Stress, Strain Pressure

8/13/2019 Stress, Strain Pressure

1/15

Lesson 10, 11 & 12: Stress, Strain, Pressure

Contents:

Stress and Strain

Pressure

Density

Archimedes Principal and Buoyancy

Hookes Law

A material is said to be elasticif, when deformed by an applied force, it returns to itsoriginal shape when the force is removed. There are many familiar examples of this, such

as a steel springs, rubber bands, rubber balls, bows, and so on. Permanent deformation

may occur if the stress is too large.

Stress

Stress is defined as the force per unit area of a material.

i.e. Stress = force / cross sectional area:

where = stress,F= force applied, andA= cross sectional area of the object. Units of

stress:m!"or Pa.

Strain

Strain is defined as extension per unit length.

#train = extension $ original length

where,= strain, lo= the original length e = extension = %l-lo&, and l= stretched length

#train has no units because it is a ratio of lengths.

'f we apply tensile forcewe havetensile stressand tensile strain'f we apply co!"ressi#e force we have co!"ressi#e stressand co!"ressi#e strain.


2/15

$oun% o'ulus

'nstead of drawing a force ! extension graphlike a(o#e, if )ou "lot stress a%ainst strain

for an o(*ect s+owin% linear- elastic (e+a#iour, )ou %et a strai%+t line.

This is because stress is proportional to strain. The gradient of the straight!line graph is

the (oung)s modulus, *

* is constant and does not change for a given material. 't in fact represents )stiffness)

property of the material. +alues of the young modulus of different materials are often


3/15

listed in the form of a table in reference boos so scientists and engineers can loo them

up.

Units of the (oung modulus *- m 2or Pa.

Hookes a!

"For an elastic material, the strain is directly proportional to the stress."

or !ith in the elastic limit" the extension is directly proportional to the stretching force.

Pressure

Pressure if force #y area. The force or thrust is acted at right angle to the surface.

Pressure = orce$Area

P $ F%A

&xample

The following diagram shows a wooden bloc of mass /0 g ept on a floor. 1hich

surface exerts highest pressure on the floor2

1eight of the bloc1 = mg = /0 x 30 = /00

Area of A = lb = 4 x 3 = 4 m"

Area of 5 = lb = " x " = 6 m"

Area of 7 = lb = " x3 = " m

"

Pressure exerted by surface A = $A = /00$4 = 366.8 $m"

Pressure exerted by surface 5 = $A = /00$6 = 94.4 $m"

Pressure exerted by surface 7 = $A = "/0 $m "

Ans- #urface 7 %which has the least area& exerts the highest pressure on to the floor.


4/15

Liui' Pressure

:ravitational force tries to pull a li;uid downwards in its container. This causes pressureon the container, and pressure on any object put into the li;uid.

The following apply to any li;uid in an open container

Pressure acts in all direction

Pressure increases with depthPressure depends on the density of the li;uid

Pressure does not depend on the shape of the container.

P = hg

1here P is li;uid pressure, is density of the li;uid, h is depth of li;uid and g is

gravitational field strength %30$g&

&xample

The following diagram shows a simple hydraulic system which consists of " pistons< the

load piston and effort piston. The system is field with oil. 7alculate the oad is the effortis /00

The pressure exerted on the oil by the effort piston = $A = /00$0.03m"

= /0,000 $m"

#ince the pressure in a li;uid exerts in all direction, same pressure will be on the loadpiston.


5/15

$0.3m" = /0,000 $m"

= /0,000 x 0.3 = /000

&xample

A tan > m long, 4m wide, and "m deep is filled to the brim with paraffin of density 900

g$m4.

a& 1hat is the pressure on the base2b& 1hat is the thrust %force& on the base2

P = hg

P = 900 x > x 30

Pressure on the base = 4",000 $m"

P = $A4",000 = $6m"

orce on the base = 4",000 x 6 = 3?",000

ensit)

@ensity is mass per unit volume

@ensity = mass$volume

$ m%'

Unit of density is g$cm4

or g$m4

&xample


6/15

erosene has density 0.9" g$cm4. ind the volume of /0g of erosene

$ m%'

0.9" = /0$v

v = /0$0.9"v = 63 cm4

rc+i!e'es Princi"al an' uo)anc)

Buoyant Force( )he up!ard force that fluids exert on all matter.

Archimedes* Principle( A principle that states that the #uoyant force on an o#+ect in afluid is an up!ard force e,ual to the !eight of the 'olume of fluid that the o#+ect

displaces.

An object in a fluid will sin if the object)s weight is greater than the buoyant force. The

buoyant force, in effect, eeps objects afloat. To eep the object afloat, though, the

buoyant force must be e;ual to the object)s weight, otherwise, it will sin.


7/15

Practice Buestions3uestion 1

3uestion 2


8/15

3uestion4

3uestion 5


9/15

3uestion 5

3uestion 6


10/15

3uestion 7

3uestion8

%a& A builder is building a bric wall. Ce has /00 brics delivered, all neatly stacedtogether. *ach bric measures 0." m x 0.3 m x 0.06 m and is a solid bloc, as shown

below.

%i& 7alculate the volume of one bric.

%ii& The bric has a density of ">00 g$m4. #how that the mass of one bric is ".99 g.

%iii& 1hat is the mass of the stac of brics2%bome other brics have the same siDe and are made of the same material, but they

have a hollow in one face, as shown below.


11/15

%i&Cow does the mass of one of these brics compare with the mass of one of thebrics in a-ii&2

%ii& The hollow of one bric is filled level with wet cement, as shown below.

The bric now has a mass of ".?3 g. 7ompare this with the mass given in a-ii&. 1hatdoes it tell you about the density of the wet cement2

3uestion 9In an experiment, different weights are hung on the end of a spring, and the length of the

spring is measured. The results are as follows.

%a& 1hat is the length of the unstretched spring2

%b& #ome of the extensions have been calculated for you.

7omplete the table by writing in the remaining extensions.

%c& %i& En the graph paper plot a graph of weight against extension. %ii& @raw the best straight line through your points.

%iii& The experimenter has read one of the lengths incorrectly. 1hich one is it2 1hat

do you thin the length reading should have been2%d& The spring is now attached to a bloc resting on a rough surface, as shown below.


12/15

As the pulling force is increased, the bloc just starts to move to the right when the

spring is 69 mm long.

%i& 1hat is the extension of the spring when it is 69 mm long2%ii& Use your graph to find the force that causes this extension.

%iii& 1hat is the value of the friction force as the bloc starts to move2

3uestion

(ou are given a steel spring hanging from a support, a load and a 40 cm rule.

%a& 'n the space below, describe carefully the steps you would tae in order to measure

the extension of the spring when the load is hanging on it. (ou may draw a diagram if

this helps you to answer the ;uestion.

3uestion A student measures the mass and the volume of four samples of rock A, B, C and D.

The results are shown below.

%a& %i& @escribe in detail how a measuring cylinder is used to find the volume of roc A.

%ii& *xplain why the volume of roc @ cannot be found with an ordinary laboratory

measuring cylinder.%b& 7alculate the density of roc A.

%c& Three of the rocs are made from the same material. #tate and explain which of the

rocs is made from a different material.

3uestion 10

The densities of three solids are


13/15

aluminium " 800 g$m4,

concrete " "00 g$m4, wood 600 g$m4,

5locs having identical dimensions are made of these three substances. The blocs arestood on a horiDontal surface, as shown below.

%a& %i& 1hich bloc has the greatest mass2 Cow do you now this2

%ii& 1hich bloc has the greatest weight2

%iii& 1hich bloc exerts the greatest pressure on the horiDontal surface2

%b& The wood bloc can be placed on the horiDontal surface in any one of three ways, A, 5 or 7.

%i& 'n which position does the wood bloc exert the greatest pressure2 %ii& Cow do you now this2

3uestion 11

'n a spring!stretching experiment, the following values were found for the extension of

the spring.

%a& Plot these values on a graph.

%b& A mistae was made with measuring one of the extensions. En the table above, put a

circle around the incorrect extension.


14/15

%c& After a load of about / , the graph begins to curve upwards. #uggest what is

happening to the spring when the load is greater than / .

%d& @escribe how you would measure the extensions if you were doing this experiment.

3uestion 12

@escribe an experiment to find the average density of a small roc sample of

approximately 300 g mass.

%a& @raw a labelled diagram of the apparatus.

%b& ist all the measurements which must be taen.

%c& *xplain how to wor out the average density from the measurements taen.

3uestion 14

The following figure shows apparatus that may be used to compare the strengths of two

springs of the same siDe, but made from different materials.

%a&%i& *xplain how the masses produce a force to stretch the spring.

%ii& *xplain why this force, lie all forces, is a vector ;uantity.%b& ig.3." shows the graphs obtained when the two springs are stretched.

%i& #tate which spring is more difficult to extend. Buote values from the graphs to

support your answer.%ii& En the graph of spring ", mar a point P at the limit of proportionality. *xplain your

choice of point P.


15/15

%iii&Use the graphs to find the difference in the extensions of the two springs when a

force of 3/ is applied to each one.

3uestion 14

A boat floating in water has a mass of 3000 g.

%a& 1hat is the weight of the boat2

%b& 1hat is the upthrust on it2

%c& 1hat weight of water does it displace2%d& 'f the boat floats in denser salty water, what effect does this have on

Stress, Strain Pressure

Documents

Transcript of Stress, Strain Pressure