The Law of Hooke

This paper is not supposed to be a substitution for a structured study from a laboratory. The Lab Report Assistant is essentially a description of the queries, diagrams as necessary, and data tables of the experiment that should be covered in a formal laboratory report. The aim is to encourage the writing of lab reports by students by presenting this data in an editable file that can be submitted to a teacher.
The Observations
Data Table 1.
Force (N)
Top position of spring, cm
The bottom position of spring, cm
Elongation, cm
Bottom reading – a top reading
Data Point 1
0
31.9
70.7
38.8
Data Point 2
1
32.0
71.1
39.1
Data Point 3

2

32.1

74.3

42.2

Data Point 4

3

32.1

79.1

47.0

Data Point 5

4

32.3

83.6

51.3

Data Point 6

5

34.4

88.3

55.9

Data Point 7

6

32.4

92.6

60.2

Data Point 8

7

32.5

97.2

64.7

Data Point 9

8

32.4

101.9

69.5

Data Point 10

9

32.5

106.5

74.0

Data Table 2.

Force (N)

Accumulated (cm) Elongation (stretch)

Accumulated (m) Elongation (stretch)

Elastic PE

(Joules)

Data Point 1

0

31.9

0.32

0.051

Data Point 2

1

63.9

0.64

0.204

Data Point 3

2

96.0

0.96

0.460

Data Point 4

3

128.1

1.28

0.820

Data Point 5

4

160.4

1.60

1.280

Data Point 6

5

194.8

1.95

1.902

Data Point 7

6

227.2

2.27

2.576

Data Point 8

7

259.7

2.60

3.380

Data Point 9

8

292.1

2.92

4.263

Data Point 10

9

324.6

3.25

5.281

Calculations and Analysis

For each data row in each of your tables calculate: Elastic PE =

For each spring and the rubber band, plot the accumulated elongation (X-axis) versus the applied force (Y-axis) on a computer spreadsheet.

Find the spring constant for the springs in Newton/meters from the slope of each graph. (Refer to the Excel tutorial in the Introduction section). Spring constant, , where F is in Newton and x is in meters. Therefore, the units are N/m.

K=2/0.2=10N/m

Find the “spring” constant for the rubber band from the slope of the curve using the linear portion

Slope=2-1/0.2-0.1=10Sample Graph. Rubber Band.

Questions

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

Relative stiffness is a measurement of resistance e to deformation when the spring constant is defined as K where F=kx. The more the constant the more the force needed to achieve a unit deformation.

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

Elastic potential energy can mostly be stored by devices like springs due to compression and stretching. There is no elastic potential energy stored if the spring is not stretched or compressed. The amount of potential energy increases when the spring is compressed(Gross et al, 2017).

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

Rubber band graph was not linear since the rubber band did not regain its shape after being stretched.

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

Spring. Hooke’s law of elasticity states that the extension of a spring is directly proportional to the load applied to

Explain what happens to the “spring constant” of the rubber band for the nonlinear part of your curve. No constant can be applied because proportionality doesn’t exist when the rubber band is stretched past a point where it can return to its original shape.

Reference

Gross, D., Ehlers, W., Wriggers, P., Schröder, J., & Müller, R. (2017). Stress, Strain, Hooke’s Law. In Mechanics of Materials–Formulas and Problems (pp. 1-28). Springer Berlin Heidelberg.