Chapter 11 Flashcards
Density
Density is the mass per unit volume of an object. Objects made from low density materials typically have a lower mass
How can we find which has more density
To find how much more dense one substance is compared with another.
We can measure the mass of equal volume of the two substances.
The substance with the greater mass in the smae volume is more dense.
For example a lead sphere of volume 1cm³ has a mass of 11.3g whereas an aluminium sphere of the same volume has a mass of 2.7g.
Desnity of a substance
Is defined as its mass per unit volume.
Density = what?
M/V
Mass = m
Volume = v
Density = p
Density = kgm-³
Cubiod
M / width x base x height
Cylinder
M / π x r² x height
Sphere
H / 4/3 x π x r³
Ireegular solid
M / volume pf water displaced
Alloy
Is a mixture of two or more metals
Desnity of alloys calculation
Mass of metal A = Pa Va,
Mass of metal B = Pb Vb
Total mass = Pa Va + Pb Vb
P = Pa Va + Pb Vb / V
= PaVa / v + PbVb/v
Centimetres³ into metres³
100³ = 1,000,000 = 10⁶
How to work out desnity of a regular solid
Masure its mass using a top pan balance
Meausre its dimensions by using a venier calipers then calculate its volume using an appropriate equation
Then calculate the density from mass / volume
How to work out the density of a liquid
Masure the mass of an empty measuring cylinder. Pour some of the liquid into the measuring cylinder and measure the volume of the liquid directly.
Measure the mas of the cylinder and the liquid to enbale the mass of the liquid to be calculated
Then do mass / volume
How to measure the density of an irregular solid
Measure the mass of an object
Immerse the object on a thread in liquid in a measuring cylinder observe the increase in the liquid level. This is the volume of the object
Then calculate the density by using mass / volume
Example question 1
Volume = 0.05m x 0.08m x 0.2 = 8x10-⁴
Desnity = p=m/v
= 2.5 / 8x10-4
= 3125
alloy tube of volume 1.8x 10-4 m° consists of 60% aluminium
and 40% magnesium by volume. Calculate a the mass of Ai aluminium,
Aii magnesium in the tube, b the density of the alloy. The density of
aluminium = 2700 kg m-3. The density of magnesium = 1700 kg m-3
Ai) Aluminium = 2700kgm-3 2700 x (1.8x10-4 x0.6) Mass = 0.29kg
Aii) Magnesium = 1700kgm-3 1700 x (1.8x10-4 x 0.4) Mass = 0.12kg
B)0.29 + 0.12 / 1.8x10-4 = 2277
=2300kgm-3
Hookes law 1660
The force needed to stretch a spring is directly proportional to the extension of the spring from its natural length, provided the elastic limit is not exceeded.
Up to the limit of proportionality
Force = what? Hookes law equation
F = k x ΔL F = force K = spring constant (Nm-1) ΔL = change in length (m)
What is spring constant
This is a simple measure of stiffness but doesn’t take into account the objects physical dimensions.
Y axis = force
X axis = extension
Line = elastic and inelastic lastic
The bottom half of the line is elastic
The top half of the line is inelastic lastic
Half way is the elastic limit of proportional
Gradient = K
Spirngs in parallel
Srpings in a parallel with extend less for a given force
K total = k1 +k2 …
Springs in series
1 / ktotal = 1/k1 + 1/k2
Energy stored in a spring is the area under the …
F = k x ΔL
½ x (KxΔL)xΔL
Ep = ½ x FxΔL = ½ xKxΔL²
Ep elastic potential energy stored in a stretched spring
Deformation of a spring
Stress is the force per unit cross-sectonal area applied to a sample or material: σ = F/A σ = stress (nm-2 or Pa) F = force (n) A = cross sectional area (m2)
Strain
Is the extenson per unit length undergone by a sample of material: ε = ΔL / L ε = strain ΔL = extension L v length (m) Tensile = under tensile
Young modulas
Is a comprehensive measurment of a materials stiffness is given by:
E = σ÷ε = F/A ÷ ΔL/L = FxL / AxΔL
E = young modulas (Pa or Nm-2)
Graph
Stress y axis
Strain x axis
Look at (photo)
Stuff we can read off:
Stiffness from E, gradient of straight line section
Strength from UTS
Elasticity from strain in straight line secton
Ductility from strain under plastic deformation
Necking occurs between UTS and B
Tensile stress equation
σ = F/A F = force A = area σ = stess
Brittel
Material snaps without any noticable yeild. Glass breaks without any give.
Ductile
Material can be drawn into a wire copper is more ductile than steel
Stretches easily without breaking
Stiffness
the stiffness of different materials can be compared using the
gradient of the stress-strain line, which is equal to the Young
modulus of the material. Thus steel is stiffer than copper.
Strength
The strength of a material is its ultimate tensile stress (UTS), which
is its maximum tensile stress. Steel is stronger than copper because its
maximum tensile stress is greater.
Metal wire
Metal wire stretches elastically until elastic limit is reached
Further deformation is platsic and permanent
Rubber
Deformation does not obey Hookes law , as limit of proportionality is very low
However elastic limit is high so returns to its orginal
Polythene
Polythene immediately exceeds both the elastic limit and the limit of proportionality.
Deformation is permanent and non proportional
Area
Area under a force vs extention graph is the enegry stored
Area under loading curve for rubber is greater than unloading curve
This tells us the difference in energy into the internal enrgy of the rubber.
Describe how you would use this arrangement to measure the mass of the rock
sample. State the measurements you would make and explain how you would use
the measurements to find the mass of the rock sample.
Measure intital length Put a known masss on it (mg) Measure new length Le - li = extension K = E/e alternatively put more known masses on and measure several extensions Plot Force vs extension and calculate gradient Change in Y / chnage in X = F/e = spring constant = K Put on rock Measure extension Use graoh to find the force Force Y axis Extension X axis Divide force by G = mass
Mass = what ?
Mass = density x volume
What is meant by the elastic limit of a wire
The maxium amount that a material can be stretched and still to its orginial length when the force is removed
Young modulus ratio
Ratio of tensile stress to tensile strain
Young modulus equation
E = FxL / A x ΔL A = area E = young modulus F = force ΔL = change in length
Young modulus
Cross sectional area
The cross sectional area chnages as the rod is compressed or stretched
Tesnile strain
ε = e/L E = extension L = length ε = strain
Tesnile stress
Teh stretching force applied per unit cross sectional
Tensile strain
Extesnion produced per unit length
Loading
Must obey hookes law from A to B where B is the limit of proportionality beyond at B elastic limit reached undergoes plastic deformation
Unloading
At C the load is removed linear relation between stress and strain which does not return to its original length
