8/10/2019 LAW OF HOOKE
1/24
You MUST investigate and use Hookes Law, F = kx, and know that it applies only to some materialsYou SHOULD identify the uncertainty in measurements. (Most)You COULD calculate the elastic strain energy Eelin a deformed material sample, using the expression Eel=1/2Fx, and from the area under its force/extension graph
KeywordsElastic Behavior, Plastic Deformation, Directly Proportional
Measuring Hookes Law
Lets get into the Delorean
8/10/2019 LAW OF HOOKE
2/24
You MUST investigate and use Hookes Law, F = kx, and know that it applies only to some materialsYou SHOULD identify the uncertainty in measurements. (Most)You COULD calculate the elastic strain energy Eelin a deformed material sample, using the expression Eel=1/2Fx, and from the area under its force/extension graph
KeywordsElastic Behavior, Plastic Deformation, Directly Proportional
Measuring Hookes Law
Task
Identify the relationship between force and extensionof a spring.
Use PowerPoint on VLE to draw correct table, decidewhether it is di rect ly o r inversely propor t ional, to
identify dependent, independent and control
variablesand calculate the uncerta inty.
Draw a graph. Graph should include results from all 3experiments and have 3 separate lines of best fit.
Use work done equation and graph to calculate
elast ic strain energy.
8/10/2019 LAW OF HOOKE
3/24
You MUST investigate and use Hookes Law, F = kx, and know that it applies only to some materialsYou SHOULD identify the uncertainty in measurements. (Most)You COULD calculate the elastic strain energy Eelin a deformed material sample, using the expression Eel=1/2Fx, and from the area under its force/extension graph
KeywordsElastic Behavior, Plastic Deformation, Directly Proportional
Measuring Hookes Law
Results tables
Headings should be clear
Physical quantities should have units
All measurements should be recorded (not just theaverage)
Correct s.f. should be used.
The average should have the same number of s.f. as the original
measurements.
3.05 0.15 0.13 0.140.14
8/10/2019 LAW OF HOOKE
4/24
You MUST investigate and use Hookes Law, F = kx, and know that it applies only to some materialsYou SHOULD identify the uncertainty in measurements. (Most)You COULD calculate the elastic strain energy Eelin a deformed material sample, using the expression Eel=1/2Fx, and from the area under its force/extension graph
KeywordsElastic Behavior, Plastic Deformation, Directly Proportional
Measuring Hookes Law
Force (N)Extension (cm)
Test 1 Test 2 Test 3 Mean
8/10/2019 LAW OF HOOKE
5/24
You MUST investigate and use Hookes Law, F = kx, and know that it applies only to some materialsYou SHOULD identify the uncertainty in measurements. (Most)You COULD calculate the elastic strain energy Eelin a deformed material sample, using the expression Eel=1/2Fx, and from the area under its force/extension graph
KeywordsElastic Behavior, Plastic Deformation, Directly Proportional
Measuring Hookes Law
Each axis should belabelled with a quantityname (or symbol) and its
unit.
lengthof
spring
cm
FN
8/10/2019 LAW OF HOOKE
6/24
You MUST investigate and use Hookes Law, F = kx, and know that it applies only to some materialsYou SHOULD identify the uncertainty in measurements. (Most)You COULD calculate the elastic strain energy Eelin a deformed material sample, using the expression Eel=1/2Fx, and from the area under its force/extension graph
KeywordsElastic Behavior, Plastic Deformation, Directly Proportional
Measuring Hookes Law
Both vertically and horizontally your points should
occupy at least halfof the available graph paper
GOOD POOR AWFUL
8/10/2019 LAW OF HOOKE
7/24
You MUST investigate and use Hookes Law, F = kx, and know that it applies only to some materialsYou SHOULD identify the uncertainty in measurements. (Most)You COULD calculate the elastic strain energy Eelin a deformed material sample, using the expression Eel=1/2Fx, and from the area under its force/extension graph
KeywordsElastic Behavior, Plastic Deformation, Directly Proportional
Measuring Hookes Law
Best fit linesBest fit lines can be curves!
The line should be drawn so thatthere are roughly the samenumber of points above andbelow.
Anomalous points should berechecked. If this is not possiblethey should be ignored whendrawing the best-fit line
too hightoo low
too steep
too shallowcorrect
8/10/2019 LAW OF HOOKE
8/24
You MUST investigate and use Hookes Law, F = kx, and know that it applies only to some materialsYou SHOULD identify the uncertainty in measurements. (Most)You COULD calculate the elastic strain energy Eelin a deformed material sample, using the expression Eel=1/2Fx, and from the area under its force/extension graph
KeywordsElastic Behavior, Plastic Deformation, Directly Proportional
Measuring Hookes Law
Measuring gradients
gradient = y-step (y)
x-step (x)
The triangle used to find thegradient should be shown on thegraph.
Each side of the triangle shouldbe at least 8cmlong.
Gradients usually have a unit.
y
x
8/10/2019 LAW OF HOOKE
9/24
You MUST investigate and use Hookes Law, F = kx, and know that it applies only to some materialsYou SHOULD identify the uncertainty in measurements. (Most)You COULD calculate the elastic strain energy Eelin a deformed material sample, using the expression Eel=1/2Fx, and from the area under its force/extension graph
KeywordsElastic Behavior, Plastic Deformation, Directly Proportional
Measuring Hookes Law
Direct proportionPhysical quantities are directlyproportional to each other if when one ofthem is doubled the other will also double.
A graph of two quantities that are directlyproportional to each other will be:
a straight line ANDpass through the origin
The general equation of the straight line in thiscase is: y = mx, in this case, c= 0
y
x
m
8/10/2019 LAW OF HOOKE
10/24
You MUST investigate and use Hookes Law, F = kx, and know that it applies only to some materialsYou SHOULD identify the uncertainty in measurements. (Most)You COULD calculate the elastic strain energy Eelin a deformed material sample, using the expression Eel=1/2Fx, and from the area under its force/extension graph
KeywordsElastic Behavior, Plastic Deformation, Directly Proportional
Measuring Hookes Law
Inverse proportionPhysical quantities are inverselyproportional to each other if when one ofthem is doubled the other will halve.
A graph of two quantities that are inverselyproportional to each other will be:
a rectangular hyperbola has no y- or x-intercept
Inverse proportion can be verified by drawing
a graph of yagainst 1/x.This should be:
a straight line ANDpass through the origin
The general equation of the straight line inthis case is: y = m / x
y
1 / x
m
y
x
8/10/2019 LAW OF HOOKE
11/24
You MUST investigate and use Hookes Law, F = kx, and know that it applies only to some materialsYou SHOULD identify the uncertainty in measurements. (Most)You COULD calculate the elastic strain energy Eelin a deformed material sample, using the expression Eel=1/2Fx, and from the area under its force/extension graph
KeywordsElastic Behavior, Plastic Deformation, Directly Proportional
Measuring Hookes Law
Mean value
Mean value calculated by adding the readings
together and dividing by the number ofreadings.
Readings: 45g; 44g; 44g; 47g; 46g; 45g
Mean value of mass :
= (45+44+44+47+46+45) / 6
= 45.2 g
8/10/2019 LAW OF HOOKE
12/24
You MUST investigate and use Hookes Law, F = kx, and know that it applies only to some materialsYou SHOULD identify the uncertainty in measurements. (Most)You COULD calculate the elastic strain energy Eelin a deformed material sample, using the expression Eel=1/2Fx, and from the area under its force/extension graph
KeywordsElastic Behavior, Plastic Deformation, Directly Proportional
Measuring Hookes Law
The uncertainty (or probable error) inthe mean value of a measurement is
half the range expressed as a value
Example: If mean mass is 45.2g and the
range is 3g then:
The probable error (uncertainty) is 1.5g
8/10/2019 LAW OF HOOKE
13/24
You MUST investigate and use Hookes Law, F = kx, and know that it applies only to some materialsYou SHOULD identify the uncertainty in measurements. (Most)You COULD calculate the elastic strain energy Eelin a deformed material sample, using the expression Eel=1/2Fx, and from the area under its force/extension graph
KeywordsElastic Behavior, Plastic Deformation, Directly Proportional
Measuring Hookes Law
Uncertainty in a single readingOR when measurements do not vary
The probable error isequal to the precision in
reading the instrument
For the scale oppositethis would be:
0.1 without the magnifyingglass
0.02 perhaps with themagnifying glass
8/10/2019 LAW OF HOOKE
14/24
You MUST investigate and use Hookes Law, F = kx, and know that it applies only to some materialsYou SHOULD identify the uncertainty in measurements. (Most)You COULD calculate the elastic strain energy Eelin a deformed material sample, using the expression Eel=1/2Fx, and from the area under its force/extension graph
KeywordsElastic Behavior, Plastic Deformation, Directly Proportional
Measuring Hookes Law
Percentage uncertainty
percentage uncertainty = probable error x 100%
measurement
Example: Calculate the % uncertainty the mass
measurement 45 2g
percentage uncertainty = 2g x 100%45g
= 4.44 %
8/10/2019 LAW OF HOOKE
15/24
You MUST investigate and use Hookes Law, F = kx, and know that it applies only to some materialsYou SHOULD identify the uncertainty in measurements. (Most)You COULD calculate the elastic strain energy Eelin a deformed material sample, using the expression Eel=1/2Fx, and from the area under its force/extension graph
KeywordsElastic Behavior, Plastic Deformation, Directly Proportional
Measuring Hookes Law
Combining percentage uncertainties1. Multiplication or Division
Add the percentage uncertainties together.
Examples:
1. Calculate the percentage uncertainty in force causing a
mass of 50kg 10% to accelerate by 20 ms -25%.
F = ma
Hence force = 1000N 15% (10% plus 5%)2. Calculate the percentage uncertainty in the density of amaterial of mass 300g 5% and volume 60cm32%.
D = M / V
Hence density = 5.0 gcm-37% (5% plus 2%)
8/10/2019 LAW OF HOOKE
16/24
You MUST investigate and use Hookes Law, F = kx, and know that it applies only to some materialsYou SHOULD identify the uncertainty in measurements. (Most)You COULD calculate the elastic strain energy Eelin a deformed material sample, using the expression Eel=1/2Fx, and from the area under its force/extension graph
KeywordsElastic Behavior, Plastic Deformation, Directly Proportional
Measuring Hookes Law
Significant figures and uncertaintyThe percentage uncertainty in a measurement or calculation
determines the number of significant figures to be used.
Example:mass = 4.52g 10%
10% of 4.52g is 0.452g
The uncertainty should be quoted to 1sf only.i.e. 0.5g
The quantity value (4.52) should be quoted to the same
decimal places as the 1sf uncertainty value.i.e. 4.5
The mass value will now be quoted to only 2sf.
mass = 4.5 0.5g
8/10/2019 LAW OF HOOKE
17/24
You MUST investigate and use Hookes Law, F = kx, and know that it applies only to some materialsYou SHOULD identify the uncertainty in measurements. (Most)You COULD calculate the elastic strain energy Eelin a deformed material sample, using the expression Eel=1/2Fx, and from the area under its force/extension graph
KeywordsElastic Behavior, Plastic Deformation, Directly Proportional
Measuring Hookes Law
Hooke
s law
The force(F ) needed to stretch a spring is directlyproportional to the extension(L ) of a spring from itsnatural length.
F L
Adding a constant of proportionality:
F = k Lkis called the spring constant
The spring constant is the force required to produce anextension of one metre.
unit = Nm-1
M i H k L
8/10/2019 LAW OF HOOKE
18/24
You MUST investigate and use Hookes Law, F = kx, and know that it applies only to some materialsYou SHOULD identify the uncertainty in measurements. (Most)You COULD calculate the elastic strain energy Eelin a deformed material sample, using the expression Eel=1/2Fx, and from the area under its force/extension graph
KeywordsElastic Behavior, Plastic Deformation, Directly Proportional
Measuring Hookes Law
Elastic limit
Up to a certain extension if the force is removed thespring will return to its original length. The spring issaid to be behaving elastically.
If this critical extension is exceeded, known as theelastic limit, the spring will be permanently stretched.
Plasticbehaviour then occurs and Hookes law is nolonger obeyed by the spring.
M i H k L
8/10/2019 LAW OF HOOKE
19/24
You MUST investigate and use Hookes Law, F = kx, and know that it applies only to some materialsYou SHOULD identify the uncertainty in measurements. (Most)You COULD calculate the elastic strain energy Eelin a deformed material sample, using the expression Eel=1/2Fx, and from the area under its force/extension graph
KeywordsElastic Behavior, Plastic Deformation, Directly Proportional
Measuring Hookes Law
QuestionA spring of natural length15cm is extended by 3cmby a force of 6N. Calculate
(a) the spring constant and(b) the length of the springif a force of 18N is applied.
(a)F = k L k = F / L= 6N / 0.03m
spr ing constant , k
= 200 Nm-1
(b)F = k L
L = F / k
= 18N / 200 Nm-1
L= 0.09 m
= 9 cm
And so thespring
s length
= 24 cm
M i H k L
8/10/2019 LAW OF HOOKE
20/24
You MUST investigate and use Hookes Law, F = kx, and know that it applies only to some materialsYou SHOULD identify the uncertainty in measurements. (Most)You COULD calculate the elastic strain energy Eelin a deformed material sample, using the expression Eel=1/2Fx, and from the area under its force/extension graph
KeywordsElastic Behavior, Plastic Deformation, Directly Proportional
Measuring Hookes Law
Elastic strain energy
The graph opposite shows
how the force varies as thespring extends.
The work done in extending
the spring is given by:work = force x distance
0
force
extension
M i H k L
8/10/2019 LAW OF HOOKE
21/24
You MUST investigate and use Hookes Law, F = kx, and know that it applies only to some materialsYou SHOULD identify the uncertainty in measurements. (Most)You COULD calculate the elastic strain energy Eelin a deformed material sample, using the expression Eel=1/2Fx, and from the area under its force/extension graph
KeywordsElastic Behavior, Plastic Deformation, Directly Proportional
Measuring Hookes Law
Elastic strain energy
= average tensile force x extension
= F L
= area under the curve
= energy sto red in the spr ing
and so:
elastic strain energy = F L0
F
area = F L
L
force
extension
M i H k L
8/10/2019 LAW OF HOOKE
22/24
You MUST investigate and use Hookes Law, F = kx, and know that it applies only to some materialsYou SHOULD identify the uncertainty in measurements. (Most)You COULD calculate the elastic strain energy Eelin a deformed material sample, using the expression Eel=1/2Fx, and from the area under its force/extension graph
KeywordsElastic Behavior, Plastic Deformation, Directly Proportional
Measuring Hookes Law
Answers
tensile force extension strain energy
120 N 2 m
40 N 15 cm
3 kN 50mm 150 J
2MN 6 m 12 J
Complete:
120 J
3 J
100
4
M i H k L
8/10/2019 LAW OF HOOKE
23/24
You MUST investigate and use Hookes Law, F = kx, and know that it applies only to some materialsYou SHOULD identify the uncertainty in measurements. (Most)You COULD calculate the elastic strain energy Eelin a deformed material sample, using the expression Eel=1/2Fx, and from the area under its force/extension graph
KeywordsElastic Behavior, Plastic Deformation, Directly Proportional
Measuring Hookes Law
Question
A spring of original length 20cm
extends to 25cm when a weight
of 4N is hung from it. Calculate:
(a) the elastic strain energy
stored in the spring,
(b) the spring constant
(c) the length of the spring when
it is storing 0.5 J of energy.
(a)strain energy
= F L
= x 4N x 0.05m
strain energy= 0.10 J
Meas ring Hookes La
8/10/2019 LAW OF HOOKE
24/24
You MUST investigate and use Hookes Law, F = kx, and know that it applies only to some materialsYou SHOULD identify the uncertainty in measurements. (Most)You COULD calculate the elastic strain energy Eelin a deformed material sample, using the expression Eel=1/2Fx, and from the area under its force/extension graph
Keywords Elastic Behavior Plastic Deformation Directly Proportional
Measuring Hookes Law
(b)F = k L k = F / L= 4N / 0.05mspring constant, k = 80 Nm-1
(c)strain energy = F Land F = k Lwhen combined
give: strain energy = k (L)2 L = (2 x strain energy / k)= (2 x 0.5 / 80)= (0.0125)
= 0.112mTherefore spring length = 20cm + 11.2cm
= 31.2 cm