Materials

Question 1

How to find density of a regular solid?

(how to reduce uncertainty?)

Answer 1

Measure mass using top pan balance.
Measure dimensions using Vernier caliper or micrometer and calculate volume using appropriate eq.
Calculate density, ρ = m / v

Question 2

Density of liquid?

(how to reduce uncertainty?)

Answer 2

Mass of empty cylinder. Add liquid (use as much liquid as possible to reduce % error). Mass of cylinder + liquid. Volume of liquid in cylinder. Calculate density.

Question 3

Density of irregular solid?

Answer 3

Measure mass. Immerse in liquid in measuring cylinder and observe rise in liquid level. This is volume. Calculate density.

Question 4

Density of alloys?

Answer 4

Mass of alloy, m = ρAVA + ρBVB
Density of alloy, ρ = m/v
= (ρAVA + ρBVB) / V
= ρAVA / V + ρBVB / V

Question 5

1 m^3 into cm^3?

Answer 5

10^6 cm^3

Question 6

What is the tension in a spring (describe) ?

Answer 6

A stretched spring exerts a pull on the object holding each end of the spring. This pull, referred to as the tension in the string, is equal and opposite to the force needed to stretch the spring.

Question 7

What is Hooke’s law?

Answer 7

States that the force needed to stretch a spring is directly proportional to the extension of the string from its natural length, UP to a limit of proportionality. F = k ΔL

Question 8

What is k?

Answer 8

k is spring constant/stiffness constant. the greater the value of k the stiffer the spring.

Question 9

Springs in parallel:

Answer 9

k = k1+ k2

(same ΔL)

Question 10

Springs in series:

Answer 10

1/k = 1/k1 + 1/k2

(same F)

Question 11

Elastic potential energy is stored in a stretched spring. What’s the eq?

Answer 11

Ep = 1/2 F ΔL = 1/2 k ΔL^2

Question 12

What is elasticity?

Answer 12

Elasticity of a solid material is its ability to regain its shape after it has been deformed or distorted and the force that deformed it has been released.

Question 13

Deformation that stretches an object is …

Answer 13

..tensile.

Question 14

Deformation that compresses an object is…

Answer 14

..compressive.

Question 15

How to test how easily different materials stretch?

(experiment) (graph axes)

Answer 15

Add weights, measure, using a set square and metre ruler, ΔL from L0 each time, then unload until no weights.

ΔL(y) against T (x)

Question 16

Steel spring ΔL-T graph:

Answer 16

Straight line through origin because of Hooke’s law.

Question 17

Rubber band ΔL-T graph:

Answer 17

Rubber band extends easily when it’s stretched. However, becomes fully stretched and very difficult to stretch further when its been lengthened considerably.

got an acceleration start curving up then at end curves towards other direction so s shaped. at all points its below the spring line.

Question 18

Polythene string ΔL-T graph:

Answer 18

Polythene string ‘gives’ and stretches easily after its initial stiffness is overcome. However, after ‘giving’ easily, it extends little and becomes difficult to stretch.

got a very shallow start then curves up steeply and changes direction at end. at all points its below the spring line and the rubber band line.

Question 19

How can we measure extension of a wire under tension ?

Answer 19

Using Searle’s apparatus.
Micrometer attached to control wire adjusted so the spirit level between the control and test wire is horizontal. Each time weight added, micrometer readjusted. Readjustments are the ΔL.

Question 20

For a wire under tension, tensile stress is?

Units?

Answer 20

Tensile stress = tension per unit cross-sectional area.
σ = T / A

Units Pa or Nm^-2

Question 21

For a wire under tension, tensile strain is?

Units?

Answer 21

Tensile strain = extension per unit length.
ε = ΔL / L0

No units bc its a ratio.

Question 22

We have a stress-strain graph. Try drawing it, inc limit of proportionality, elastic limit, yield point 1 and 2, plastic flow, UTS, and breaking point.

Answer 22

First directly proportional. Instant it stops being directly proportional is P (limit of proportionality). Just beyond it we have E (elastic limit) then a peak of this mini n shape called Y1 and the bottom of this n shape called Y2. Kind of looks like a walking stick at an angle rn. From here extends at an angle to the right, reaching a shallow peak (UTS) and curving down to a stop at B (breaking point).

Question 23

From 0 to limit of proportionality, P, stress ∝ strain. Gradient is Young modulus, E:

Answer 23

E = σ/ε = T L0 / ΔL A

Question 24

Beyond P line curves and continues beyond elastic limit, E, to yield point Y1, which is:

Answer 24

which is where the wire weakens temporarily.

Question 25

The elastic limit, E, is:

Answer 25

the point beyond which the wire is permanently stretched and suffers plastic deformation.

It doesn’t regain its original length when the force applied to it is removed.

Question 26

Beyond Y2, a small increase in…

Answer 26

a small increase in stress causes a large increase in strain as the material of the wire undergoes plastic flow.

Question 27

Beyond the maximum tensile stress, the ultimate tensile stress (UTS), wire loses its strength, ….

Answer 27

wire loses its strength, extends, and becomes narrower at its weakest point.

Question 28

Increase in stress occurs due to reduced area of cross-section at this point until..

Answer 28

until wire breaks at point B.

UTS sometimes called breaking stress.

Question 29

The stiffness of different materials can be compared using…

Answer 29

the gradient of the stress-strain graph, which is equal to Young modulus of the material.

Question 30

The strength of a material is..

Answer 30

is its UTS, which is its max tensile stress.

Question 31

A brittle material…

(stress-strain graph)

Answer 31

snaps without any noticeable ‘give’ eg glass breaks without any give.

straight gradient then stops at a small curve for glass

Question 32

A ductile material…

(stress-strain graph)

Answer 32

can be drawn into a wire.

eg copper graph drawn out more horizontally

Question 33

Toughness is a measure of?

Answer 33

The energy needed to break a material.

Question 34

Loading and unloading curves on F-ΔL graph for metal wire, rubber band, and polythene string.

Answer 34

How does the strength of a material change as a result of being stretched? Lets find out!

Question 35

Metal wire
Draw and describe loading and unloading curve.

Answer 35

It’s loading and unloading curves are the same provided its elastic limit isn’t exceeded. Wire returns to L0 when unloaded. Beyond elastic limit, unloading line parallel to loading line. Wire slightly long when unloading - has permanent extension.

Question 36

Rubber band
Draw and describe loading and unloading curve.

Answer 36

Change of length during unloading is greater than during loading for a given change in tension. Rubber band returns to L0, but unloading curve is below loading curve except at zero and max extensions. Remains elastic as it regains its L0, but it has a low limit of proportionality.

Question 37

Polythene string
Draw and describe loading and unloading curve

Answer 37

Extension during unloading is greater than during loading for a given change in tension. String doesn’t return to same L0 when completely unloaded. polythene string has low limit of proportionality and plastic deformation.

So graph looks like rubber when loading (kind of flowy N shape completely stretched horizontally) and when unloading its an angled line down (kind of like loading on wire but steeper)

Question 38

Polythene is a polymer. Use this to explain its behaviour above.
(Compare unstretched with stretched)

Answer 38

Before stretched, molecules are tangled together. Weak bonds/ cross-links form between molecules. When under tension, easily stretches as weak cross-links break. In stretched state, new weak cross-links form and when tension removed string stays stretched.

Question 39

Rubber band is also polymer. It behaves differently though. Explain its behaviour.
(Compare stretched with unstretched)

Answer 39

Molecules curled and tangled in unstretched state. When under tension, molecules straightened out but curl up gain when tension is removed - gains initial length.

Question 40

Work done using which graph?

Answer 40

T-ΔL graph.

Question 41

Metal wire/spring work done?
How to find it, and where did the work done go (energy transfer)?

Answer 41

Provided limit of proportionality isn’t exceeded, to stretch wire to ΔL, work done = 1/2TΔL. Because elastic limit isn’t reached, work is stored as elastic energy in the wire. Because graph is same for unloading as loading, all energy stored in wire can be recovered when wire unloaded.

Question 42

Rubber band work done?

How it’s calculated, what’s the work done transfers, where is energy held?

Answer 42

Work done to stretch rubber band = area under loading curve. Work done by rubber band when unloading = area under unloading curve. Area between loading and unloading curves represents difference between energy stored in rubber band when its stretched and the useful energy recovered from it when its unstretched. Difference occurs bc some of the energy stored in rubber band becomes internal energy of molecules when band unstretched.

Question 43

Polythene string work done?
What does this area represent?

Answer 43

As it doesn’t regain L0, the area between the loading and unloading curves represents work done to deform the material permanently, as well as internal energy retained by the polythene when its unstretched.