# Fan Cart: Exploring Force and Acceleration (multi-video)

### Summary

This multi-video DMV provides an opportunity for students to explore the relationship between the force exerted on an object and the object's acceleration. An electric fan provides a force that causes a low-friction cart to accelerate along a track. Students can measure the force, and make other measurements to determine the resulting acceleration.

Using the next-generation DMV Player, students can vary the amount of force on the cart to determine the mathematical relationship between the amount of force and the acceleration. They can test their relationship using video with an Einstein doll on the cart.

## Files

### Instructor Note

When teaching with this video, direct students to the student video library, which provides student access to all videos without links to instructor materials and solutions.This video is only visible using the Next-generation DMV Player There are six videos visible:

- Introduction, which explains the measurements students can make. This video is not intended for data collection, just to give students an overview of the videos.
- Fan-force 1-4
- Einstein riding the cart

For all the videos except the introduction, students can select 30 fps (normal speed) so they can see the actual speed of the cart, or 240 fps ( 8x slow motion, or 1/8 speed). The frame counter is only visible on the 240 fps video.

Sample data on a google doc.

## Teaching Materials

Students can use the first video as a introduction. Key points:

- The spring shown in the inset allows students to measure the force exerted by the fan. The spring is calibrated in Newtons.
- The cart accelerates during the time interval from when the small ribbon is cut, until the time when the yellow light on the cart turns off, indicating that the fan motor is turned off. Students use the frame counter to measure this time interval.
- After the fan turns off, students can measure the final velocity as the cart coasts along the track.
- Using these measurements, students can calculate the acceleration of the cart while the fan is on.

Ok, what can we do with this? One possibility is to use Newton's Second Law and the measurements from a *single* video to determine the mass of the cart. Different students or student groups can try different fan force settings and compare the results.

Another way to use these videos is to plot the relationship between the acceleration (y-axis) and fan force (x-axis). The slope will yield the reciprocal of the mass of the cart. The negative y-intercept shows track friction. Here is a sample graph of acceleration vs force. Using this approach, students can test their relationship by using the sixth video to find Einstein's mass. The actual mass of the Einstein doll is 51.2 g. The actual mass of the cart is 275.2 g

Why do the results vary? In some cases, the calculated mass of the cart is noticeably higher than the actual mass, and other times it is much closer. The measurements and scales we use are as true-to-life as we can make them, so any variation is likely caused by real-world deviation from theory. Here are some possible sources of error for students to consider:

- friction on the track (but this should be constant for all trials)
- the track is not level (again, consistent for all trials)
- speed of cart is not constant after fan motor turns off

Although the cart should roll with constant speed once the fan turns off, students can explore whether it actually does. For example, the cart could slow due to friction after the fan turns off. Or, the fan could be spinning fast enough that the cart continues to accelerate even after the light turns off. Here are two experiments that students can do to determine which one. They could measure the speed of the cart during the first 10 cm of coasting, and compare it to the speed during the last 10 cm. If the speed of the cart is faster during the last 10 cm, this means the fan is continuing to provide force after the motor turns off. Second, students can compare trials where the fan speed is low to trials where fan speed is high. They'll notice that low fan-speed trials, the calculated mass of the cart is higher than the predicted value, showing that track friction slows the cart. During high fan-speed trials, the calculated mass of the cart is nearly the same as the actual value, showing that the residual fan force compensates for the track friction nearly perfectly.

Here is a sample data set.