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Had a look Nearly there Nailed it!M1

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W1 W2

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.

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.

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.

Motion under gravityWhen 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.

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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:

(a) the plane is smooth

(b) P and Q are modelled as particles(c) the string is inextensible

(d) the string is light(e) the pulley is smooth. (5 marks)

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.

Pulleys and stringsLearn these three modelling facts for questions involving pulleys.

1 The pulley is SMOOTH – the

magnitude of the TENSION in the string will be the same on both sides of the pulley.

2 The string is INEXTENSIBLE – the

magnitude of the ACCELERATION will be the same for both particles.

3 The string is LIGHT – you can

IGNORE the WEIGHT of the string in any calculations.

An inextensible tow-bar, string or rod only

affects acceleration. Don’t talk about the

tension in the tow-bar in your answer.

2.5 m s�2 2.5 m s�2

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