Stats & Mechs - Chapter 8: Modelling Assumptions

Question 1

Particle Model

Answer 1

Dimensions of the object are negligible

Question 2

Particle Modelling Assumptions

Answer 2

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

Question 3

Rod Model

Answer 3

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

Question 4

Rod Model Assumptions

Answer 4

• Mass is concentrated along a line
• No thickness
• Rigid (doesn’t bend)

Question 5

Lamina Model

Answer 5

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

Question 6

Lamina Modelling Assumptions

Answer 6

• Mass is distributed across a flat surface

Question 7

Uniform Body Model

Answer 7

Mass is distributed evenly

Question 8

Uniform Body Model Assumptions

Answer 8

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

Question 9

Light object Model

Answer 9

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

Question 10

Light object Model Assumptions

Answer 10

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

Question 11

Inextensible string Model

Answer 11

A string that does not stretch under load

Question 12

Inextensible string Model Assumptions

Answer 12

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

Question 13

Smooth Surface Model Assumptions

Answer 13

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

Question 14

Rough Surface Model

Answer 14

If a surface is not smooth, it is rough

Question 15

Rough Surface Model Assumptions

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

Wire Model

Answer 16

Rigid thin length of metal

Question 17

Wire Model Assumptions

Answer 17

• Treated as one dimensional

Question 18

Smooth and light pulley Model

Answer 18

A pulleys you consider will be smooth and light

Question 19

Smooth and light pulley Model Assumptions

Answer 19

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

Question 20

Bead Model

Answer 20

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

Question 21

Bead Model Assumptions

Answer 21

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

Question 22

Peg Model

Answer 22

A support from which a body can be suspended or rested

Question 23

Peg Model Assumptions

Answer 23

• Dimensionless and fixed
• Can be rough or smooth as specified in question

Question 24

Air resistance Model

Answer 24

Resistance experienced as an object moves through the air

Question 25

Air resistance Model Assumptions

Answer 25

• Usually modelled as being negligible

Question 26

Gravity Model

Answer 26

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

Question 27

Gravity Model Assumptions

Answer 27

• 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 9.8 ms^-2, unless otherwise stated in the question