Materials (Unit 2)

Question 1

Density

Answer 1

Mass per unit volume

Question 2

Units of density

Answer 2

kg m^-3

Question 3

Hooke’s Law

Answer 3

Extension is proportional to the force applied, up to the limit of proportionality.

Question 4

Features of graph of force against extension confirming Hooke’s Law

Answer 4

Straight line, through the origin.

Question 5

Units of spring constant

Answer 5

Nm^-1

Question 6

Springs in series

Answer 6

Both springs experience the same force, F.

The total extension (of both springs together) is the sum of the extension of each spring individually.

Question 7

(Identical) Springs in parallel

Answer 7

The force, F, applied to the spring combination is shared across each of the springs individually (if there are two identical springs, each spring experiences a force of 1/2F.
All springs have the same extension (and equals the extension for the spring combination).

Question 8

Elastic Limit

Answer 8

The maximum amount a material can be stretched by a force and still return to its original length when the force is removed

Question 9

Limit of Proportionality

Answer 9

Point beyond which force is no longer proportional to extension.

Question 10

Elastic behaviour

Answer 10

material will return to its original length (when force removed) with no permanent extension.

Question 11

Plastic behaviour

Answer 11

material will be permanently extended (when force is removed).

Question 12

Area under a force/extension graph

Answer 12

area under a graph of force against extension is work done on spring and hence the energy stored, as it is loaded.
or
area under a graph of force against extension is the work done by the spring, and hence energy released, as it is unloaded.

Question 13

Area between the loading and unloading curves of an elastic band

Answer 13

internal energy retained, eg as heat, within the elastic band

Question 14

Derivation of

energy stored = ½ F(delta)l

Answer 14

• Energy stored in a stretched spring = work done stretching the spring.
• Work done = Force x distance (moved in the direction of the force)
• As spring is stretched the force gets bigger (and so isn’t constant).
• Force is proportional to Extension, so,
average force = ((F+0)/2 ), which = ½ F.
• The work done = average force x distance moved
• Energy stored = work done = ½ F delta L
• This is the area under the graph of Force against Extension (½ base x height).

Question 15

Derivation of
energy stored = ½ F(delta)L
from a graph of force against extension

Answer 15

• W=Fs, so area beneath line from origin to L represents the work done to compress/extend spring.
• work done (on spring) equals the energy it stores.
• area under graph = area of triangle = ½ base x height, therefore energy stored = ½ F x L.

Question 16

Tensile stresstensile (stretching) force divided by its cross-sectional area

Answer 16

tensile (stretching) force divided by its cross-sectional area

Question 17

Units of stress

Answer 17

Pa or Nm-2

Question 18

Tensile strain

Answer 18

extension of material divided by its original length

Question 19

Units of strain

Answer 19

None

Question 20

Breaking stress (ultimate tensile stress)

Answer 20

(tensile) stress needed to break a solid material

Question 21

Description of stiffness

Answer 21

requires a large force (or stress) for a small deformation (or extension)

Question 22

Description of fracture

Answer 22

Non-brittle fracture
Material necks (becomes narrower at its weakest point) which reduces the cross-sectional area so increases stress at that point until the wire breaks (at that point)
Brittle fracture
No plastic deformation, usually snaps suddenly without any noticeable yield (through crack propagation).

Question 23

Description of brittle

Answer 23

a material that fractures without any plastic deformation

Question 24

Description of ductile

Answer 24

material can be drawn into a wire (exhibits a lot of plastic deformation)

Question 25

Description of strength (or weakness)

Answer 25

Material with a higher (or lower) breaking stress.

Question 26

Young Modulus

Answer 26

ratio of tensile stress to tensile strain

Question 27

Units of Young Modulus

Answer 27

Pa or Nm-2

Question 28

Use of stress/strain curves to find Young Modulus

Answer 28

from a graph of stress against strain, Young Modulus is the gradient of the linear section of the graph (the region where stress and strain are directly proportional)

Question 29

Area under a graph of stress against strain

Answer 29

energy stored per unit volume

Question 30

One simple method of measuring Young Modulus

Answer 30

Measurements to make
• Original length of wire, L, with a ruler
• Diameter of wire with a micrometer
• Mass attached to end of wire
• Length of stretched wire with a ruler.
Reducing Uncertainty in each measurement
• Repeat measurements of length
• Repeat measurements of diameter of wire at different points
• Check for zero error on electronic scales
• Check for zero error on micrometer
How measurements are used to determine Young Modulus
• F=weight=mg
• Extension L = stretched length – original length
• Cross-sectional area of wire A = (pi)d2 / 4.
• Stress = F/A; Strain = L/L
• Plot a graph of stress (y-axis) against strain (x-axis)
• Young Modulus is gradient of linear section of graph

Question 31

Interpretation of force against extension curves

Answer 31

See sheet

Question 32

Interpreting stress/strain graphs

Answer 32

See sheet