Mathematical modelling in mechanicsEdexcel International A Level Maths: Mind map

Exam questions on Mathematical modelling in mechanics

1. 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
2. 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
3. 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