Maths - Mechanics

s meaning and unit

The displacement of an object from a given point (metres)

t meaning and unit

The time taken (seconds)

Velocity

The rate of change in displacement

2 features of a displacement-time graph

1. x-axis: time, y-axis: displacement
2. Gradient = velocity

Average velocity =

displacement/time

What does it mean if a graph is a straight line?

The gradient (e.g. velocity for displacement-time graph) is constant

Average speed =

total distance/time

What does it mean if a displacement-time graph is a curved line?

The velocity is changing and the object is accelerating

2 features of a velocity-time graph

1. x-axis: time, y-axis: velocity
2. Gradient = acceleration

v meaning and unit

The velocity of an object (metres per second)

Acceleration

The rate of change in velocity

What does the area between a velocity and time graph and the horizontal axis represent?

The distance travelled

u symbol meaning

Initial velocity

v symbol meaning

Final velocity

a symbol meaning

Acceleration

5 SUVAT formulae

1. From gradient of graph: v = u + at
2. From area under graph: s = (u+v)/2 * t
3. From eliminating t from formula 1: v^2 = u^2 + 2as
4. From eliminating v from formula 1: s = ut + 1/2 * at^2
5. From eliminating u from formula 1: s = vt - 1/2 at^2

What is the acceleration due to gravity and its symbol?

9.8 ms^-2 downwards (symbol = g)

Time of flight

The total time that an object is in motion from the time it is projected upwards to the time it hits the ground

Speed of projection

The initial speed when an object is projected upwards

Force diagram

A diagram showing all the forces acting on an object

How do you represent forces on a force diagram

As an arrow pointing in the direction in which the force acts

When is an object in equilibrium?

When the forces acting upon it are balanced

Newton's first law of motion

An object at rest will stay at rest and that an object moving with constant velocity will continue to move with constant velocity unless an unbalanced force acts on the object.

R(arrow) meaning

The direction where you are resolving the forces - the direction you resolve in becomes the positive direction so add forces in this direction and subtract forces in the opposite direction

What is the effect of a resultant force acting on an object?

It will cause the object to accelerate in the same direction as the resultant force

i-j notation with vectors

i = horizontal, j = vertical
As column vectors, they are (i j)

Newton's second law of motion

The force needed to accelerate a particle is equal to the product of the mass of the particle and the acceleration produced (F = ma)

Gravity

The force between any object and the earth

Weight

The force due to gravity acting on an object

Equation of motion for a body of mass 'm' kg

F = ma

How does tension act?

It pulls out (away from particles)

How does thrust act?

It pulls in (towards particles)

Particle

Dimensions of the object are negligible

Particle modelling assumptions (2)

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

Rod

All dimensions but one are negligible (e.g. a pole / beam)

Rod modelling assumptions (3)

- Mass is concentrated along a line
- No thickness
- Rigid (doesn't bend/buckle)

Lamina

Object with area but negligible thickness (e.g. a sheet of paper)

Lamina modelling assumptions (1)

- Mass is distributed across a flat surface

Uniform body

Mass is distributed evenly

Uniform body modelling assumption (1)

Mass of object is concentrated at a single point at the geometrical centre of the body (the centre of mass)

Light object

Mass of the object is small compared to other masses (e.g. a string / pulley)

Light object modelling assumptions (2)

- Treat object as having 0 mass
- Tension the same at both ends of a light string

Inextensible string

A string that does not stretch under load

Inextensible string modelling assumption

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

Smooth surface modelling assumption

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

Rough surface modelling assumption

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

Wire

Rigid, thin length of metal

Smooth and light pulley modelling assumptions (2)

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

Bead

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

Bead modelling assumptions (2)

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

Peg

A support from which a body can be suspended or rested

Peg modelling assumptions (2)

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

Air resistance

Resistance experienced as an object moves through the air (it opposes motion)

Air resistance modelling assumption

Usually modelled as being negligible

Gravity modelling assumptions (3)

- 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

Normal reaction

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

Friction

A force which opposes the motion between two rough surfaces

Tension

The forcing acting on an object when it is being pulled along by a string

Thrust

The force acting on an object when it is being pushed by a light rod

Compression

The force acting on a light rod when it pushes an object

Buoyancy

The upward force on a body that allows it to float or rise when submerged in a liquid

What does it mean if the gradient of a velocity-time graph is:
1. increasing
2. decreasing
3. 0 (i.e. a stationary point)?

1. The object is accelerating
2. The object is decelerating
3. The acceleration is 0

Instead of using one of the SUVAT formulae, what is an alternate way of finding the velocity when you have the equation for displacement?

Differentiating the equation for displacement (integrate velocity equation for displacement equation)

Instead of using one of the SUVAT formulae, what is an alternate way of finding the acceleration when you have the equation for velocity?

Differentiating the equation for velocity (integrate acceleration equation for velocity equation)

In a pulley, what is the force acting on the particle that is horizontal (e.g. on a table)?

Only its tension

How can you improve a graph of a vehicle's velocity against time?

There should be a smooth change from acceleration to constant velocity and vice versa

What is the effect of air resistance on acceleration and initial velocity?

Acceleration decreases - initial velocity increases

What would happen if a string was not light? (2)

Tension would not be the same on either side of the string - would increase as you go up as supporting more string

Assumptions when modelling the motion of a vehicle e.g. train with a graph? (4)

1. Assume vehicles have no length

2. Vehicles are particles

3. Assume any times when stopping e.g. stations are points

4. Assuming platforms (if a train) have no length