Modelling in mechanics

Question 1

Define + Assumptions: Particle

Answer 1

-Dimensions of the object are negligible

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

Question 2

Define + Assumptions: Rod

Answer 2

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

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

Question 3

Define + Assumptions: Lamina

Answer 3

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

1. Mass is distributed across a flat surface

Question 4

Define + Assumptions: Uniform Body

Answer 4

-Mass is distributed evenly

1. Mass of the object is concentrated at a single point at the geometrical centre of the body, the centre of mass

Question 5

Define + Assumptions: Light object

Answer 5

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

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

Question 6

Define + Assumptions: Inextensible string

Answer 6

-String that does not stretch under load

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

Question 7

Define + Assumptions: Smooth Surface

Answer 7

1. Assume there is no friction between the surface and any object on it

Question 8

Define + Assumptions: Rough Surface

Answer 8

-If a surface is not smooth it is rough by default

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

Question 9

Define + Assumptions: Wire

Answer 9

-Rigid thin length of metal

1. Treated as one-dimensional

Question 10

Define + Assumptions: Smooth and light pulley

Answer 10

-All pulleys you consider will be smooth and light

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

Question 11

Define + Assumptions: Bead

Answer 11

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

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

Question 12

Define + Assumptions: Peg

Answer 12

-A support from which a body can be suspended or rested

1. Dimensionless and fixed
2. Can be rough or smooth as specified in question

Question 13

Define + Assumptions: Air resistance

Answer 13

-Resistance experienced as an object moves through the air

1. Usually modelled as being negligible

Question 14

Define + Assumptions: Gravity

Answer 14

-Force of attraction between all objects. Acceleration due to gravity is denoted by g

1. Assume that all objects with mass are attracted towards the Earth
2. Earth’s gravity is uniform and acts vertically downwards
3. g is constant and is taken as 9.8m/s^2, unless otherwise stated in the question