Measurement & Estimating

Geometry

With the trip to the amusement park only days away, it is prudent to examine how a student might begin to make appropriate measurements. The use of accelerometers while at the amusement park adds to the experience and the enjoyment of students in several ways. It gives the students a direct way to check any calculated values for accelerations and “g” forces that they have made as well as providing an opportunity for students with less sophisticated math backgrounds to quantitatively study the rides. It also provides a creative, hands-on activity for the classroom where students can design, construct and test the devices to be used at the amusement park. Trying to foresee and provide for all of the contingencies to be encountered at the park can lead to several days of class discussion and problem solving sessions.

There are basically two types of accelerometers, vertical and horizontal. Both directions are relative to the seat the rider sits in on the ride, with vertical taken as perpendicular to the seat.

Horizontal Accelerometer: this can be used to measure heights and accelerations by recording only the angle from the vertical.

FBD

• Materials: plastic protractor, string, small rubber stopper with hole, large plastic drinking straw masking tape.
• Calibrating: When holding this device so that the straw is horizontal to the ground, there are two forces acting on the rubber stopper. Gravity and the tension in the string. T can be resolved into its x and y components. The string supplies the force necessary to accelerate the stopper to the left or to the right. The stopper is accelerating in the horizontal direction only.
• Measuring Heights:  One of the nice features of the horizontal accelerometer is its double use as a clinometer. By sighting the top of the object through the drinking straw, the angle of inclination can be determined from the protractor by subtracting 90 from the angle indicated by the string. Depending on which base line the student is able to measure, the height of object can be found by using the appropriate formula.

Estimating Distances: how in the world can I estimate the distance?

Estimating distance is not as difficult as it might seem. Basic students might be terrified when told that they don’t have access to a meter stick, tape measure or other device which produces hard numbers. Since students don’t have access to the rides themselves, what are they to do? I think the key is repeating structures of the rides themselves. All that’s really needs to be measured is the length of a single unit of the ride that repeats along the ride. This can be done with measured pacing (knowing one’s own stride and repeating the walk).

Now what do I do?

The final key can be found in the preparation before the field trip. Almost everything can be boiled down to a combination of length and time, with a little help from mass and acceleration estimation. Knowing how to boil down each question into the subsequent parts will transform a hairy problem into a very accessible… well… bald one I guess.