The Caliper

Force Plate in an Elevator (extended version of article)

Data Collection and Analysis in an Elevator

When teaching the concept of weight, physics teachers like to discuss what a person would weigh in a moving elevator. Quite often this involves a thought experiment, and the discussion is based around the feelings a person has experienced on an elevator. Now with our Force Plate, instead of performing a thought experiment, you can collect actual weight data in an elevator. Here is a graph of a person's apparent weight as an elevator moved upward. The graph shows that the person's "initial" weight was around 810 N. As the elevator accelerated upward, his weight increased to about 890 N, which is close to a 10% increase. When the elevator stopped, the weight decreased, and again by about 10%.

Here's a graph showing the same person's weight as the elevator descended. As the elevator began its motion, the person's weight decreased, and as the elevator stopped the weight increased. As in the upward trip, this elevator produced around a 10% change in weight. It is interesting to notice the shape of the graph as the elevator came to a stop. The elevator produced a sharp change in weight as it slowed down, but then there is a gradual almost exponential like change in weight. This same behavior can be seen while moving in either direction.

Here is a set of graphs from a different elevator. On this occasion we used a Force Plate to measure weight, a Low-G Accelerometer to measure acceleration and a Barometer to measure height. This elevator services nine floors in a local hotel and takes about 20 seconds to go from the first floor to the ninth floor. The first graph shows the weight of a person as the elevator traveled from the ground level to the ninth floor. Like the elevator described above, this elevator also produced about a 10% change in weight. We don't know if this is coincidental or a common design criteria. As we rode this elevator a number of times, we observed its operation. The elevator did not immediately go to the intended floor and open the door. Instead it seemed to slow down in advance of the floor and repositioned itself to bring it level with the hotel floor. The force graph even shows this adjustment. Notice the force changes at 22.4 s and 23.4 s.

The next graph is a height calculation based on the barometric pressure readings. It shows an increase in height of about 21 m.

What would you expect the graph for the accelerometer data to look like? Newton's 2nd Law tells us that the acceleration should be directly proportional to the force, therefore the graphs should have the same shape. Here's the actual data. It certainly looks like the graph of Force vs. Time.

If you graph Force vs. Acceleration, you should get a scatter plot showing a linear trend. Linear regression analysis of the data should produce the mass of the elevator rider. It looks as if our rider had a mass of about 100 kg.

Let's take the analysis of the acceleration data a little further. If we integrate the accelerometer data, we should get the change in velocity of the elevator. Here's the graph of that calculation.

Notice that the elevator slows at 22.4 s and 23.4 s. These changes match what we see on the Force vs. Time graph.

If you then integrate the velocity data, you should get a graph showing the change in position; here's that graph. It shows a height change of about 24 m, which is similar the barometer-based data.

We hope that this article gets you to thinking about experiments that you and your students can try. Let us know what you come up with.