Hooke’s Law Lab Report
Max Binkle, 12 MPW, 13.10.2013
1. Aim
In the experiment I wanted to test whether strawberry laces obey Hooke’s Law, when they
break and – if they obey the law – where their elastic limit is.
The result can be used when eating them e.g. to know when you have to stop to pull when
one end is in your mouth.
2. Theory
2.1. The Hooke’s Law and stretching work
When you apply tension F onto an elastic object it is extended proportionally to the force
you apply. Each object needs a different force applied to show the same extension x.
Therefor each object has a different spring or force constant k. This can be calculated by
the formula:

The stretching (or squeezing) work W you do stretching (or squeezing which
doesn’t really make sense for the laces) is half of the tension you apply times the
distance you deform it:
The equation is not W=Fx because F is not a constant force and therefor you need the
proportionality factor
2.2. The extension-tension graph
The extension-tension graph shows if an object obeys Hooke’s Law or not.
If it obeys Hooke’s Law, the gradient has to be constant and its value is the force
constant k.
As soon as the gradient changes the last measurement before it has shown you the
elastic limit. From that point on the object is plastically deformed and doesn’t obey
Hooke’s Law anymore.
If the object doesn’t obey Hooke’s Law from the start at all, the graph is never a straight
line.
2.3. Measurements
In my experiment I measured the mass I used to cause tension and the start length and
the successive lengths of the lace. I used
to calculate the tension caused by
the mass by the formula F=g*m.
I calculated the extension as the difference between the successive lengths and the first
length.
3. Method
3.1. Variables
I read the mass from the weights I used to cause the tension. I put both in to the table.
Then I read the lengths with a ruler and calculate the extension as the difference of the
first measurement and the successive measurements.
3.2. Constants
I needed some constant variables. I assume that the room temperature stayed the same.
A change in temperature would affect the consistence of the laces and thereby change
the force constant k. I used one lace per experiment (mass from 10g-210g). If I had
used different laces I would have had to assume that each lace is the same. If I assumed
that but they weren’t, this would fake the results because the force constant k would
change.
3.3. Experiment diagram
boss
clamp
Strawberry lace
ruler (in cm and mm)
mark
weigth (each 10 g)
stand
3.4. The experiment step by step
First I put up a stand and put two clamps hold by bosses on it. Into the lower clamp I
clamped a ruler vertically. Into the upper one I tied a strawberry lace I had marked before
to make the measurement easier. Then I tied a holder into the lower end of the lace.
Now I started to put the weights of each 10g onto the holder carefully. After the first
weight I measured the length with the help of a setsquare (because of the rectangle).
This length was my initial length. After each weight I measured the successive lengths
and calculated the extension as a difference.
4. Results
4.1. Table
mass [g]
10
20
30
40
50
60
70
80
90
100
110
120
130
140
150
160
170
180
190
200
210
Test 1
length
[mm]
Test 2
length2
[mm]
tension
extension [mm]
[N]
0,0981
261 --------------0,1962
264
3
0,2943
270
9
0,3924
275
14
0,4905
280
19
0,5886
285
24
0,6867
291
30
0,7848
296
35
0,8829
302
41
0,981
308
47
1,0791
321
60
1,1772
329
68
1,2753
334
73
1,3734
340
79
1,4715
345
84
1,5696
350
89
1,6677
363
102
1,7658 accidental
undefined
snap
1,8639
1,962
2,0601
snap
extension2
[mm]
220 --------------224
228
232
236
241
245
250
255
260
265
275
280
285
291
297
300
315
335
360
4
8
12
16
21
25
30
35
40
45
55
60
65
71
77
80
95
115
140
undefined
4.2. Graphs
4.2.1. Test 1
1,8
1,6
1,4
tension [N]
1,2
1
0,8
elastic limit
0,6
0,4
0,2
0
0
20
40
60
80
100
120
extension [mm]
4.2.2. Test 2
2,5
tension [N]
2
1,5
1
elastic limit
0,5
0
0
20
40
60
80
extension [mm]
100
120
140
160
5. Conclusion
5.1. Test 1
In test 1 the graph starts as a straight line. That means that the gradient is constant for
that part of the graph. That means the lace obeys Hooke’s Law up to the point, where the
gradient changes. The gradient changes at the point (47, 0.981). Because we know, that
the gradient represents the force constant, we can calculate the constant for this lace:
The point, where the gradient changes, is the elastic limit of this special strawberry
lace. Afterwards the gradient of the graph becomes more and more inconstant.
The lace snapped accidentally while measuring the extension at the applied force caused
by 180 g, when I touched it. I assume that this was close to the point, where it had
snapped anyways.
5.2. Test 2
In test 2 the graph starts as a straight line. That means that the gradient is constant for
that part of the graph. That means the lace obeys Hooke’s Law up to the point, where the
gradient changes. The gradient changes at the point (45, 1.0791). Because we know,
that the gradient represents the force constant, we can calculate the constant for this
lace:
The point, where the gradient changes, is the elastic limit of this special strawberry lace.
Afterwards the gradient of the graph becomes more and more inconstant.
When I applied the force caused by 210 g the lace snapped.
5.3. Total
My tests both showed that the strawberry laces obey the Hooke’s Law until a certain
tension that has to be defined for each several lace. That means that I didn’t completely
reach my aim as found out that the laces obey Hooke’s Law but didn’t find a constant
snapping point which would have been useful to know how strong I may pull a lace out of
my mouth that is clamped between my teeth without breaking it.
6. Evaluation
6.1. Validity/Possible errors
The material of the laces is not completely homogeneous and they are not the same thick
at every point. That means that there are weak points, where the laces show plastic
behavior earlier and are more likely to snap.
The knot is a point where the material cannot be deformed as well as at other points of
the laces. This can – occasionally – affect the deformation behavior of the laces.
The air temperature makes the material softer or harder. If the consistence of the material
changes during the experiment, this leads to a change in the force constant k and
pretends the lace not to obey Hooke’s Law even if it actually does.
Wed air affects the consistence of the laces as well as the laces attract water and
become softer if in contact with water. This affects the force constant in the same way a
change of air temperature would.
When you tie a knot the lace can have an angle relatively to the vertical. This causes
tangential forces that affect the force constant when you calculate it later on. It just
distorts the graph which means that it doesn’t change your result between obey or not
obey.
6.2. Improvements
To avoid any trouble caused by the knot you can wind a reel of lace around the clamp to
fix the lace for the experiment. Or you could glue it noticing that the glue could chemically
react with the laces.
To eliminate errors caused by wed air and temperature changes you need a thermometer
to check that the temperature stays the same and an air dryer.
6.3. Further research
You could research the deformation behavior of chewing gum and gummi bears.