Thursday, January 8, 2015

Hooke’s Law

WTBI

Hooke’s Law: an elastic object’s displacement is proportional to its restoring forces. This speed lab examines this proportionality with minimal verbiage.* Two-day labs deserve to be succinct.

Proc.

Equipment: meter stick; two springs; rubber band; and a LabQuest, connected to a force probe, zeroed when horizontal. First, springA lines the edge of the meter stick. Its initial length lengthi is measured. It is displaced ∆x in five trials, resulting in final length lengthf. The force probe measures F. The same trials are repeated for springB and elastic. I hesitate to include multimedia; they say, “a picture is worth a thousand words”. But I must succumb, for science:

Mandatory GIF.
Spring stretching.

Force readout.
All data is recorded below.

TrialItemlengthilengthf∆xFk
1
springA
6.5 cm
10 cm 0.035 m -0.04 N 1.14
1.15
2 15 cm 0.085 m -0.10 N 1.18
3 20 cm 0.135 m -0.16 N 1.18
4 25 cm 0.185 m -0.20 N 1.08
5 30 cm 0.235 m -0.27 N 1.15

TrialItemlengthilengthf∆xFk
1
springB
28.5 cm
33.5 cm 0.05 m-1.9 N38.0
42.28
2 38.5 cm 0.10 m-4.0 N40.0
3 43.5 cm 0.15 m-6.4 N42.7
4 48.5 cm0.20 m-9.1 N45.5
5 53.5 cm 0.25 m-11.3 N 45.2

TrialItemlengthilengthf∆xFkk̅**
1
elastic
17.0 cm
22 cm0.05 m-2.0 N40.0 23.8
2 27 cm0.10 m-2.9 N29.0
3 32 cm0.15 m-3.7 N24.7
4 37 cm0.20 m-4.3 N21.5
5 42 cm-0.25 m-5.0 N20.0

The spring constant: k, consistent in an object. To calculate: F = -kx. The calculation is complete, yielding values for k. k is averaged to produce .

TA’s


This speed lab made Hooke’s Law concrete, understandable. The proportional relationship between force, displacement is clear, embodied by the force constant. Generally, the calculated values for k are consistent except for elastic’s trial 1, an outlier caused by error. This consistency exemplifies the validity of Hooke’s Law and introduces the expected invariableness of k.

*I’m serious about this. Removing words is surprisingly time-consuming.
**Trial 1 is omitted.

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