M1
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Modelling assumptions
In mechanics you MODEL real-life situations. The means that you make ASSUMPTIONS which
simplify your calculations. You need to understand the effects of different modelling assumptions.
Rods and moments
By modelling a plank or beam as a ROD you
can ignore its WIDTH.
If a rod is UNIFORM, the weight acts
at the MIDPOINT of the rod.
In a NON-UNIFORM rod, the weight does
not necessarily act at the midpoint.
R
You model objects on a rod as PARTICLES.
This means you can assume their WEIGHTS
act at a SINGLE POINT.
Supports are SMOOTH, so the moments
about that point are EQUAL if the rod is in
equilibrium.
W1
W2
rod only
An inextensible tow-bar, string or
ut the
abo
affects acceleration. Don’t talk
wer.
tension in the tow-bar in your ans
2.5 m s�2
The diagram shows a car pulling a caravan.
The car is attached to the caravan by a light,
inextensible tow-bar. The caravan and car
accelerate together at 2.5 m s−2. State how you
can use the assumption that the tow-bar is
inextensible.
(1 mark)
The caravan and car will have the same
acceleration.
Motion under gravity
When an object moves freely under gravity,
you ignore AIR RESISTANCE. This means the
acceleration is CONSTANT. You also model
objects as PARTICLES, so their weight acts at
a single point. In M1 questions, you are also
assuming that the motion is VERTICAL.
A block P of mass 0.8 kg is accelerating down
a smooth plane inclined at an angle 30° to the
horizontal. It is attached to a block Q of mass
0.1 kg by means of a light inextensible string
running over a smooth pulley. P and Q are
modelled as particles. State how you can use in
your calculations the modelling assumptions that:
2.5 m s�2
Pulleys and strings
Learn these three modelling facts for
questions involving pulleys.
The pulley is SMOOTH – the
magnitude of the TENSION in the
string will be the same on both sides
of the pulley.
The string is INEXTENSIBLE – the
magnitude of the ACCELERATION will
be the same for both particles.
The string is LIGHT – you can
IGNORE the WEIGHT of the string in
any calculations.
1
2
3
(a)
(b)
(c)
(d)
(e)
the plane is smooth
P and Q are modelled as particles
the string is inextensible
the string is light
the pulley is smooth.
(5 marks)
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