Mechanics - Models
Models
What is a model?
A model is a simplified representation of a physical situation, made by accepting assumptions.
What’s an example of a common assumption?
- No air resistance
- Constant gravity
- Uniform mass
What two questions need to be asked when setting up a mathematical model?
- What are your assumptions?
- What are the variables?
If the answer presented by a mathematical model is unreasonable, what should be done?
You should reconsider your assumptions.
Modelling Assumptions
When should a _ particle _ model be used?
When the dimensions of an object don’t matter.
What are the two modelling assumptions for a _ particle _ ?
- mass of the object is concentrated at a single point
- rotational forces and air resistance can be ignored
How is mass thought of in a _ particle _ model?
Concentrated at a single point.
Should air resistance be taken into account using a _ particle _ model?
No.
Should rotational forces be taken into account using a _ particle _ model?
No.
Should gravity be taken into account using a _ particle _ model?
Yes.
When should a _ rod _ model be used?
When all dimensions of an object except one don’t matter, like a pole or a beam.
What are the three modelling assumptions for a _ rod _ ?
- mass is concentrated along a line
- no thickness
- rigid (does not bend or buckle)
How is mass thought of in a _ rod _ model?
Concentrated along a line.
How is thickness thought considered in a _ rod _ model?
There is no thickness.
How is rigidity considered in a _ rod _ model?
The rod is completely rigid, it does not bend or buckle.
How many dimensions do you care about when using a rod?
1.
When should a _ lamina _ model be used?
When the object has a surface area, but negligible thickness, like a sheet of paper.
What is the modelling assumption for a _ lamina _ ?
- mass is distributed across a flat surface
How is mass thought of in a _ lamina _ model?
As distributed across a flat surfae.
When is an object said to be a _ uniform body _ ?
When the mass is distributed evenly.
How is mass considered in a _ uniform body _ ?
As concentrated at a single point at the geometrical centre of the body, the centre of mass.
In a _ uniform body _ , where is the centre of mass?
At the geometric centre of the body.
When is an object said to be a _ light object _ in mechanics?
When the mass of the object is small compared to the other masses, like a string or a pulley.
What modelling assumption can you make for a _ light object _ ?
That it has no mass.
When a string is a _ light object _ , what can be said about the tension along the string?
That it is the same at both ends of the string.
What is the _ inextensible string _ model?
A string that does not stretch under load.
What modelling assumption can be made for an _ inextensible string _ ?
Acceleration is the same in objects connected by a tight inextensible string.
What can be said about the acceleration for objects at the end of a tight inextensible string?
It is constant, i.e. they cannot stretch the string and slow down.
When should a _ smooth surface _ model be used?
When the surface in question is smooth, like ice.
What is the modelling assumption for a _ smooth surface _ ?
There is no friction between the surface and any objects on it.
When should a _ rough surface _ model be used?
When the surface is not smooth, like tarmac.
What modelling assumption do you make for a _ rough surface _ ?
Objects on the surface experiece friction when:
- They are moving
- They are being acted on by another force
When should a _ wire _ model be used?
To represent a rigid, thin length of metal.
What is the modelling assumption for a _ wire _ ?
The object is one dimensional.
In mechanics A-level, what assumption do we make about all pulleys?
That they are smooth and light.
What two modelling assumptions do you make for a _ smooth and light pulley _ ?
- Pulley has no mass
- Tension is the same on either side of the pulley
What is a _ bead _ model?
A particle with a hole in it for threading on a wire or a string.
What two modelling assumptions do you make for _ beads _ ?
- Moves freely along a wire or a string
- Tension is the same on either side of the bead
What is air resistance?
Friction or resistance experienced as an object moves through the air.
What usually occurs when modelling air resistance?
It is treated as negligible and not accounted for.
What is gravity?
A force of attraction between all objects.
What is the symbol for acceleration due to gravity?
$g$
What does the symbol $g$ mean in mechanics?
The acceleration due to gravity.
What is the value of $g$ in mechanics?
$9.8ms^{-2}$
What is the value of $g$ in physics?
$9.81ms^{-2}$
What two assumptions do we make about gravity in mechanics?
- Gravity is uniform across the Earth’s surface
- Gravity acts vertically downwards