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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

how does the earth revolute
Kevin Reply
What is the momentum
Given Reply
The product of the object's mass and it's velocity
Mvula
electric field def
FREENCO
how is ester formed
Aubrey Reply
how is n ester formed
Aubrey
Alcohol reacts with a carboxylic acid
Texas
and the reaction is catalysed by sulphuric acid
Vhulenda
an athlete with a mass of 70kg runs at a velocity of 45km . determine the athlete's momentum
Lesedi Reply
Is that a velocity or something else
msawenkosi
45km/h i guess
Texas
Change to m/s
Texas
45km/h = 12.5 m/s p=mv =70×12.5 =875 kg.m/s
Thato
what are the measures of the rates of reaction
Lesego Reply
Volume Concentration Temperature Pressure Surface Area
Thato
the principle of superposition of waves
Sfundo Reply
what is work
Kool Reply
is this a group chat
Nobuhle Reply
Hey can y'all define newton's 2nd law
mthebzification
If a resultant force act on an object...the object will accelerate in the direction of a resultant force,the acceleration of the object is directly proportional to the net force and inversely proportional to the mass of the object
mosa
how do you calculate tension force
Bulumko
use the formula Fnet=ma if there is tension connecting two objects
Sboniso
to calculate Tension, usually calculate acceleration first Draw separate free body diagrams for each body. Apply Fnet = ma to calculate Tension
Kevin
Hi people
Paul
how does temperature affect the equilibrium position
Blessing Reply
an increased temperature increases the average kinetic energy thus in turn increases the number of effective collisions........
Lwando
so...which reaction is favored between endothermic and exothermic .when temperature is increased..?
Blessing
exothermic reaction because energy is realised to the surroundings as heat and light energy ....graphical so much energy is realised as reactants to form product and because temperature is high rate of reaction is fast which means there is a successful collision
Code
INTEMENDO - INCREASE IN TEMPERATURE FAVOURS ENDOTHERMIC DETEMEXO - DECREASE IN TEMPERATURE FAVOURS EXOTHERMIC
Thato
an object will continue in a state of rest unless it is acted upon an unbalanced force
Junior Reply
Newton's Law 1
Code
First Newton's Law
Azola
Newton's first law
Surprise
newton first law
Thinavhuyo
Newton's first law
Blessing
when pressure is increased what happen to volume
Siphelo Reply
decreases
Code
care to explain?
Mpati
if pressure is applied to a pistol , the volume will decrease and particles will collide more frequently with the wall of a container .Each time they collide with the wall they exert a force on them .More collision means more force and the pressure will increase , that Boyle's Law
Code
Because the volume has decreased , the particle will collide more frequently with the wall of a container and each time they collide with the wall of a container they exert a force on them.More collision means more force so the pressure will increase , that Boyle's Law
Code
what is the difference between momentum and a change in momentum?
Chavonne Reply
Change in momentum is the impulse of the object
Rachel
Momentum is a vector quantity equal to the product of the mass of the particle and its velocity
Mmola
How to name a branched molecule from right or left?
Vadin Reply
What's Free Fall
Senzo Reply
Free Fall means there is no acting force on that object.
Dingaletu
only gravitational force
Dingaletu
no external force acting on an object
Sphiwe
by only force of gravite
Sello
but gravitational force
Sphiwe
true
Lucky
a motion in which the only force acting is gravitational force
Blessing
and an object experiencing free fall is referred as a projectile
Blessing
Do polymers form restrictedly only if compound is saturated, only?
milani 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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