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Introduction

In this chapter we will look at some mechanical (physical) properties of various materials that we use. The mechanical properties of a material are those properties that are affected by forces being applied to the material. These properties are important to consider when we are constructing buildings, structures or modes of transport like an aeroplane.

Deformation of materials

Hooke's law

Deformation (change of shape) of a solid is caused by a force that can either be compressive or tensile when applied in one direction (plane). Compressive forces try to compress the object (make it smaller or more compact) while tensile forces try to tear it apart. We can study these effects by looking at what happens when you compress or expand a spring.

Hooke's Law relates the restoring force of a spring to its displacement from equilibrium length.

The equilibrium length of a spring is its length when no forces are applied to it. When a force is applied to a spring, e.g., by attaching a weight to one end, the spring will expand and become longer. The difference between the new length and the equilibrium length is the displacement.

Hooke's law

Hooke's law is named after the seventeenth century physicist Robert Hooke who discovered it in 1660 (18 July 1635 - 3 March 1703).
Hooke's Law

In an elastic spring, the extension varies linearly with the force applied.

F = - k x

where F is the restoring force in newtons (N), k is the spring constant in N · m - 1 and x is the displacement of the spring from its equilibrium length in metres (m).

Hooke's Law - the relationship between a spring's restoring force and its displacement from equilibrium length.

Experiment : hooke's law

Aim:

Verify Hooke's Law.

Apparatus:

  • weights
  • spring
  • ruler

Method:

  1. Set up a spring vertically in such a way that you are able to hang weights from it.
  2. Measure the equilibrium length, x 0 , of the spring (i.e. the length of the spring when nothing is attached to it).
  3. Measure the extension of the spring for a range of different weights. Note: the extension is the difference between the spring's equilibrium length and the new length when a weight is attached to it, x - x 0 .
  4. Draw a table of force (weight) in newtons and corresponding extension.
  5. Draw a graph of force versus extension for your experiment.

Conclusions:

  1. What do you observe about the relationship between the applied force and the extension?
  2. Determine the gradient (slope) of the graph.
  3. Now calculate the spring constant for your spring.

Phet simulation for hooke's law

Khan academy video on springs and hooke's law

A spring is extended by 7 cm by a force of 56 N.

Calculate the spring constant for this spring.

  1. F = - kx 56 = - k × 0 , 07
    k = - 56 0 , 07 = - 800 N · m - 1
Got questions? Get instant answers now!

A spring of length 20cm stretches to 24cm when a load of 0,6N is applied to it.

  1. Calculate the spring constant for the spring.
  2. Determine the extension of the spring if a load of 0,5N is applied to it.
  1. We know:

    F = 0,6 N

    The equilibrium spring length is 20 cm

    The expanded spring length is 24 cm

  2. First we need to calculate the displacement of the spring from its equilibrium length:

    x = 24 cm - 20 cm = 4 cm = 0 , 04 m

    Now use Hooke's Law to find the spring constant:

    F = - k x 0 , 6 = - k · 0 , 04 k = - 15 N . m - 1
  3. F = 0,5 N

    We know from the first part of the question that

    k = -15 N . m - 1

    So, using Hooke's Law:

    F = - k x x = - F k = - 0 , 5 - 15 = 0 , 033 m = 3 , 3 cm
Got questions? Get instant answers now!

Questions & Answers

formula of heat reaction
Anelisiwe Reply
final energy-initial energy of substances
Chantel
what is the difference between ethene and ethane
Joy Reply
Ethane is a saturated organic molecule while ethene is unsaturated Ethane has 2 carbon atoms and 6 hydrogen atoms, while ethene has 2 Carbons and 4 hydrogens Ethane has single bond between the 2 Carbon atoms while ethene has double bond
Rito
How do you know that the reaction is in acid medium or basic medium
Miss Reply
What formular is used when source and Observer are moving towards to each other
Esihle Reply
put a + on top n - on the bottom
Sanele
what is doppler effect?
Ansiwe Reply
doppler effect is the perceived change in frequency of a sound caused by either the source or the listener
Qaqamba
moving relative to each other
Qaqamba
A Catalyst is a chemical substance that speeds up a chemical reaction.
Sheron Reply
It does this by lowering the activation energy.
Sheron
what is exothermic
Nambile Reply
reaction that releases energy
Beauty
what is a catalyst
Joseph
Catalyst is to speed up the reaction
CELO
catalyst is a substance added into a solution to speed up the process
Joseph
As it speeds up the reaction by lowering the activation energy, it does not take part in the reactants or products formed
Rito
reaction that release energy
Qaqamba
what is exothermic
Nambile Reply
reaction that gives off heat to the surroundings
Thabile
formula for calculating the heat of reaction
Anelisiwe
I need help in electrostatic
Muthuphei Reply
in exactly in electrostatic
Beauty
send the question on electrostatic maybe I can help
Beauty
factors affecting the rate of reaction
thabo Reply
hi
Xiluva
hi
Mashweme
hey
Musa
I'm xiluva ...do we help those who are having challenges on their studies?
Xiluva
I mean on physical science
Xiluva
I believe it's supposed to be like that. Helping those who are having educational challenges
Rito
Yep physical sciences more specifically
Rito
ok ....nna I need some help in physics electricity ...just hints how we do what n how to solve some of the problem... just hints
Xiluva
The first thing you can do is to understand ohm's law and the difference between a series and parallel connection concerning current, resistance and potential difference
Thendo
Hi Xiluva,not sure if this will be helpful but to understand electricity better I suggest you download Siyavula physical science books there's both a learner book and a teacher's guide I was struggling too they really did help you might be able to do some exercises after reading siyavula material
LUTHO
what diode mean
Ansiwe
diode s a part of electrical current tht allows only moves to one direction ..only ...
Frank
allows current .....to flow to one direction I meant .
Frank
ok thanks
Ansiwe
ok thanks guys
Xiluva
temperature surface area concentration addition of a catalyst
Joseph
thank you mr
Mzukisi
How to calculate e.p
zama Reply
ep=mgh
mudodzwa
Ep=mgh
Maximurm
What is polymer
Kwinda Reply
chemical compound with molecules bonded together in long ,repeating chains
Bukani
hey guys i need help with the topic of forces and their application
Monica Reply
A force is a pull or push and it can be applied in rocket launchers moving cars & stoping (breaking them).
Duncan
A force is that Agency which changes the object's state of rest or motion. A push or pull are the effects of force.
Katiso
are you sure u wantd to ask tht or u wantd to say " how many bonds are there in alkane nd their names?" ?
Frank Reply
I also think that's what she meant 'coz I don't really understand her question
LINDOKUHLE
yeah nd if that's th case , there are only single bonds wch I could say one of em tht I know is methane
Frank
I mean methane,ethane they end up to what
Sylvia
well I also assume ths is wah u lookin for .. methane , ethane , propane, butane, pentane, hexane , Heptane, octane , nonane , decane . is ths wah u wanted ?
Frank
how many alkane are there n there names
Sylvia Reply

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Source:  OpenStax, Siyavula textbooks: grade 12 physical science. OpenStax CNX. Aug 03, 2011 Download for free at http://cnx.org/content/col11244/1.2
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