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Pearson Edexcel IAL Mathematics M1.4.2 Simple applications

Practise connected-particle models with strings, pulleys, planes and friction, linking equations of motion to tension, acceleration and constraints.

Syllabus
First assessment 2019
Course
Mathematics YMA01
Level
AS

Exam points

  • write separate equations of motion for connected particles using the correct mass each time
  • apply the inextensible-string condition to use the same acceleration in both equations
  • resolve on rough planes or tables to find tension, µ, or a pulley force from 2T geometry

M1.4.2 - Simple applications question 1

[Maximum number: 2]
Figure 3

Figure 3

A particle A of mass 4 kg is held at rest on a rough horizontal table. Particle A is attached to one end of a string that passes over a pulley P. The pulley is fixed the the of the table. The other end of the string is attached to a particle B, of mass 3 kg, which hangs freely below P.

The part of the string from A to P is perpendicular to the edge of the table and A, P and B all lie in the same vertical plane.

The string is modelled as being light and inextensible and the pulley is modelled as being small, smooth and light.

The system is released from rest with the string taut. At the instant of release, A is 2 m from the edge of the table and B is 1.4 m above a horizontal floor, as shown in Figure 3.

After descending with constant acceleration for 2 seconds, B hits the floor and does not rebound.

Show that the acceleration of A before B hits the floor is 0.7 m s−20.7 \mathrm{~m} \mathrm{~s}^{-2}

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