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Physics A - Level > Mechanics and Materials (6): Materials > Flashcards

Mechanics and Materials (6): Materials Flashcards

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1
Q

What is the definition of density?

A

The mass per unit volume of a substance

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2
Q

What is the equation for density?

A

p(rho) = m/V

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3
Q

What is the unit of density?

A

kgm^-3

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4
Q

How would you determine the density of a regular solid?

A
  • Measure mass of solid using a top pan balance
  • Measure its dimensions using a vernier calliper of a micrometer and calculate its volume using the appropriate equation
  • Calculate density using rho = mass/volume
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5
Q

How would you determine the density of a liquid?

A
  • Measure the mass of an empty measuring cylinder.
  • Then pour some liquid into the cylinder and record the volume directly from the bottom of the meniscus level with the reading (to avoid parallax)
  • Use as much liquid as possible to reduce the % error in the reading
  • Measure the mass of the cylinder with water -> then the mass of the water by doing: mass of cylinder and water - mass of cylinder = mass of water
  • Calculate density using rho = mass/volume
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6
Q

How would you determine the density of an irregular solid?

A
  • Measure the mass of the object using a top pan balance
  • Fill a eureka can so that it is filled just below the spout leading to a beaker
  • Place the object in the beaker and the volume of water displaced by the solid is equal to its volume
  • Calculate density using rho = mass/volume
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7
Q

What is the definition of an alloy?

A

A mixture of two or more metals

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8
Q

How would you find the density of an alloy made of metal A with a Va and density (rho)a and metal B with Vb and density (rho)b?

Va is volume of metal A
Vb is volume of metal B

A

Mass of metal A = Va x (rho)a
Mass of metal B = Vb x (rho)b

Therefore mass of alloy = Va x (rho)a + Vb x (rho)b

Density of alloy = Va x (rho)a + Vb x (rho)b/ Vtotal

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9
Q

What is the definition of tension in a spring?

A

The pull exerted by the spring on each object holding the spring at either end.

Tension is equal and opposite to the force needed to stretch the spring.

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10
Q

State Hooke’s Law

A

The force needed to stretch a spring is directly proportional to the extension of the spring from its natural length provided the environmental conditions are kept constant

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11
Q

What is the equation that shows Hooke’s Law?

A

F = k(delta)L

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12
Q

What does k represent in the equation F = k(delta)L?

A

The spring constant (the stiffness constant)

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13
Q

A higher value of k, spring constant = …?

A

Increased stiffness of the spring

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14
Q

Describe features of a force-extension graph for a spring that follows Hooke’s Law?

A

F = k(delta)L
- Area under the graph is equal to the work done by the force on the spring
- Gradient of the graph = spring constant, k

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15
Q

What is the definition of the limit of proportionality?

A

The point after which Hooke’s Law is no longer obeyed

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16
Q

What is the definition of the elastic limit?

A

The point at beyond which the wire is permanently stretched (will never go back to its original length) and suffers PLASTIC DEFORMATION

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17
Q

Is the limit of proportionality before or after the elastic limit on a force extension graph?

A

Before

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18
Q

For two springs in parallel what is the effective spring constant?

A

k = ka + kb + kc …

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19
Q

For two springs joined end on in series what is the effective spring constant?

A

1/k = 1/ka + 1/kb …

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20
Q

How do you prove that the effective spring constant for two springs in parallel is the sum of the individual spring constants?

A
  • Move the mass with weight, W between two springs so that each spring has the same extension

Force needed to stretch spring A, Fa = ka(delta)L

Force needed to stretch spring B, Fb= kb(delta)L

As the weight is supported by both springs

W = Fa + Fb = ka(delta)L + kb(delta)L
= k(delta)L

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21
Q

How do you prove that the effective spring constant for two springs in series is: 1/k = 1/ka + 1/kb …?

A

Extension of spring A, (delta)La = W/ka
Extension of spring B, (delta)Lb = W/kb

Total extension, (delta)L = (delta)La + (delta)Lb = W/ka + W/kb = W/k

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22
Q

How do you calculate the elastic potential stored in a spring from a force extension graph?

A
  • The area under the graph
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23
Q

What is the equation for the area under the graph for a force extension graph of a material that obeys Hooke’s Law?

A

Ep = 1/2F(delta)L

OR (as F = k(delta)L)

Ep = 1/2k[(delta)L]^2

24
Q

What is the definition of the elasticity of a material?

A

The ability for the material to regain its shape after it has been deformed or distorted and the force that caused it to deform has been released

25
Q

What is deformation that stretches an object known as?

A

tensile

26
Q

What is deformation that compresses an object known as?

A

compressive

27
Q

Describe the extension-force graph for a rubber band?

A
  • First extends easily when force is applied
  • However, when it becomes fully stretched and difficult to stretch further when it has been lengthened considerably
28
Q

Describe the extension-force graph for a polythene strip?

A
  • A polythene strip initially does not extend much at all when a force is applied
  • However, at a certain amount of force it ‘gives’ and stretches easily
  • Once it has extended it becomes difficult to stretch
29
Q

What is the equation for the tensile stress for a wire under tension?

A

Tensile stress, sigma = T/A

Where A is the cross sectional area of the wire

30
Q

What is the unit of tensile stress?

A

Pa, pascal

31
Q

What is the equation for the tensile strain for a wire under tension?

A

Tensile strain, epsilon = (delta)L/L

Where (delta)L is the extension and L is the original length of the wire

32
Q

What are the units of tensile strain? Why?

A

No units, as the value is a ratio

33
Q

What is the definition of tensile stress?

A

Tension per unit cross sectional area

34
Q

What is the definition of tensile strain?

A

extension per unit length

35
Q

What is toughness a measure of?

A

The energy needed to break a material

36
Q

What is the name of the apparatus used to measure how extension varies with tension?

A

Searle’s Apparatus

37
Q

Describe the set up of Searles’s Apparatus and how it is used?

A
  • A micrometer attached to a control wire is adjusted so that the spirit level between the control and test wire is horizontal
  • When the test wire is loaded, it extends slightly causing the spirit level to drop on one side
  • The micrometer is then adjusted to make the spirit level horizontal again
  • The change in the micrometer reading is equal to the extension for that weight
  • Continue increasing the weight whilst recording extensions for each value
38
Q

When on a graph of tensile stress against tensile strain is tensile stress proportional to tensile strain?

A

In the first section of the graph up to the limit of proportionality

39
Q

What is the constant called for the stress/strain of a material?

A

Youngs Modulus

40
Q

What is the equation for Youngs Modulus?

A

TL/A(delta)L

41
Q

Describe what the graph of tensile stress against tensile strain looks like for a metal wire

A
  • Initially tensile stress is proportional to tensile strain up to the limit of proportionality, P
  • Beyond P the line curves and continues further than the elastic limit to the yield point -> this is where the wire weakens temporarily so there is a dip down in the curve down slightly to the second yield point
  • Beyond the second yield point a small increase in tensile stress causes a large increase in tensile strain up until the ultimate tensile stress (UTS) which is a maximum
  • After the UTS the wire loses its strength, extends and becomes narrower at its weakest point
  • This causes an increase in tensile stress as the cross sectional area at that point decreases until it breaks -> from the UTS the graph goes down slightly before stopping as the wire breaks
42
Q

How can the stiffness of different materials be compared using a graph?

A
  • Use the stress-strain graph
  • The gradient of the stress strain graph is equal to the Youngs Modulus of the material
43
Q

If a gradient of a material on the stress-strain graph is more steep than another, is it more or less stiff?

A

More stiff as more stress is required to obtain the same strain

44
Q

What point on a stress-strain graph is the strength of a material equal to?

A

Ultimate tensile stress

45
Q

What does the graph of a brittle material look like?

A

A brittle material snaps without any noticeable yield e.g glass. Therefore, the graph has a moderately steep gradient but will not go much further than the elastic limit

46
Q

What does the graph of a ductile material look like?

A

A ductile material can be drawn into a wire - the gradient is quite shallow as little force is required to increase the stress e.g copper is more ductile than steel

47
Q

What does a loading and unloading curve look like for a metal wire providing the elastic limit is not exceeded?

A

Loading and unloading curves are the same

48
Q

What does a loading and unloading curve look like for a metal wire when the elastic limit is exceeded?

A

The unloading line is parallel to the loading line but the wire is slightly longer when unloaded and has a permanent extension

49
Q

What does a loading and unloading curve look like for an elastic band?

A
  • The loading curve looks like a horizontal point of inflexion curve but with the flat part less defined
  • The unloading curve below the loading curve with the same sort of shape -> for unloading the change in length of the rubber band is greater for a given change in tension in comparison to loading
50
Q

Which types of materials have a low limit of proportionality?

A
  • Rubber band
  • Polythene strip
51
Q

What does the loading and unloading curve look like for a polythene strip?

A
  • Loading is the same sort of shape as an elastic band
  • The polythene strip suffers a lot of plastic deformation hence returns to a much longer extension when all the load is removed
52
Q

What are the units for Young’s Modulus?

A

Pascals, Pa

53
Q

What is one advantage of using a reference wire with a test wire in an experiment of measuring extension with a varying force applied?

A
  • Eliminates environmental changes e.g thermal expansion
  • Allows vernier scale
54
Q

Why is a reference load applied to the reference wire in the experiment of measuring extension with a varying force applied?

A

To keep the wire taut, in a straight line

55
Q

Why should the test wire be both long and thin in the experiment of measuring extension with a varying force applied?

A
  • For a given force applied you have an increased stress, therefore the wire would stretch further
  • Overall, the extension will be greater which means there will be a lower % uncertainty

Physics A - Level (23 decks)

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