LAW OF HOOKE

8/10/2019 LAW OF HOOKE

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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


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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.


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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


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Force (N)Extension (cm)

Test 1 Test 2 Test 3 Mean


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Each axis should belabelled with a quantityname (or symbol) and its

unit.

lengthof

spring

cm

FN


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Both vertically and horizontally your points should

occupy at least halfof the available graph paper

GOOD POOR AWFUL


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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


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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


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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


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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


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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


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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


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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


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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 %


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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%)


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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


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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


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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


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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


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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


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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


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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


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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


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Keywords Elastic Behavior Plastic Deformation Directly Proportional


(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

LAW OF HOOKE

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