| Section
11.1
Mechanics |
| Syllabus
Details |
References
|
You
should be able to: |
| 11.1.1
|
Scalars
and vectors
The addition
and subtraction of vectors by calculation or scale drawing;
calculations limited to two perpendicular vectors
The resolution
of vectors into two components at right angles to each other
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|
- distinguish between scalar and vector quantities and know
which category each physical quantity falls into.
- resolve a vector into horizontal and vertical components.
- see this java
applet for addition of vectors
- see this java
applet for velocity vectors
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| 11.1.2 |
Conditions
for equilibrium for two or three coplanar forces acting at a
point
Problems
may be solved either by using resolved forces or by using a
closed triangle
|
Ciccotti
and Kelly pp 98-107
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- resolve the force vectors into their components and show
that for equilibrium the sum of the horizontal forces is zero
and the sum of the vertical forces is zero.
- see java
applet for three forces in equilibrium
- solve
problems that require you to find a resultant or equilibriant
force by a scale drawing and/or calculation method
|
| 11.1.3 |
Turning
effects
Moment of
a force,
couple,
torque
The principle
of moments and its applications in simple balanced situations
e.g. seesaw.
The centre
of gravity; calculations of the position of centre of gravity
of a regular lamina are not expected.
|
Ciccotti
and Kelly pp 108-111
|
- recall
that a torque produces angular acceleration. It is the rotational
equivalent of a force. It is another term for 'moment'
- see java
applet
- define the moment of a force as the product of the force
and the perpendicular distance from the turning point.
- define a couple as the turning effect of two equal and opposite
forces. It's size being the product of one of the two identical
forces and the perpendicular distance between them
- recall that the principle of moments states that the sum
of the clockwise moments is equal to the sum of the anticlockwise
moments in a body at equilibrium.
- recall that the centre of gravity of a body is the point
through which the weight can be taken as acting. It is the
point around which the moments due to the weight of component
parts of the body are at equilibrium. The body therefore 'balances'
if supported under the centre of gravity.
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| 11.1.4 |
Displacement,
speed, velocity and acceleration
 
|
GCSE!
|
- recall and use the equations
- distinguish between speed and velocity
- distinguish between displacement and distance
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| 11.1.5 |
Uniform
and non-uniform acceleration, representation and interpretation
by graphical methods
Interpretation
of velocity-time and displacement-time graphs for motion with
non-uniform acceleration and uniform acceleration; significance
of areas and gradients
Equations
for uniform acceleration
Acceleration due to gravity g, terminal speed; detailed experimental
methods of measuring g are not required
|
Ciccotti
and Kelly pp 113-116
|
- plot and interpret displacement/time graphs.
- know that the gradient of the displacement/time graph is
the velocity
- plot and interpret velocity/time graphs.
- Know that the gradient of the velocity/time graph is the
acceleration
- know that the area under the velocity/time graph is the
distance travelled.
- see the java
applet demonstrating the motion of a car expressed in
terms of acceleration, velocity and displacement to time graphs
- understand that the four equations of motion are obtained
from the straight line velocity time graph (in other words
CONSTANT ACCELERATION). They can therefore only be used in
such a condition - e.g.. when a constant force is acting -
like an object falling under gravity, or a charge in a constant
electric field. (You should always state what constant force
is enabling you to use these equations before you do the calculation!)
- appreciation that as an object falls under gravity in the
atmosphere a counterforce due to air resistance will increase
with its speed. Therefore the net force acting on the body
will decrease until at terminal velocity there is no net force
and the object will therefore no longer accelerate.
- explain the falling of a parachutist and plot the graph
of his velocity against time and displacement against time.
|
| 11.1.6 |
Independence
of vertical and horizontal motion (calculations involving projectile
equations will not be set)
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|
- a projectile's
motion can be thought of as having two components. (resolving
the vector of velocity)
- for a falling body the vertical component of its velocity
is subject to acceleration due to gravity. It will therefore
change as time goes on.
- for a
falling body the horizontal component of its velocity is NOT
subject to gravity therefore it will be constant
- see Java
Applet 1
- see Java
Applet 2 (fire a cannon at different angles and watch
its path)
|
| 11.1.7 |
Momentum,
conservation of linear momentum
Recall and
use of p = mv
Conservation
calculations for elastic and inelastic collisions limited to
one dimension
Candidates
should have experience of analysing motion using datalogging
techniques involving data capture with appropriate sensors e.g.
light gates
Candidates
will require understanding of the application of the principles
of the conservation of linear momentum e.g. space vehicles
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|
- that there are two factors that have to be taken into consideration
when calculating the force needed to stop a moving body in
a given time - its velocity and its mass. These factors are
combined into one called its momentum. The force required
is directly proportional to each of these factors - double
one and halve the other and you need the same force!
- Momentum is a vector (because it is the product of velocity
(a vector) and mass (a scalar)) so it should have a sign indicating
direction! (you can choose - and should therefore state -
which direction on your page is positive!)
- The unit of momentum is kg m/s = Ns (the board like you
to use the latter!)
- If you add up (algebraically - taking into account the signs
due to direction!) the momentum of a set of bodies at any
point in time along a particular plane they will be constant.
So the momentum total in a straight line before a collision
will be the same as the momentum total in that same straight
line after the collision - as long as no external force is
operating along that line. This is termed the Law of Conservation
of Momentum.
- quote the Law of Conservation of Momentum as ' the total
linear momentum of a system of interacting bodies on which
no external forces are acting remains constant.'
- solve simple problems involving the Law of Conservation
of Momentum and understand how the principles apply to everyday
examples such as collisions, driving of space vehicles and
thruster packs for space men.
- an elastic collision is one in which the total kinetic energy
of the bodies before the collision is equal to the sum of
the kinetic energies after the collision - kinetic energy
is conserved in an elastic collision. This is the said to
be the case when gas molecules and some subatomic particles
collide as there is virtually no change in potential energy
of the colliding bodies.
- an inelastic collision occurs when the kinetic energy is
NOT conserved. This is the case in most large scale collisions.
- See Java
Applet
|
| 11.1.8 |
Newton's
laws of motion
Candidates
are expected to know and to be able to apply the three laws
in appropriate situations
Force as
the rate of change of momentum
For constant
mass: F = ma
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|
quote the
three Newton's laws of motion (knowing which is which!):
- Every
body continues in its state of rest or uniform motion unless
acted upon by an external force.
- The
rate of change of momentum of a body is directly proportional
to the external force acting upon that body and takes place
in the direction of the force. - this one is summarized
in the equation, but should never be 'quoted' in that form!
See Java
applet of an experiment to illustrate this
- If
a body A exerts a force on body B called the action force
then body B exerts an equal and opposite force on body A
called the reaction force. (Sometimes quoted and misunderstood
as 'to every action there is an equal and opposite reaction'
- use the above definition instead!)
- The equation
from N(II)
can be changed into the form F=ma is mass is a constant value.
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| 11.1.9
|
Work, energy,
power
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|
- work done is force applied multiplied by the distance moved
(as long as the force is applied in the same direction as
the movement direction produced). the cos factor takes that
into consideration
- define work done as product of the displacement of the body
and the co-linear component of the force applied to make it
move. (s - is displacement! - q
is the angle between the force and the direction of movement
- Power is work done over time taken - the rate of doing work
so P=Fv from the equation above!
|
| 11.1.10 |
Conservation
of energy
Application
of the principle of the conservation of energy to determine
whether a collision is elastic or inelastic. Application of
the conservation of energy to examples involving gravitational
potential energy and kinetic energy
Recall and use of
Recall and use of
|
Ciccotti
and Kelly pp 126-129
|
- You should learn the equations - you won't be given them!
- The Principle of Conservation of energy states that energy
is neither created nor destroyed, it merely changes from one
form into another.
- The total Ek and Ep of a system involving
objects moving under gravity is the same at any point in time.
- The kinetic energy at the top of an object's path is zero
so the total energy is in the form of gravitational potential
energy whereas when it hits the floor the total Ep is
zero and all of the energy is in the form of kinetic (this
ignores friction with air particles causing energy loss out
of the system as heat!). So we can say that Ek
on the ground = Ep at the top of the path.
- You should be able to do calculations involving the above
idea.
|
| 11.1.11 |
Calculations involving change of energy
DQ = mcDq
where m is the mass of the substance, c is its specific heat capacity
and Dq is the change in temperature
DQ = ml where l is specific latent
heat and m is the mass of substance changing state.
|
Ciccotti
and Kelly pp 131-137
|
- internal
energy (sometimes called the random thermal energy) of a substance
is the sum of kinetic energy and potential energy. Potential
energy is due to the interaction of neighbouring particles,
this is therefore very significant in solids and liquids but
less so in gases. Kinetic energy is due to the movement of
the particles in the substance.
- You should be able to define the specific heat capacity
of a substance as being the quantity of energy required to
raise the temperature of 1kg of the substance by 1K.
- You should realize that the biggest changes in temperature
of a given mass of a substance will occur in those that have
low specific heat capacities - because it doesn't take much
energy for them to get hotter!
- You should be able to define specific latent heat as the
energy required to change the state of 1 kg of the substance.
- You should be able to understand what is happening to the
particles in a substance when heat is added to it or taken
away
- if the substance is remote from its melting or boiling
point it will change temperature (getting hotter or colder)
as the particles vibrate faster or slower on absorbing
the heat energy - the kinetic energy component changes
significantly the potential energy component is virtually
the same..
- the amount of heat energy required to make a temperature
change of 1K will depend on the mass of the substance
(the more you have the more energy you will need, natch!)
and what it is - some structures react to heat input more
dramatically than others (this is indicated in the SHC
'c' of the substance) - low 'c' substances have particles
that are easier to 'vibrate'!
- if the substance is at its boiling/melting point the
energy given/taken away will not be used to get hotter
or colder. It will be used to change state. If absorbed
(given to the substance) it will not make the particles
vibrate any faster, but will make them freer from each
other. If being taken away, again it will not change the
vibration of the particles but rather will make them more
structured - less free - and change their state to do
that. So when latent heat is involved we are looking at
the change of potential energy not kinetic energy.
- You should be able to do calculations involving heat being
given and/or taken away.
- Remember to add up all of the components that have been
'given energy' and all of those that have 'given energy away'
and equate them in an exchange of heat problem.
|
| Section
11.2 - Molecular kinetic
theory model |
| 11.2.1 |
The equation
of state for an ideal gas
Recall and
use of pV = nRT
Where p
is the pressure of the gas
V is the
volume
n is the
number of moles
T is the
absolute temperature
R is the
molar gas constant (on data sheet)
|
Ciccotti
and Kelly pp 141-142, 144- 149
|
- recall the properties of an ideal gas
- know that the nearest we have to an ideal gas is helium
remote from its boiling point and at low pressure.
- recall and use the equation to do calculations
- know that T must be in Kelvin!
- know that a mole is the Avogadro number of particles
- be able to sketch graphs of p against V, p against T, V
against T
|
| 11.2.2 |
The molar gas constant R
The Avogadro
constant NA
Concept
of absolute zero of temperature
T (in kelvin)
is proportional to the average kinetic energy of molecules for
an ideal gas
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- know that NA is the number of particles in a
mole of gas
- appreciate where the figure of -273oC becoming
0K comes from (extrapolation of p/T and V/T graphs)
- understand how temperature of particles relates to their
kinetic energy and mean square speed (Lowe and Rounce is excellent
for this!)
|
| 11.2.3 |
Pressure
of an ideal gas
Assumptions
leading to and derivation of
|
Ciccotti
and Kelly pp 142-143
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- you have very few derivations to learn! Make sure you know
this one well! You must learn the assumptions too and use
words to explain how to derive it!
|
| 11.2.4 |
Internal
energy
Relation
between temperature and molecular kinetic energy.
The Boltzmann
constant
Random distribution
of energy amongst particles in a body
Thermal
equilibrium
|
Ciccotti
and Kelly pp 142- 144
|
- internal energy of an ideal gas is only kinetic - it has
(by definition no potential energy!)!
- internal energy (sometimes called the random thermal energy)
of a gas is the sum of kinetic energy and potential energy
but the potential energy is so tiny that it can often be ignored.
Potential energy is due to the interaction of neighbouring
particles, this is therefore very significant in solids and
liquids
- average molecular kinetic energy for a gas sample is directly
proportional to absolute temperature in an ideal gas. (sketch
the graph from the equation!)
- the Boltzmann constant k is simply R/NA
- the equation opposite is for a single average molecule (to
find the total energy for a gas sample you would have to multiply
by nNA)
- thermal equilibrium occurs when there is no net flow of
heat energy between two bodies - they are at the same temperature
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Recommended Background Reading 
