Mechanics

A scalar quantity

A quantity with magnitude only

A vector quantity

A quantity with a magnitude and direction

The definition of displacement

Distance in a given direction from a point

The definition of instantaneous speed

The change in distance per unit time at an instant in time (the gradient of a tangent of a distance - time graph) - AS THE INCREMENT IN TIME TENDS TO ZERO

The definition of average speed

The total distance divided by the total time

The definition of velocity

The CHANGE IN displacement per unit time

The definition of acceleration

The rate of change of velocity

Obtaining velocity from a graph

Gradient of a displacement against time graph

Obtaining displacement from a graph

Area of a velocity against time graph

Obtaining acceleration from a graph

The gradient of a velocity against time graph

Can only use if acceleration is constant

suvat equations

The most important thing to remember in F = ma

F is the resultant force (largest force - smallest force) Sometimes there is only one force

The newton

The force needed to accelerate a mass of 1kg at 1ms^-2

What is the relationship between drag force and velocity

Drag force is proportional to the velocity squared

What affects the magnitude of the drag force

Surface area / density or viscosity of the fluid Drag is proportional to speed squared

The definition of terminal velocity

When the driving forces balance the resistive forces and the acceleration is zero.

The definition of centre of gravity

The point from where the objects entire weight appears to act

The definition of a couple

A pair of equal forces acting in opposite directions that produce rotation about a pivot

The definition of Torque

One of the forces in a couple multiplied by the perpendicular distance between the two forces

The definition of a moment

Force multiplied by the perpendicular distance from the pivot

The definition of equilibrium

No resultant force AND NO NET moment

The definition of the principle of moments

The sum of clockwise moments about a pivot is equal to the sum of anti clockwise moments about a pivot. WHEN IN EQUILIBRIUM

What should you look out for in a moment problem

Have they given you this distance from the pivot? Is the force and distance from the pivot at 90 degrees. Have all forces from the pivot been included (including the weight of the beam)?

The definition of density

Mass per unit volume

The definition of pressure

Force per unit cross sectional area

The definition of thinking distance

The distance travelled from seeing an obstacle to applying the brakes

The definition of braking distance

The distance travelled from applying the brakes to coming to a complete stop

The definition of stopping distance

Thinking distance + braking distance

The proportionality between thinking distance and velocity

The thinking distance is proportional to velocity (THIS IS BECAUSE THE BODY IS MOVING AT CONSTANT. DISTANCE = SPEED X TIME)

The proportionality between braking distance and velocity

The braking distance is proportional to velocity squared (here we are decelerating and so must use suvat. v^2 = u^2 + 2 as where u = 0)

The equation normally involved with thinking distance

constant speed formula

The equation normally involved when a car is braking

the equations of constant acceleration, F = ma, or energy transfers (k.e = w.d)

Some factors affecting thinking distance

Intoxication, initial speed

Some factors affecting braking distance

Initial speed, mass of the car, the incline, the magnitude of the frictional forces (discuss worn tyres / brakes, road conditions, weather conditions)

How air bags, crumple zones and seat belts work

Increasing the impact time reduces the deceleration which reduces the impact force (F = ma). Using Impulse F t = change in momentum. A larger impact time will reduce the average force if the change in momentum is constant

Or discuss energy transfers (K.E = W.D). Increasing the stopping distance reduces the force for the same initial Ke

The definition of work done

Force multiplied by the distance MOVED in the direction of the force

The Joule

The energy transferred when one Newton moves an object 1m in the direction of the force

8 Joules

The energy transferred when 1 Newton moves an object 8m in the direction of the force

What is important when calculating work

The force x distance moved must be in the same direction

The definition of the principle of conservation of energy

Energy cannot be created or destroyed only converted from one form to another

The definition of Kinetic Energy

The Energy associated with a mass, m, moving at a velocity, v. K.E = 1/2 m v^2

What should you always write at the start of a energy transfer problem

energy at start = energy at end + W.D (if required)

The definition of power

The work done per unit time OR the energy transferred per unit time

The definition of the Watt

The power when one joule is transferred per second

The definition of 8 Watts

The power when 8 joules is transferred per second

The efficiency of all systems

less than 100%. This is due to friction doing work to other forms such as heat.

The definition of efficiency

The ratio of useful energy output to the total energy input. Or replace energy with power

Sankey diagrams

Diagrams which have an arrow in (total energy input) and arrows out (energy outputs). Put the useful energy coming out at the top.

Tensile force

A force pulling something apart

The elastic limit

The point beyond which a material will not return to its original shape once the force is removed

Hook's law

Force is proportional to extension until the elastic limit

The force constant, k (stiffness)

The force per unit extension

What can we obtain from the area under a force - extension graph

Elastic Potential energy

What can we obtain from the gradient of a force - extension graph

The force constant

The definition of stress

Force per unit cross sectional area (the same as pressure)

The definition of strain

The extension per unit original length

The definition of Young's modulus

The stress per unit strain

The definition of ultimate tensile strength

The maximum stress a material can withstand before breaking

The definition of elastic deformation

The material will go back to its original shape once the force is removed

The definition of plastic deformation

The material will not go back to its original shape once the force is removed

The definition of brittle

A material which breaks at the elastic limit

The definition of a ductile material

A material which undergoes a large amount of plastic deformation before breaking

Newton's first law

A body will remain at rest or travel at uniform motion unless acted on by a RESULTANT force

Newton's second law

The resultant force is proportional to the rate of change of momentum and acts in the same direction

Newton's third law

If Body A exerts a force on body B then body B will exert the same force but in the opposite direction on body A. The force will be of the same type. This is why the weight and reaction force are not a pair

When can we apply F = m a

When the mass of the body / system remains constant

What is very important to remember about F = m a

F is the resultant force (larger force - smaller force. Unless there is only one force involved such as frictional forces in a braking car)

Linear Momentum

The produce of mass and velocity. Momentum = mass x velocity

What mistake might you make in a head on collision

Momentum is a vector and therefore can be positive OR negative. In a head on collision the momentum before = mv - MU

What is the change in momentum in a rebound

mv - ( -mu) = mv + mu

What is the change in momentum in an elastic rebound

mv - (-mu) where v = u SO 2mv

Define the impulse of a force

The average force acting during a collision x the time of the collision

What can we obtain from a force - time graph?

The area under the line equals the impulse (total change in momentum). By knowing the area one could then calculate either the velocity or the mass of the object. Area = Impulse = mv - mu

Explain why crumple zones / air bags / seat belts minimise the forces acting on a passenger using momentum

F t = mv - mu. Because the change in momentum is constant one could minimise the force by increasing the impact time

The principle of conservation of momentum

The total momentum before a collision is equal to the total momentum after a collision

An elastic collision

The total K.E before a collision is equal to the total K.E after a collision and momentum is conserved

An inelastic collision

The total K.E after a collision is less than the total K.E after the collision, however momentum is conserved

Why is momentum always conserved in a collision

Both objects will experience the same impulse during a collision. Impulse = F t. From Newton's third law both objects will experience the same force and the time of the collision will also be the same.

Why is K.E often lost during a collision

The K.E will be transferred into other forms such as heat as a body experiences plastic deformation

What will happen when the force is removed after the elastic limit

The material will not return to its original length. The same gradient must be drawn from the point of release parallel to the initial loading gradient - THIS IS BECAUSE THERE ARE THE SAME INTERMOLECULAR FORCES BETWEEN BONDS AS IT IS THE SAME MATERIAL

Component of weight acting parallel to the plane

sin component of weight

Component of weight acting perpendicular to the plane

cos component of weight