets in the table with the correct units.

•  The last question on the lab report asks you to report your result in standard form and, in your own words, discuss what you expected in comparison to your experimental result.  Mention possible reasons for any difference.

If all has gone well today, you will have verified that the change in momentum is equal (or close) to the integral of the force over time, that is, the impulse-momentum theorem is true.

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