Module 1

How Much Spring Is in a Spring?

Student Guide

Jennifer Heidema, Jim Little, Rick Ramirez, Steve Semken,
Nancy Topoozian

INTRODUCTION

Springs are commonly used as sources of "pull," and as shock absorbers (i.e. sources of "push"). How does a spring work? How many different kinds of springs are there? Can we use mathematics to describe the motions of objects affected by springs? How many useful objects that have "springlike" behavior, such as elastic bands and bungee cords, can you think of?

OBJECTIVES

To investigate the motion of a cart propelled by a spring.
To understand and interpret motion graphs: position versus time, velocity versus time, and acceleration versus time.
To find a mathematical function that predicts the amount that a spring stretches as a function of the strength with which the spring is pulled.
To understand how springs are useful as sources of stored energy.

MATERIALS

TI-83 Graphing Calculator	Motion Detector
Calculator Based Laboratory (CBL)	Cable to link TI-83 with CBL
cart	spring
horizontal track	Graph paper and colored pencils
index card (5" x 8")	masking tape
force probe	meter stick
BALLDROP program	PHYSICS program

PROCEDURE

Discuss with your group a plan to measure the motion of the cart on the horizontal track after you release the stretched spring.

Set up the track with the cart attached to the spring as shown.
Place the motion detector at the opposite end of the track on its side, and connect to the CBL as shown.
Use the index card to reflect the motion detector's ultrasonic pulses, which will increase the visibility of the cart to the motion detector.
Attach the spring to the hole in the opposite end of the cart.
Attach the other end of the spring to the post atop the bumper at the end of the track. Secure the spring to the post with tape.
Set the wheels of the cart in the grooves of the track

Start the program titled BALLDROP in the TI-83 calculator.
To start collecting data, push enter on the calculator. The motion detector should make a ticking sound, indicating that it is activated.
Press trigger on the CBL. The screen on the CBL should indicate that it is sampling, or taking data (distance and time).

Brainstorm with your group to design an experiement using the materials provided that addresses the question: What is the relationship between the amount a spring is stretched and the resulting motion of the cart?

Run at least three experiments to determine the motion graphs (d vs t, v vs t) of the cart with the spring stretched by three different amounts. Be sure to measure and record the extent that the spring is stretched just before you release it for each of the three experiments.
Discuss with your group the slopes of plots you have obtained from the three sets of motion graphs. Account for similarities or differences in the d vs t and v vs t graphs. What do the slopes of these plots signify?
Find the acceleration of the cart for each of the three distances you stretched the spring (i.e. for each experiment).
Replace the motion detector with the force probe, and for each of the extents you stretched the spring above, measure the force that the spring exerts on the force probe. Use the physics program to measure the force of the spring as a function of the amount the spring is stretched.
Find a mathematical function that relates the force exerted by the spring when extended as a function of the amount that the spring is stretched. Discuss the graph and the function with your group.

Can you use the mathematical function you found to predict the force exerted by the spring if you know how much it is stretched from its normal position? What kind of motion (constant speed or accelerated motion) does the stretched spring cause?

APPLICATION QUESTIONS

Sparky plans to try bungee jumping into the Salt River Canyon. He will be jumping from a protruding ledge high above jagged rocks at the bottom of the canyon. What specific (quantitative) things should Sparky know about himself, his bungee cords, and his jump site, if he is to make a thrilling but safe jump? (In other words, he needs to fall just far enough!)
The force of gravity exerted by the Earth is not exactly the same at all places over its surface. Gravity varies slightly with elevation (i.e. distance from the Earth's center of mass) and with the density of different bodies of rock in the crust. Suggest a way to use a spring in order to measure the force of gravity in different places.
How might the manufacturers of mousetraps determine the sizes of springs that are used in their products?
You need to build a gate in a fence surrounding your swimming pool, and install a spring that will shut the gate each time it is opened. Describe the characteristics of the spring you would buy?