1.1. To understand what happens when an To understand what happens when an increasing force is applied to a wire or springincreasing force is applied to a wire or spring

2.2. To understand how springs in series and To understand how springs in series and parallel behaveparallel behave

3.3. To understand how to calculate the energy To understand how to calculate the energy stored in a stretched springstored in a stretched spring

4.4. Use this as a vehicle to check graph plottingUse this as a vehicle to check graph plotting

Book Reference : Pages 164-166Book Reference : Pages 164-166

http://www.rdg.ac.uk/acadepts/sp/picetl/publish/ISEs/Forces2.htm

What happens when you apply increasing What happens when you apply increasing tension to a spring or wire?tension to a spring or wire?

Hooke’s Law states Hooke’s Law states that...the change in that...the change in length produced by a length produced by a force on a wire or spring force on a wire or spring is directly proportional is directly proportional to the force applied.to the force applied.

Extension Extension Force Applied Force AppliedL L F F

We’ll see We’ll see latter that latter that Hooke’s law Hooke’s law only applies only applies within limitswithin limits

L (m)

To turn a proportionality into an equation To turn a proportionality into an equation we need to introduce a constant of we need to introduce a constant of proportionality...proportionality...

L L F F F = F = kkLL

We call k the We call k the spring constant spring constant and it defines and it defines how stiff the spring ishow stiff the spring is

How can we find K experimentally?How can we find K experimentally?What should we do to minimise errors? What should we do to minimise errors?

Take care to avoid confusion Take care to avoid confusion between overall length & between overall length & extensionextension

Take the Take the gradient of the gradient of the graph :graph :

FF22 – F – F11

LL22 – L – L11

F

L

L (m)

1.1. Make the Make the “gradient triangle“gradient triangle” as large as possible” as large as possible2.2. Avoid outliers, choose data points which are on Avoid outliers, choose data points which are on

the linethe line

L (m)

When we undertake an experiment we When we undertake an experiment we should only change one variable at a should only change one variable at a time to make it a fair test. We call this time to make it a fair test. We call this the the ““independent variable”independent variable”

Quantities we measure, (and subsequently calculate) are Quantities we measure, (and subsequently calculate) are called called “dependent variables”“dependent variables”. All other variables which . All other variables which are kept the same are called the are kept the same are called the “control variables”“control variables”

Often graphs have the independent variable Often graphs have the independent variable along the bottom and the dependent up the sidealong the bottom and the dependent up the side

Hooke’s law is a notable exception Hooke’s law is a notable exception

C stops obeying Hooke’s law... After the limit of C stops obeying Hooke’s law... After the limit of proportionality the material behaves in a ductile proportionality the material behaves in a ductile fashion. The material stretches more with a small fashion. The material stretches more with a small extra force.extra force.

Spring constant : Spring constant : material A is material A is stiffer than B and stiffer than B and CC

L (m)

Springs in parallel share the load Springs in parallel share the load & have the same extension & have the same extension acting like a single spring with a acting like a single spring with a combinedcombined spring constant spring constant

The force needed to stretch The force needed to stretch springs p & q respectively is:-springs p & q respectively is:-FFpp = = kkppL & FL & Fqq = = kkqqLL

The tension is given by W = The tension is given by W = FFp p + F+ Fq q and so... and so...

W = W = kkppL + L + kkqqL which can be considered L which can be considered

equal to equal to kkL where k is the L where k is the effectiveeffective spring spring constantconstant

p q

L

Springs in series share the same Springs in series share the same tension which is equal to Wtension which is equal to W

The extensions in the two springs The extensions in the two springs is given by:-is given by:-LLpp = W/ = W/kkpp & & LLqq = W/ = W/kkqq

The total extension is The total extension is LLpp + + LLqq

= W/= W/kkpp + W/ + W/kkq q = = WW/k/k = = 1/1/kkpp + 1/ + 1/kkq q = = 11/k/k

where k is the where k is the effectiveeffective spring constant spring constant

p

qL

The stretched spring The stretched spring has elastic potential has elastic potential energy. Work has been energy. Work has been done because the force done because the force moves through a moves through a distance.distance.The distance moved by the force is The distance moved by the force is L, the L, the force involved ranges from 0 to F and so the force involved ranges from 0 to F and so the average is F/2average is F/2

EEpp = ½F = ½FLL

Only valid for Only valid for where Hooke’s where Hooke’s law is obeyedlaw is obeyed

1.1. We’ve seen Hooke’s law and how we can use We’ve seen Hooke’s law and how we can use it to establish the spring constantit to establish the spring constant

2.2. We’ve discussed variables and how to We’ve discussed variables and how to accurately establish the spring constant accurately establish the spring constant experimentallyexperimentally

3.3. We’ve seen how combinations of springs in We’ve seen how combinations of springs in parallel and series can act as a single springparallel and series can act as a single spring

4.4. We have related the elastic potential energy We have related the elastic potential energy in a stretched spring to the work done in a stretched spring to the work done stretching the springstretching the spring