Cycle I Physics

John Dewey High School

Mr. Klimetz

Hooke's Law Apparatus

2 helical springs

1-10 gram slotted mass

2-20 gram slotted masses

4-50 gram slotted masses

1-100 gram slotted mass

pencils with erasers

calculator

graph paper

Force = Elasticity Constant x Elongation

where force is expressed in Newtons, elongation is expressed in meters, and the elasticity constant is therefore expressed in Newtons/meter. The elasticity constant, which is a constant of proportionality relating the amount of applied force required to produce a specific elongation, is specific to a particular material or object. Weak (or easily stretchable) bodies possess a low elasticity constant whereas strong (or resistant) bodies possess a high elasticity constant.

1. Assemble the Hooke's Law Apparatus as instructed (see picture at right). Make sure that the wire pointer attached to the mass caddy is horizontal and set at the zero centimeter mark on the scale attached to the upright of the apparatus. (The scale is adjusted merely by sliding it either up or down the upright.) Also make sure that the caddy is freely suspended, and does not contact the apparatus in any way.

2. Add masses incrementally to the spring caddy such that the total amount of mass suspended is

20g, 30g, 40g, 50g, 70g, 90g, 100g, 130g, 160g, 190g, 220g, 250g

3. Observe each elongation produced by each mass increment by noting the position of the wire pointer with respect to the vertical metric scale. Record your elongation values to the level of precision permitted by the scale (0.1 cm). Enter all observations in the data table provided.

4. Convert all masses to kilograms, calculate their respective weights, and record.

5. Convert all elongations to meters and record.

6. Divide weight by elongation (in meters) and record. This is your elastic constant.

Create a Force versus Elongation graph of your measurements in which force values are placed along the ordinate (y-axis) and elongation values are placed along the abscissa (x-axis). After all twelve data points for each spring have been plotted, sketch-in a "best-fit" line which averages (or normalizes) the points to a single linear function. Then determine the slope of your best fit lines. The slope of each line is equal to the average elasticity constant for each respective spring. Check this value by calculating the average of the elasticity constants determined numerically and listed in the data table.

1. How do the spring constants you have determined relate to the behavior of the springs? Does the physical "feel" of the springs when stretched between your fingers support your determinations? How do the spring constants determined mathematically compare to those derived by graphical means?

2. Drawing best-fit lines such as the ones we have just produced is a form of data interpolation (or estimating). Write an equation that expresses the relationship between applied force and elongation for each of your best-fit lines.

3. Extrapolation is the process whereby we extend an established numerical relationship between two variables beyond the limits of our observed and recorded data. Explain why extrapolation would not be useful (and wise) in this particular situation.

5. The cables of a suspension bridge as well as the elements of many man-made structures are designed to behave elastically. Briefly explain why it is absolutely necessary that such elements function elastically.

4. Briefly explain the meaning and significance of the elastic limit and why it should be avoided.

6. Hooke's Law is a direct relationship. Briefly explain what this means and how your data illustrate this.