Force and Acceleration

by Robert Tinker and Carolyn Staudt

t is now easy to take probeware out of the lab. To demonstrate the flexibility of this we took a handheld computer with probes (see Figure 1) to a playground. We were looking for a real-life situation where we could easily demonstrate the relationship between the force on an object and its acceleration. Using probes it is possible to record force and acceleration at the same time, and so we looked for such a situation.

Our equipment was very easy to assemble and operate. We started with a Palm™ handheld computer. We used the "Low-g" acceleration probe and the "Student Force" probe from Vernier. The interface and software was from ImagiWorks. Both probes connect to the Palm through the interface. We also used ImagiWorks software on the host Macintosh computer to upload the results using Palm's "Hot Sync" system software and cradle.

The ImagiWorks software is remarkably sophisticated, growing out of research The Concord Consortium did with Elliot Soloway and ImagiWorks founder Wayne Grant. Groups of datasets are stored with calibration data, notes, and sketches in file structures called experiments. This makes the software a complete record-keeping package that is ideal for fieldwork. The software also communicates with PCs for later analysis.

Measuring force and acceleration at the same time isn't as easy as it sounds because we had to measure all the forces on the object being accelerated. At first we tried pushing a person across the floor in a wheeled chair, but the force of friction was hard to measure. We had to find a situation with less friction.

That's what led us to a playground swing, which is a very low friction device. We velcroed the acceleration probe to the seat of a "rocking horse" swing (see Figure 2) and pushed it forward with the force probe. The result should be that the acceleration is proportional to the force (F=m*a).

One problem to take into consideration is the force of the support rope. The only time that it doesn't exert a horizontal force is when the swing is at its lowest position. To get the best data, we started pushing the empty swing just before it reached its lowest point, and continued pushing until it reached the same distance on the other side of the lowest point.

Figure 3 shows some data from our experiment extracted from a spreadsheet program. You can see at a glance that the upper force curve and the lower acceleration curve are similar. In fact, they are proportional, with the force being between seven and nine times the acceleration. There is some error in the measurement because of the force applied by the support rope that we didn't measure. Still, these data are convincing direct evidence that force causes acceleration and that the ratio between them is the mass.

To test this further, we put a child on the swing (see Figure 2). Now, a much greater force should be needed for the same acceleration. The ratio of force to acceleration should be larger, reflecting the added mass of the person. And, in fact, the acceleration was so small that we couldn't put it on the same graph (see Figure 4) with the force without multiplying the acceleration by a factor of 170 (compared to the factor of seven to nine that worked for the empty swing). As you can see, the two lines of the graph don't quite line up. In fact, the acceleration seems to be ahead of the force and the visible bumps between the two lines on the graph appear to be delayed. Possible reasons might include that the child anticipated the push and that he shifted his weight as the swing moved forward. The two lines are about the same height, showing that more force is needed for the same acceleration when the mass increases.

These two experiments make it clear that:

Force and acceleration are proportional.
More mass makes it harder to accelerate.

We are not the only ones fascinated by the acceleration sensor. At the grand finale of a recent keynote address, Steve Jobs had a colleague jump 20 feet into an air bag clutching their new portable iBook™ attached to an accelerometer. They used the wireless networking capacity of the iBook to successfully send the data in real time to a stationary iBook. We don't recommend this for students, however!

We hope readers will continue experimenting on their own. Can you get better force and acceleration data on a swing or another device? Be sure to visit our Probe Sight web page for more information on probes and how they can be used.

Robert Tinker is president of The Concord Consortium. Carolyn Staudt is a curricuclum developer and a teacher professional development specialist for The Concord Consortium.
bob@concord.org
carolyn@concord.org

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