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Edexcel A-Level Mathematics AS M1.1 Mathematical Models in Mechanics Questions

Practise explaining how mechanics models use assumptions about particles, rods, light strings and resistance to turn physical situations into solvable problems.

Syllabus
First assessment 2019
Course
Mathematics YMA01
Level
AS

Exam points

  • state modelling assumptions such as smooth surfaces, particles or light strings from the context
  • suggest realistic refinements and explain how they change forces, motion or calculations

Covered syllabus points

M1.1.1 - Basic ideas of mathematical

Question 1

[Maximum number: 1]
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.

State which of the modelling assumptions you have used in order to answer part (a).

Question 2

[Maximum number: 1]
Figure 4

Figure 4

A particle P of mass 4 m lies on the surface of a fixed rough inclined plane.
The plane is inclined to the horizontal at an angle α\alpha where tan⁡α=34\tan \alpha=\frac{3}{4}
The particle P is attached to one end of a light inextensible string.
The string passes over a small smooth pulley that is fixed at the top of the plane. The other end of the string is attached to a particle Q of mass m which lies on a smooth horizontal plane.

The string lies along the horizontal plane and in the vertical plane that contains the pulley and a line of greatest slope of the inclined plane.

The system is released from rest with the string taut, as shown in Figure 4, and P moves down the plane.

The coefficient of friction between P and the plane is 14\frac{1}{4}
For the motion before Q reaches the pulley

State where in your working you have used the information that the string is light.

Question 3

[Maximum number: 1]
Figure 4

Figure 4

One end of a light inextensible string is attached to a particle A of mass 2 m. The other end of the string is attached to a particle B of mass 3 m. The string passes over a small, smooth, light pulley P which is fixed at the top of a rough inclined plane. The plane is inclined to the horizontal at an angle α\alpha, where tan⁡α=34\tan \alpha=\frac{3}{4}

Particle A is held at rest on the plane with the string taut and B hanging freely below P, as shown in Figure 4. The section of the string AP is parallel to a line of greatest slope of the plane.

The coefficient of friction between A and the plane is 12\frac{1}{2}
Particle A is released and begins to move up the plane.
For the motion before A reaches the pulley,

State how you have used the information that P is a smooth pulley.

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