Modelling in Mechanics

Question 1

What is the common model of a particle?

Answer 1

Dimensions of the object are negligible

Question 2

What is the common model of a rod?

Answer 2

All dimensions but one are negligible, like a pole or a beam

Question 3

What is the common model of a lamina?

Answer 3

Object with area but negligible thickness, like a sheet of paper

Question 4

What is the common model of a uniform body?

Answer 4

Mass is distributed evenly

Question 5

What is the common model of a light object?

Answer 5

Mass of the object is small compared to other masses, like a string or a pulley

Question 6

What is the common model of an inextensible string?

Answer 6

A string that does not stretch under load

Question 7

What is the common model of a wire?

Answer 7

Rigid thin length of metal

Question 8

What is the common model of a smooth and light pulley?

Answer 8

All pulleys you consider will be smooth and light

Question 9

What is the common model of a bead?

Answer 9

Particle with a hole in it for threading on a wire or string

Question 10

What is the common model of a peg?

Answer 10

A support from which a body can be suspended or rested

Question 11

What is the common model of air resistance?

Answer 11

Resistance experienced as an object moves through the air

Question 12

What is the common model of gravity?

Answer 12

Force of attraction between all objects (acceleration due to gravity = g)

Question 13

What are the modelling assumptions for particles?

Answer 13

• mass of the object is concentrated at a single point

* rotational forces and air resistance can be ignored

Question 14

What are the modelling assumptions for a rod?

Answer 14

• mass is concentrated along a line
• no thickness
• rigid (does not bend or buckle)

Question 15

What are the modelling assumptions for a lamina?

Answer 15

• mass is distributed across a flat surface

Question 16

What are the modelling assumptions for a uniform body?

Answer 16

• mass of the object is concentrated at a single point at the geometrical centre of the body - the centre of mass

Question 17

What are the modelling assumptions for a light object?

Answer 17

• treat object as having zero mass

* tension the same at both ends of a light string

Question 18

What are the modelling assumptions for an inextensible string?

Answer 18

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

Question 19

What are the modelling assumptions for a smooth surface?

Answer 19

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

Question 20

What are the modelling assumptions for a rough surface?

Answer 20

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

Question 21

What are the modelling assumptions for a wire?

Answer 21

• treated as one-dimensional

Question 22

What are the modelling assumptions for a smooth and light pulley?

Answer 22

• pulley has no mass

* tension is the same on either side of the pulley

Question 23

What are the modelling assumptions for a bead?

Answer 23

• moves freely along a wire of string

* tension is the same on either side of the bead

Question 24

What are the modelling assumptions for a peg?

Answer 24

• dimensionless and fixed

* can be rough or smooth as specified in question

Question 25

What are the modelling assumptions for air resistance?

Answer 25

• usually modelled as being negligible

Question 26

What are the modelling assumptions for gravity?

Answer 26

• assume that all objects with mass are attracted towards the earth
• earth’s gravity is uniform and acts vertically downwards
• g is constant and is taken as 9.8ms-2 unless otherwise stated