M - Statistics & Mechanics 1 - 8) Modelling in mechanics

Question 1

Meaning and modelling assumptions of a particle

Answer 1

• Meaning: dimensions of the object are negligible

Modelling assumptions:

• Mass of the object is concentrated at a single point
• Rotational forces and air resistance are ignored

Question 2

Meaning and modelling assumptions of a rod

Answer 2

• Meaning: all dimensions except one are negligible, like a pole or beam

Modelling assumptions:

• Mass is concentrated along a line
• No thickness
• Rigid (no bend or buckle)

Question 3

Meaning and modelling assumption of lamina

Answer 3

• Meaning: object with area but negligible thickness, like a sheet of paper

Modelling assumption:

• Mass is distributed across a flat surface

Question 4

Meaning and modelling assumption of a uniform body

Answer 4

• Meaning: mass is distributed evenly

Modelling assumption:

• Mass of the object is concentrated at a single point at the geometrical centre of the body (centre of mass)

Question 5

Meaning and modelling assumptions of a light object

Answer 5

• Meaning: mass of the object is small compared to other masses, like a string or pulley

Modelling assumptions:

• Treat object as having zero mass
• Tension is the same at both ends of a light string

Question 6

Meaning and modelling assumption of an inextensible string

Answer 6

• Meaning: string that doesn’t stretch under load

Modelling assumption:

• Acceleration is the same in objects connected by a taut inextensible string

Question 7

Meaning and modelling assumption of a smooth surface

Answer 7

• Meaning: surface that is smooth

Modelling assumption:

• Assume that there is no friction between the surface and any object on it

Question 8

Meaning and modelling assumption of a rough surface

Answer 8

• Meaning: if a surface is not smooth, then it’s rough

Modelling assumption:

• Objects in contact with the surface experience a frictional force if they are moving or are acted on by a force

Question 9

Meaning and modelling assumption of a wire

Answer 9

• Meaning: rigid, thin length of metal

Modelling assumption:

• Treated as one-dimensional

Question 10

Meaning and modelling assumptions of a smooth and light pulley

Answer 10

• Meaning: all pulleys will be smooth and light

Modelling assumptions:

• Pulley has no mass
• Tension is the same on both sides of the pulley

Question 11

Meaning and modelling assumptions of a bead

Answer 11

• Meaning: particle with a hole in it for threading on a wire or string

Modelling assumptions:

• Moves freely along a wire or string
• Tension is the same on both sides of the bead

Question 12

Meaning and modelling assumptions of a peg

Answer 12

• Meaning: a support from which a body can be suspended or rested

Modelling assumptions:

• Dimensionless and fixed
• Can be rough or smooth

Question 13

Meaning and modelling assumption of air resistance

Answer 13

• Meaning: resistance experienced as an object moves through the air

Modelling assumptions:

• Modelled as being negligible

Question 14

Meaning and modelling assumptions of gravity

Answer 14

• Meaning: force of attraction between all objects

Modelling assumptions:

• Assume that all objects with mass are attracted towards the Earth
• Earth’s gravity is uniform and acts vertically downwards
• Gravity is constant and is taken as 9.8 m/s²

Question 15

Examples of forces in a force diagram

Answer 15

• Weight
• Normal reaction
• Friction
• Tension
• Thrust or compression
• Buoyancy
• Air resistance