Objective:

To investigate the relationship between force and stretching distance for various elastic objects such as springs and rubber bands.

Introduction:

The elastic properties of matter are involved in many physical phenomena. When matter is deformed (compressed, twisted, stretched, et cetera) and the deforming forces are sufficiently small, the material will return to its original shape when the deforming forces are removed. In such cases, the deformation is said to take place within the elastic limit of the material, i.e., there is no permanent deformation. The slight stretching of a rubber band is an example of an elastic deformation. Steel wires, concrete columns, metal beams and rods and other material objects can also undergo elastic deformations. For many materials, it is approximately true that when the material is stretched or compressed, the resisting or restoring force that tends to return the material to its original shape is proportional to the amount of the deformation but points in a direction opposite to the stretch or compression. This idealized behavior of matter is called Hooke's Law. Today’s lab will allow you to test the accuracy of Hooke’s law for simple objects.

Simplified Theory


Hooke’s Law is the statement that the restoring force acting on an object is proportional to the negative of the displacement (deformation) of the object. In symbols,


F = -k x (1)

Here, F is the restoring force provided by whatever is being stretched (or squeezed), x is the displacement of the thing being stretched (or squeezed)., and k is the constant of proportionality. The negative sign (-) is important and just says that the restoring force is opposite in direction to the displacement. For example, if a spring is stretched by something in a certain direction, the spring will exert a restoring force on that something but in the opposite direction. Equation (1) also says that for an object which obeys Hooke’s law (such as a spring), the more it is stretched or squeezed, the greater will be the restoring force supplied by the object on whatever is doing the stretching or the squeezing. An applied force (F) acting on our “Hookean” object will cause it to be displaced (stretched or squeezed) by some amount (x). The ratio of the change in applied force (∆F) and the change in the resulting displacement (∆x) is called the spring constant (k).


k = ∆F/∆x (2)

Today’s experiment will test this relationship for elastic objects. By hanging different masses from the object we can control the amount of force acting on it. We can then measure for each applied weight the amount that the elastic object "stretches.” Since Equation (1) is the equation for a straight line, a graph of F (the weight) versus x (the "stretch") will should yield a line with slope k . Equation (2) tells us the same thing and its appearance should remind you of how to compute the slope of a straight line.


Instructions:

  1. Each person in your lab group must read every page in this online procedure. Along the way, there will be questions that you must answer.
  2. Designate one person in your group as the Data Recorder. This person should open the Google document Experiment 10 - Hooke's Law for the approved answer template.
  3. When this Google document opens, sign in to your Google account.
  4. From theFILE Menu, chooseMake a copy...
  5. From theFILE Menu, chooseRename...and rename the document as follows: Exp 10 - Period (1, 3, 6, or 8) - Group #.
  6. Share this document with the members of your group and with Mr. Skubis at HSTScience@gmail.com.
  7. As a group, answer all questions. Remember to use complete sentences and be mindful of grammar, spelling, and punctuation.
  8. REMEMBER: **Plagiarism** is a form of **Academic Dishonesty** which carries harsh consequences. DO YOUR OWN WORK!

Procedure:

  1. Attach a 50 g weight hook and any additional slotted masses to the spring as indicated on trial 1 on the chart for Spring A. The parameter mass will represent the total mass on the spring.
  2. Place the meter stick vertically alongside the hanging mass. Measure the elongation of the spring and record it as the Initial Length (cm). This initial length is the same for all masses added to the spring. Always be sure to measure starting at the same place, either on the table or on the clamp.
  3. Place additional slotted masses to the hook to get to the mass indicated on the data table. Read the meter stick and record Final Length (cm). Repeat, finding remaining final lengths for the indicated mass totals.
  4. Move to a different station and repeat the above procedural steps.



Calculations (Show 3 sig figs.)

Record the stretching distance in meters and the weight in Newtons. Given masses in grams includes the mass of the hanger, remember to change to kilograms and then convert to Newtons.
  • Column A – the mass you want to hang from each spring, do not exceed these given maximums.
  • Column B – Measure the length of the spring when the initial mass is attached.
  • Column C – Measure the length of the spring when additional mass is attached.
  • Column D – Subtract the initial length from the final length to find how far the spring stretched.
  • Column E– Convert the stretch distance from centimeters to meters.




Graphical Analysis:


Excel Instruction

  1. You will be making 4 total graphs. One each for A,B, and C separately and one graph that will have D,E, and F on it.
  2. In column A type in masses.
  3. In column B type the stretch distances in meters.
  4. Click in C1 and type =A1*9.80 hit enter. Highlight C1 and copy that down for the rest of the data. You now have distance in B and weight in C.
  5. Highlight B and C and click chart wizard (top center of toolbar).
  6. Select x-y scatter, dots with no lines.
  7. Click finish, right click on a data point select "add trendline"
  8. Select options - click set intercept through 0 and display equation on chart.
  9. Repeat for springs B and C.
  10. Its the same basic idea for graphing D,E, and F together. Column A gets masses, This time put the weight in B and type the stretch distances in C-E. Highlight B-E for graphing. This graph will be the inverse of what you need, take 1/slope to get k value in N/m.