Introduction

Objectives

To use physics to analyze and explain the motion of a falling slinky

To learn how to obtain motion data using video and video analysis software

Description

This project will involve videotaping the fall of both a plastic and metal slinky when dropped from several configurations. To determine which parts of the slinky begin falling first, the slinky's coils will be tracked over time using video, and later, the video analysis program VideoPoint. Finally, concepts of physics will be used to determine why the slinky falls as it does in the various drop configurations.

The plastic slinky will be dropped from all configurations, but the metal slinky will be dropped from only a vertical relaxed configuration to better investigate the resulting motion produced by this type of drop.

Table of Contents

General Measurements

Distance from camera to plane of motion (plastic slinky experiments only)	8.560 m
Height of center of camera lens off floor for clips at 1X magnification (all clips except vertical relaxed bottom clips) for 2X magnification (plastic slinky experiments only*)	**1.412 m +/- 0.010 m 1.193 m +/ 0.010 m
Distance between top of each black line on the distance scale (all experiments)	0.010 m
for vertical relaxed bottom clips at 2X magnification, the tripod was lowered, keeping the lens parallel to the plane of motion. *estimate of error is given, since a meter stick was used to measure these distances, and for distances greater than one meter, the meter stick had to be lifted above its previous position without any marker to locate the 1-meter mark.

Plastic Slinky Measurements

Vertical relaxed length	1.853 m
Contracted length	0.077 m
Horizontal relaxed length	0.147m - 0.265 m
Inner coil radius	0.080 m
Outer coil radius	0.094 m
Surface area of one coil	0.075 m²
Number of coils	39 coils
Total surface area (~18 times greater than that of the metal slinky)	2.9 m²
Thickness of one coil	0.002 m
Mass	0.13000 kg

Metal Slinky Measurements

Vertical relaxed length	0.058 m
Contracted length	2.138 m
Inner coil radius	0.069 m
Outer coil radius	0.073 m
Surface area of one coil	0.0018 m²
Number of coils	90 coils
Total surface area (~18 times less than that of the metal slinky)	0.16 m²
Thickness of one coil	~0.0005 m (measured to be less than 0.001 m)
Mass	0.23086 kg

Definitions of Measurements

1. Vertical relaxed length is measured by holding a coil at one end of the slinky and allowing the slinky to relax under gravity. The distance between the two end coils is the relaxed length.

2. Contracted length is the distance between the two end coils (top and bottom of the slinky) when the slinky is sitting on one end on a flat surface.

3. Horizontal relaxed length (length at horizontal equilibrium) is measured by turning the plastic slinky on its side on the same flat surface from which the slinky will be dropped, then stretching the slinky outwards at both ends until the slinky begins to contract. The distance between the two end coils is measured at equilibrium. The lengths given above are the lower and upper limits; before dropping, it was impossible to keep the slinky at the same relaxed length. Because of this, the horizontal relaxed length was measured six times while the slinky was on the flat surface, and the smallest and largest length measurements were recorded. A horizontal relaxed length is not given for the metal slinky, because no horizontal drops were done for this type of slinky.

4. Inner radius is measured by finding the inner diameter of one of the end coils, then dividing by 2.

5. Outer radius is measured the same way as the inner radius, except the outer diameter of one of the end coils is used.

6. Surface area is calculated from the inner and outer radius, and perhaps thickness if this problem is to be treated three-dimensionally. Ignoring thickness, the equation for surface area of one coil is A = p(R_out² - R_in²), where R_out = outer radius of coil, and R_in = inner radius of coil. Multiply this number by the number of coils to get total surface area.

7. Number of coils is found by locating the beginning of one of the end coils. One coil is defined as the part of the slinky located between the beginning of one end coil and the point directly beneath. Count the coils.

8. Thickness is measured with a metric ruler placed across the width of one coil.

9. Mass was measured using an OHAUS Lime-O-Gram electronic balance, with a centigram (0.0001 kg) accuracy.

Experimental Setup

the white pole with black stripes to the left of the background is the distance scale. The black stripes are positioned at 10 cm intervals. The slinky is held in the plane of motion.

Investigations of Falling Slinky Motion

Different types of plastic slinky drops	Observations of a plastic slinky being dropped from different configurations
Different types of metal slinky drops	Observations of a metal slinky, dropped from the vertical relaxed configuration
Physics of a dropped plastic slinky	Results and possible explanations for plastic slinky motion
Physics of a dropped metal slinky	Results and possible explanations for metal slinky motion
Conclusion