How to calculate the spring constant of a rubber band

Calculations and Analysis:

1. For each data row in each of your tables calculate: Elastic PE = 1/2kx2

2. For each spring and the rubber band, plot the accumulated elongation (x-axis) versus the

applied force (y-axis) on a computer spreadsheet.

3. Find the spring constant for the springs in Newtons per meter from the slope of each

graph. (Refer to the Excel tutorial in the Introduction section). Spring constant, K=F/x, where F is in Newton and x is in meters. Therefore, the units are N/m.

4. Find the “spring” constant for the rubber band from the slope of the curve using the

linear portion of the graph.

Lab Report Name: ____________________

Section: ___________________

EXPERIMENT: Hooke’s Law

DATA TABLE 1: Spring 1

NOTE: Accumulated elongation is the total distance from the reference point, not the sum of increments.

Force (N)

Accumulated (cm) Elongation (stretch)

Accumulated (m) Elongation (stretch)

Elastic PE

(Joules)

Data Point 1

0.7

1

0.05

Data Point 2

1.1

2

0.07

Data Point 3

1.8

3

0.08

Data Point 4

2.4

4

0.10

Data Point 5

3.1

5

0.12

Data Point 6

3.7

6

0.14

Data Point 7

4.3

7

0.16

Data Point 8

4.8

8

0.17

Data Point 9

n/a

n/a

n/a

Data Point 10

n/a

n/a

n/a

DATA TABLE 2: Spring 2

NOTE: Accumulated elongation is the total distance from the reference point, not the sum of increments.

Force (N)

Accumulated (cm) Elongation (stretch)

Accumulated (m) Elongation (stretch)

Elastic PE

(Joules)

Data Point 1

0.6

1

0.045

Data Point 2

1.4

2

0.07

Data Point 3

2.0

3

0.945

Data Point 4

2.5

4

0.11

Data Point 5

3.0

5

0.14

Data Point 6

3.6

6

0.16

Data Point 7

4.7

7

0.19

Data Point 8

4.9

8

0.22

Data Point 9

n/a

n/a

n/a

Data Point 10

n/a

n/a

n/a

DATA TABLE 3: Rubber band

NOTE: Accumulated elongation is the total distance from the reference point, not the sum of increments.

Force (N)

Accumulated (cm) Elongation (stretch)

Accumulated (m) Elongation (stretch)

Elastic PE

(Joules)

Data Point 1

0.6

1

0.06

Data Point 2

1.3

2

0.075

Data Point 3

1.8

3

0.09

Data Point 4

2.9

4

0.105

Data Point 5

3.1

5

0.125

Data Point 6

3.5

6

0.15

Data Point 7

4.2

7

0.20

Data Point 8

4.8

8

0.23

Data Point 9

n/a

n/a

n/a

Data Point 10

n/a

n/a

n/a

Questions:

A. How does the relative stiffness of a spring relate to its spring constant?

B. How does PE change relative to the stretch of the spring?

C. Indicate on your graph for the rubber band where the linear behavior stops. What does this mean?

D. Which is stronger in the region where Hooke’s law is obeyed, the spring or the rubber band? Explain.

E. Explain what happens to the "spring constant" of the rubber band for the non-linear part of your curve.