8. Modelling in Mechanics

Question 1

What is a particle?

Answer 1

Dimensions of the object are negligible

Question 2

What are the modelling assumptions of a particle?

Answer 2

Mass of the object is concentrated at a single point.
Rotational forces and air resistance can be ignored

Question 3

What is a rod?

Answer 3

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

Question 4

What are the modelling assumptions of a rod?

Answer 4

Mass is concentrated along a line.
No thickness.
Rigid (does not bend or buckle)

Question 5

What is a lamina?

Answer 5

An object with area, but negligible thickness, like a sheet of paper.

Question 6

What are the modelling assumptions of lamina?

Answer 6

Mass is distributed along a flat surface

Question 7

What is a uniform body?

Answer 7

Mass is distributed evenly

Question 8

What are the modelling assumptions of a uniform body?

Answer 8

Mass of object is concentrated at a single point at the geometrical centre of the body; its centre of mass

Question 9

What is a light object?

Answer 9

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

Question 10

What are the modelling assumptions of light objects?

Answer 10

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

Question 11

What is an inextensible string?

Answer 11

A string that does not stretch under load

Question 12

What are the modelling assumptions of an inextensible string?

Answer 12

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

Question 13

What are the modelling assumptions of a smooth surface?

Answer 13

Assume there is no friction between a surface and the objects on it

Question 14

What is a rough surface?

Answer 14

If a surface is not smooth, it is rough (duh)

Question 15

What are the modelling assumptions of a rough surface?

Answer 15

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

Question 16

What is a wire?

Answer 16

A rigid, thin length of metal

Question 17

What are the modelling assumptions of a wire?

Answer 17

It is treated as one dimensional

Question 18

What is a smooth and light pulley?

Answer 18

All pulleys you consider will be smooth and light (yay)

Question 19

What are the modelling assumptions of smooth and light pulleys?

Answer 19

Pulley has no mass.
Tension is the same either side of the pulley

Question 20

What is a bead?

Answer 20

A particle with a hole in it for threading on a wire or string

Question 21

What are the modelling assumptions of a bead?

Answer 21

Moves freely along a wire or string.
Tension is the same on either side of the bead.

Question 22

What is a peg?

Answer 22

A support from which a body can be suspended or rested

Question 23

What are the modelling assumptions of a peg?

Answer 23

Dimensionless and fixed.
Can be rough or smooth as specified.

Question 24

What is air resistance?

Answer 24

Resistance experienced as an object moves through air.

Question 25

What are the modelling assumptions of air resistance?

Answer 25

Usually modelled as negligible

Question 26

What is gravity?

Answer 26

A force of attraction between all objects. Acceleration due to gravity is denoted by g (9.8 ms^-2).

Question 27

What are the modelling assumptions of gravity?

Answer 27

Assume all objects with mass are attracted towards the Earth.
Earth’s gravity is uniform and acts vertically downwards.
g is constant and taken as 9.8 unless otherwise stated in question.