A flat object of negligible thickness.

What is a rigid body?

An object of finite size that does not bend or change shape.

What does inextensible mean for a string?

It does not stretch, so its length is constant and connected particles have the same acceleration.

What follows from a string being light?

The tension is the same throughout the string.

What does a light smooth pulley imply?

The tension is the same on both sides of the pulley.

What force does a smooth surface exert?

Only a normal reaction, with no friction.

A particle with a hole through it that can slide on a wire or string.

A fixed support of negligible size.

Why does ignoring air resistance overestimate a ball's height?

Air resistance would add to the deceleration, so the ball would rise less far.

What is the modelling cycle?

Assume, solve, compare with data, then refine and repeat.

What is a non-uniform rod?

A rod whose mass is unevenly spread, so its weight does not act at the midpoint.

Mathematical modelling in mechanicsEdexcel International A Level Maths: Flashcards

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What is a particle in mechanics?

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What is a particle in mechanics?: An object with mass but no size; all of its mass is at one point.
What is a lamina?: A flat object of negligible thickness.
What is a rigid body?: An object of finite size that does not bend or change shape.
What is a light rod?: A rod with negligible mass.
Where does the weight of a uniform rod act?: At its midpoint.
What does inextensible mean for a string?: It does not stretch, so its length is constant and connected particles have the same acceleration.
What follows from a string being light?: The tension is the same throughout the string.
What does a light smooth pulley imply?: The tension is the same on both sides of the pulley.
What force does a smooth surface exert?: Only a normal reaction, with no friction.
What is a bead?: A particle with a hole through it that can slide on a wire or string.
What is a peg?: A fixed support of negligible size.
Why does ignoring air resistance overestimate a ball's height?: Air resistance would add to the deceleration, so the ball would rise less far.
What is the modelling cycle?: Assume, solve, compare with data, then refine and repeat.
What is a non-uniform rod?: A rod whose mass is unevenly spread, so its weight does not act at the midpoint.

Exam questions on Mathematical modelling in mechanics

A ball of mass 0.4 kg is thrown vertically upwards from ground level at 14 m s⁻¹. A student models the ball as a particle and ignores air resistance.
Explain why the model gives a maximum height that is greater than the true maximum height.2 marks
A crate is pulled across a horizontal floor by a rope attached to the front of the crate. The crate is modelled as a particle, the rope as a light inextensible string and the floor as smooth.
State what is assumed about the forces on the crate by modelling the floor as smooth, and state one way in which the real motion would differ from the model.2 marks
A uniform rod PQ has mass 8 kg and length 3 m. It is modelled as a rigid rod and is held horizontal by two vertical strings, one attached at each end. The strings are modelled as light and inextensible. Take g = 9.8 m s⁻².
Explain what is meant by modelling the rod as (i) uniform and (ii) rigid. State the distance from P at which the weight of the rod is assumed to act.3 marks

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Written by the Exaim team, led by Shaun Daswani (Head of Upper Secondary, Improve ME Institute; MSc Financial Mathematics, Imperial College London; BSc, UCL) and Jason Daswani (operational lead, Improve ME Institute; LSE).