Modelling in Mechanics - Maths Edexcel A-Level

Particle

• Used if the dimensions of an object are negligable

• Assumes the mass of the object is concentrated at a single point

• Ignores rotational forces

• Assumes object has negligable mass

• Ignores air resistance

Rod

• Used if all dimensions but one are negligible

• Assumes mass is concentrated along a line

• Assumes object has no thickness

• Assumes object is rigid (will not bend/buckle)

• Assumes mass is concentrated at a single point in the geometrical centre of the body

Lamina

• Used for an object with area but negligible mass

• Assumes mass is distributed across a flat surface

• Assumes object is rigid (will not bend/buckle)

• Assumes mass is concentrated at a single point in the geometrical centre of the body

Uniform body

• Used if mass is distributed evenly

• Assumes mass ins concentrated at a single point in the geometrical centre of the body

• Assumes there is no friction

• Used if object is rigid and thin

Light object

• Used if the mass of the object is small compared to other masses

• Treats the object as having zero mass

• Assumes the tension is the same at both ends of a light string

• Used for a string that does not stretch under load

• Assumes mass is focused in the geometrical centre of the object

Inextensible string

• Used for a string that does not stretch under load

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

• Assumes tension is the same at both ends of a light string

• Used for a rigid, thin length of metal

Smooth surface

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

• Assumes any objects in contact with it experience a uniform frictional force

• Assumes it has no mass

Rough Surface

• Used for smooth surfaces

• Used for any surfaces that are not smooth

• Assumes any objects in contact with the surface experience a frictional force if they are moving and acted upon by a force

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

Wire

• Used for a rigid, thin length of metal

• Treats the object as one-dimentional

• Used for a particle with a hole in it for threading a wire or string

• Assumes there is no friction between this and the bead

Smooth and light pulley

• Used for all pulleys

• Assumes pulley has no mass

• Assumes tension is the same on either side of the pulley

• Assumes tension on the side of the pulley closer to the heavier mass = 2T