# Hooke's Law Study Sheet

Hooke's Law Study Sheet

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• Created on: 04-11-12 09:00

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Physics Factsheet
www.curriculum-press.co.uk Number 83
Experiments- Hooke's Law and Young Modulus
Factsheet 27 went through the elasticity theory required at A-level (and
probably further) in some detail. Practical Hints:
1. Use only small masses. This gives you more data points. It also
In this Factsheet we will look at some of the experimental work linked to makes it less likely you will exceed the limit of proportionality.
the topic. We will concentrate on how best to make the practical work 2. Repeat readings with decreasing masses to ensure there is no
produce accurate and reliable data, and the graphical work and calculations hysteresis effect.
resulting. 3. Some springs are manufactured with the coils forced so tightly together
that it takes a significant force to begin separating them. This may
Hooke's Law provides information on the properties of a specific device affect the starting point of the graph. Use only the straight-line section
(spring, length of wire, etc). The Young modulus gives us a value for a to find the gradient.
material (steel, copper, glass, etc).
Example:
Hooke's Law refers to a specific device; the Young modulus A student performs an experiment to find the spring constant of a
refers to a material. steel spring, obtaining these results:
Hooke's Law (revision): Mass / g Ave. extension / 10-3 cm
0.0 0.0
F 5.0 0.1
10.0 0.5
P 15.0 0.8
20.0 1.3
25.0 1.8
30.0 2.1
0 e Find the spring constant.
In the proportional region, between O and P (the limit of proportionality):
Solution:
Rewrite the table:
F = ke where F is the applied force (N)
e is the extension (m) Weight/10-3N Ave. extension / 10-3 m
k is the spring constant (Nm-1)
0 0
49 1
Practical Hint: 98 5
Throughout these practicals, always do repeats and averages where 147 8
possible, and take care with significant figures and units. 196 13
245 18
294 21
Finding the spring constant, k, of a steel spring.
F/10-3N
300
This is a standard practical going back to
250
GCSE level. A series of masses are carefully
added to the mass holder, and measurements 200
of extension and weight are recorded in a
m table. 150
100
The results are then graphed: 50
F
0 2 4 6 8 10 12 14 16 18 20 22 24
The spring constant, k, e/10-3m
is the gradient (from k = F / e). k = gradient = (200 × 10-3 ) / ( 17 × 10-3 ) = 12 Nm-1
Notice the care that must be taken with the units, and that the best
e straight line should not be started from the origin in this situation.
1

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Experiments- Hooke's Law and Young Modulus Physics Factsheet
Combinations of Springs Practical Hints:
Experimental work is often performed to verify the rules for combining Use small extensions for the spring (small masses) to ensure that you are
springs in series and parallel. operating in the Hooke's Law region. However remember using very
small extensions will increase the percentage error in the measurement.…read more

### Page 3

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Experiments- Hooke's Law and Young Modulus Physics Factsheet
The Young modulus (revision):
As mentioned, the Young modulus is a property of a material. Instead of A graph of results will resemble this example:
applied force, we use tensile stress (the force applied per unit cross-
sectional area); instead of extension, we use tensile strain (the fractional F/N
increase in length).
Stress = F/A (Nm-2)
Strain = e/l (no units) where l is the original length.…read more