Modelling in mechanics Worked Solutions — A-Level Maths

Fully worked, step-by-step solutions to A-Level Modelling in mechanics questions. See exactly how to solve problems on modelling, particle, light-string, inextensible.

modellingparticlelight-stringinextensiblesmoothuniform-rod
A-Level70 questionsStep-by-step solutions
Question 1
2 markseasy
In mechanics modelling, what does the assumption of a particle mean?

Worked solution

  1. Recall the modelling term

    particle

    This is a standard assumption in A-Level mechanics.

  2. State what may be ignored

    The object has no rotational effects and all its mass acts at a single point.

    The assumption simplifies the model by ignoring a complicating effect.

  3. Select the correct meaning

    The object has no rotational effects and all its mass acts at a single point.

    This is the standard interpretation.

Answer
The object has no rotational effects and all its mass acts at a single point.
Question 2
2 markseasy
In mechanics modelling, what does the assumption of a light string mean?

Worked solution

  1. Recall the modelling term

    light string

    This is a standard assumption in A-Level mechanics.

  2. State what may be ignored

    The string has negligible mass, so its weight does not affect the tension.

    The assumption simplifies the model by ignoring a complicating effect.

  3. Select the correct meaning

    The string has negligible mass, so its weight does not affect the tension.

    This is the standard interpretation.

Answer
The string has negligible mass, so its weight does not affect the tension.
Question 3
2 markseasy
In mechanics modelling, what does the assumption of a inextensible mean?

Worked solution

  1. Recall the modelling term

    inextensible

    This is a standard assumption in A-Level mechanics.

  2. State what may be ignored

    The string does not stretch, so connected particles share the same speed.

    The assumption simplifies the model by ignoring a complicating effect.

  3. Select the correct meaning

    The string does not stretch, so connected particles share the same speed.

    This is the standard interpretation.

Answer
The string does not stretch, so connected particles share the same speed.
Question 4
2 markseasy
In mechanics modelling, what does the assumption of a smooth mean?

Worked solution

  1. Recall the modelling term

    smooth

    This is a standard assumption in A-Level mechanics.

  2. State what may be ignored

    There is no friction, so no frictional force opposes motion.

    The assumption simplifies the model by ignoring a complicating effect.

  3. Select the correct meaning

    There is no friction, so no frictional force opposes motion.

    This is the standard interpretation.

Answer
There is no friction, so no frictional force opposes motion.
Question 5
2 markseasy
In mechanics modelling, what does the assumption of a uniform rod mean?

Worked solution

  1. Recall the modelling term

    uniform rod

    This is a standard assumption in A-Level mechanics.

  2. State what may be ignored

    The mass is distributed evenly along the rod, so its weight acts at the midpoint.

    The assumption simplifies the model by ignoring a complicating effect.

  3. Select the correct meaning

    The mass is distributed evenly along the rod, so its weight acts at the midpoint.

    This is the standard interpretation.

Answer
The mass is distributed evenly along the rod, so its weight acts at the midpoint.

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