Mechanics - Modelling in Mechanics

Question 1

What is the “particle” model and the modelling assumptions?

Answer 1

Particle - Dimensions of the object are negligible.

Modelling Assumptions:

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

Question 2

What is the “rod” model and the modelling assumptions?

Answer 2

Rod - All dimensions but one (length) are negligible, like a pole or a beam.

Modelling Assumptions:

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

Question 3

What is the “lamina” model and the modelling assumptions?

Answer 3

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

Modelling Assumptions:
- mass is distributed across a flat surface

Question 4

What is the “uniform body” model and the modelling assumptions?

Answer 4

Uniform Body - Mass is distributed evenly.

Modelling Assumptions:
- mass of the object is concentrated at a single point at the geometrical centre of the body - the centre of mass

Question 5

What is the “light object” model and the modelling assumptions?

Answer 5

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

Modelling Assumptions:

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

Question 6

What is the “inextensible string” model and the modelling assumptions?

Answer 6

Inextensible String - A string that does not stretch under load.

Modelling Assumptions:
- acceleration is the same in objects connected by a taut inextensible string

Question 7

What is the “smooth surface” model and the modelling assumptions?

Answer 7

Smooth Surface - The surface is completely flat/smooth.

Modelling Assumptions:
- assume that there is no friction between the surface and any object on it

Question 8

What is the “rough surface” model and the modelling assumptions?

Answer 8

Rough Surface - If a surface is not smooth, it is rough.

Modelling Assumptions:
- objects in contact with the surface experience a frictional force if they are moving or are acted on by a force

Question 9

What is the “wire” model and the modelling assumptions?

Answer 9

Wire - Rigid thin length of metal.

Modelling Assumptions:
- treated as one-dimensional

Question 10

What is the “smooth and light pulley” model and the modelling assumptions?

Answer 10

Smooth and Light Pulley - All pulleys you consider will be smooth and light.

Modelling Assumptions:

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

Question 11

What is the “bead” model and the modelling assumptions?

Answer 11

Bead - 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 either side of the bead

Question 12

What is the “peg” model and the modelling assumptions?

Answer 12

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

Modelling Assumptions:

• dimensionless and fixed
• can be rough or smooth as specified in question

Question 13

What is the “air resistance” model and the modelling assumptions?

Answer 13

Air Resistance - Resistance experienced as an object moves through the air.

Modelling Assumptions:
- usually modelled as being negligible

Question 14

What is the “gravity” model and the modelling assumptions?

Answer 14

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

Modelling Assumptions:

• 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 in the question

Question 15

What is the weight?

Answer 15

The weight (or gravitational force) of an object acts vertically downwards.

Question 16

What is the normal reaction?

Answer 16

The normal reaction is the force which acts perpendicular to a surface when an object is in contact with the surface.

Question 17

What is the friction?

Answer 17

The friction is a force which opposes the motion between two rough surfaces.

Question 18

What is the tension?

Answer 18

If an object is being pulled along by a string, the force acting on the object is called the tension in the string.

Question 19

What is the thrust or compression?

Answer 19

If an object is being pushed along using a light rod, the force acting on the object is called the thrust or compression in the rod.

Question 20

What is buoyancy?

Answer 20

Buoyancy is the upward force on a body that allows it to float or rise when submerged in a liquid.

Question 21

What is air resistance?

Answer 21

Air resistance opposes motion.

Question 22

What is a vector quantity?

Answer 22

A vector is a quantity which has both magnitude and direction.

Question 23

What are examples of vector quantities?

Answer 23

• displacement: distance in a particular direction
• velocity: rate of change in displacement
• acceleration: rate of change of velocity
• force/weight: described by magnitude, direction and point of application

Question 24

What is a scalar quantity?

Answer 24

A scalar quantity has magnitude only,

Question 25

What are examples of scalar quantities?

Answer 25

• distance: measure of length
• speed: measure of how quickly a body moves
• time: measure of ongoing events taking place
• mass: measure of the quantity of matter contained in an object

Question 26

Are vector and scalar quantities positive or negative?

Answer 26

Scalar quantities are always positive. When considering motion in a straight line (1-dimensional motion), vector quantities can be positive or negative.

Question 27

What is distance?

Answer 27

Distance is the magnitude of the displacement vector.

Question 28

What is speed?

Answer 28

Speed is the magnitude of the velocity vector.