Lap report

Momentum and Impulse

Theory

Impulse-Momentum Theorem: The change in an object’s momentum is identical to the

total impulse force that changed it:

𝑃𝑓 − 𝑃𝑖 = ∆𝑃 = 𝐹∆𝑡

Apparatus

Force probe, two carts, track, motion sensor, LabQuest Mini, rubber band, string, 0.250

kg and 0.500 kg bar mass, and a 1.000 kg or 0.500 kg mass to calibrate the force probe.

Procedure

• Set up and level your track.

• Find the mass of your cart and bar masses.

• If needed, switch your force probe to the ± 10 N scale.

• Attach the motion sensor and force sensor to the LabQuest Mini.

• Place the motion sensor at one end of the track, and the force sensor at the other

end, braced against an end stop.

• Calibrate your force probe. (Note: the force probe will be used lying flat on the

track in this experiment, so the zero force calibration point should be set with the

probe in that position. )

• Set the duration of the experiment to 2.00 s and the samples/second to 30.

• Tie a length of string between the force sensor and the rubber band; attach the

rubber band to the cart.

• Place the cart near the force probe, letting the excess string hang to the side of the

track so as to avoid getting caught in the wheels of the cart.

• Click on Collect at the same time that you send the cart toward the motion sensor.

The card should bounce back toward the force probe due to the rubber band.

Make sure that the recorded motion catches both before and after the bounce.

• Copy all the time, force, and position data into the Data tab of the worksheet.

Analysis

• On the position vs. time graph in Logger Pro fit a straight line to the region just

before the rubber band starts to pull on the cart to determine the velocity. Note

the initial velocity in the worksheet, and copy the selected time and position data

as well.

• Repeat the previous item for the region just after the bounce.

• On the force vs. time graph, shade the area under the curve, from zero on one

side to zero on the other side of the bump, and note in the worksheet the elapsed

time during which the impulse occurred. (Logger Pro will show you Δt in the

lower left corner when you have a section of the graph selected.)

• Select the entire force graph and find its total area by using the Integral button in

Logger Pro; record this value as total impulse in your worksheet.

• Copy the position vs. time and force vs. time graphs, with their fits or

integration, to your worksheet’s Graphs tab.

• Calculate and record the momentum before and after the bounce.

• Calculate and record the total change in momentum of the cart.

• Calculate and record an unbiased percent error (preferring neither one) between

the change in momentum and the total impulse.

Repeat this procedure and analysis for a total of four trials, each with a different total

mass. Calculate and record the average percent error for these trials; do these results

imply that the change in momentum is equal to the total force that produces it?

Create a graph of impulse time over mass from your four trials, and a graph of impulse

time over initial velocity. Do these graphs suggest any particular relationship between

either the mass or the initial velocity, and the impulse time? Save these graphs in the

Comparison tab of the worksheet.

Report

Include a conclusion, as described in the Lab Report Rubric, in the conclusion tab of the

worksheet. It should discuss the questions raised in the two previous paragraphs, using

the results of the experiment to support the conclusions reached. The discussion of

sources of error should contain at least two that are not due to error by the

experimenter or the instruments.