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, spring_A lines the edge of the meter stick. Its initial length length_i is measured. It is displaced ∆x in five trials, resulting in final length length_f. The force probe measures F. The same trials are repeated for spring_B 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.

Trial	Item	lengthi	lengthf	∆x	F	k	k̅
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

Trial	Item	lengthi	lengthf	∆x	F	k	k̅
1	springB	28.5 cm	33.5 cm	0.05 m	-1.9 N	38.0	42.28
2			38.5 cm	0.10 m	-4.0 N	40.0
3			43.5 cm	0.15 m	-6.4 N	42.7
4			48.5 cm	0.20 m	-9.1 N	45.5
5			53.5 cm	0.25 m	-11.3 N	45.2

Trial	Item	lengthi	lengthf	∆x	F	k	k̅**
1	elastic	17.0 cm	22 cm	0.05 m	-2.0 N	40.0	23.8
2			27 cm	0.10 m	-2.9 N	29.0
3			32 cm	0.15 m	-3.7 N	24.7
4			37 cm	0.20 m	-4.3 N	21.5
5			42 cm	-0.25 m	-5.0 N	20.0

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 k̅.

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.