Introductory Laboratory Apparatus

2002 AAPT Apparatus Competition, Boise State University

Name: E. J. Galvez; R. E. Williams; J. C. Amato

Address: Department of Physics and Astronomy, Colgate University, Hamilton NY 13346

Phone: (315) 228-7205

Fax: (315) 228-7187

E-mail: Egalvez@Colgate.edu

Archimedes:

A Black Box Mechanics Laboratory

Archimedes is an adaptation of a previously reported black box exercise. A cylindrically symmetric solid is concealed within a long opaque PVC pipe and attached by a string to an Atwood’s apparatus . The pipe is partially filled with water. Students are challenged to determine the dimensions and density of the solid, which they can accomplish by recording its apparent weight as it is lowered into the water. We run this laboratory as a modeling exercise: students must develop their own theoretical picture and experimental procedure. The exercise demands careful observation and insightful interpretation of data, two essential components of professional research.

Description

Black box laboratories are common in introductory electricity and magnetism courses. In the past few years, however, we have designed a number of black box exercises for use in our introductory calculus-based and algebra-based mechanics courses. In the black box mode, relatively simple and inexpensive apparatus can provide highly challenging, satisfying lab experiences. Students clearly enjoy these exercises: It is not unusual to find a small number of students working diligently and productively beyond the three hour lab period to identify correctly the contents of the black box. In our opinion, the black box labs are the highlight of our introductory laboratories.

The experiment described below is an adaptation of a previously reported lab exercise. It is presently used in the algebra-based introductory mechanics course, and is designed to be a modeling exercise. The physics of buoyancy is reviewed at the beginning of the lab period, but students are expected to design and implement their own experimental procedure.

A cylindrically symmetric object is hidden within a vertical 4 foot length of 4 inch diameter white PVC pipe. A standard PVC cap is glued (for a waterproof seal) to the bottom of the pipe. The top of the pipe is closed by a removable (unglued) PVC cap with a 0.5 inch diameter center hole. The pipe is partially filled with water. Each apparatus has a unique “unknown” object, fabricated from two polystyrene rods of different diameter, ranging from 1.9 cm (0.75 in) to 5.1 cm (2.00 in). The overall length of the object ranges from 30 – 40 cm, and the mass ranges from 160 to 400 g. The polystyrene object is hung from a string which passes through the hole in the top cap to an Atwood’s apparatus for measuring its apparent weight , where r is the density of water and V(y) is the volume of water displaced by the object when it is at height y. The apparent weight W is equal to the surface tension provided by the external calibrated mass M. By plotting M vs. y, from complete submersion of the object to full extraction from the water, the object’s total mass m, density r, and overall length can be determined, along with the diameter and length of each cylindrical segment.

where r = 1.0 g/cm³, and dV = Ady for each length of constant cross-section A. The slope of the graph M(y) gives the cross-sectional area A, and the locations of the kinks in the graph yield the lengths of each section.

At full extraction, M = 213 g, the total mass of the object, and at full immersion, M = 11 g. The calculated density of polystyrene is found as follows:

For the first section of the graph,

and similarly for the second section:

The correct answers are d₁ = 1.91 cm (0.75 in) and d₂ = 3.18 cm (1.25 in).

However, the overall length of the polystyrene, found from the graph, is about 2.5 cm too short. The lengths of each section are proportionally short as well. This is easily understood but a little too complicated for students to unravel. As the polystyrene enters the water, the water level rises about 2.5 cm, reducing the apparent distance between the fully extracted and fully immersed positions.

Conclusion

The experiment described above has worked well in our introductory algebra-based mechanics course populated by life science and pre-medical students. It is very inexpensive (< $50), easy to construct, and trouble free. Results for the density and diameters of the polystyrene are within about 5 % of directly measured values. The error in the length is larger (7 %), but can be reduced by choosing smaller diameter rods or by using a larger PVC pipe. More importantly, the experiment is an opportunity for students to apply their understanding of physics to solve a puzzle. It is a good example of how physics allows us to “see beyond the visible.”

Black Box Mechanics Laboratory Equipment List
4'x4" PVC drain pipe		$6.48	Home Depot
4" end caps	2@1.59 ea	$3.18	Home Depot
Super pulley	2@ 16.00 ea	$32.00	Pasco Scientific, qty 9 Cat# ME-9450
Polystyrene rod		$16.00	Crubell Plastics
	Total	$57.66
PVC Cement	quart	$4.73
Wgt. Set, Fishline, Timer, Hanger and Clamps most Physics deptartments have available.