Is there an Equation for a Spring?

Photo of Lab

As we have seen in class a spring is an elastic object in that if you apply a force to the spring it will stretch and if this force is removed the spring will return to its orignal shape. This lab is concerned with answering the question "Is there an equation for a spring?", or in other words can we describe how a spring will stretch mathematically?

Part 1: When you pull on a spring is it easier at first and then harder, or aways the same?

Part 2: There is a setup on your table which will allow you to measure how far your spring will stretch as you add masses. These masses supply a force to the spring. What force is this? How do you obtain that force from the mass?

Part 3: Line up the weight hanger so that its bottom lines up with the zero on the scale. This is the mark that all measurements will be made relative to. The scale numbers mark off centimeters (cm) so this will be your unit for distance. Gradually add mass (use the units of grams) and measure the distance stretched as you add mass. Be careful not to add too much mass since as you know if you stretch a spring too far it will not go back to its original shape and the spring is ruined. Remember as you add mass you use the total mass on the hanger for each distance measurement. So, as you add mass the mass will get larger and the distance stretched will get larger. Continue to add mass until you have ten measurements at least.

Part 4: Now from your answers in part 2 for each mass determine the amount of force this represents. In our case since we are using grams and centimeters, g = 980 cm/s^2. The resulting unit for force in this system of measurement is called a dyne. Next to each calculated force put the distance the spring stretched.

Part 5: Now let's make a graph of our data to help us see the relationship between the applied force and the distance stretched. The amount of force applied is on the y-axis and the distance stretched is on the x-axis. Make a plot of your data remembering to use as much of the graph paper as possible. Draw a best line through your data points. Describe the shape of this line. From looking at your data points and your line describe a general relationship that you see as far as force versus distance. Do you know of an equation that may describe this? If so, what is it? Did your spring act as you thought it might from your answers in part 1?