Mechanics

Acceleration

Change in velocity per unit time.

$a=\frac{\Delta v}{\Delta t}$

Newton's Laws of Motion

1st Law (Inertia):

An object will remain at a constant velocity unless acted upon by a resultant force.

Inertia is the resistance of a body to move or stop moving once it has stared.

2nd Law:

The resultant force is proportional to the rate of change of momentum.

$F=\frac{m\Delta v}{\Delta t}=ma$

The resultant force and acceleration act in the same direction

Note:

Two objects of unequal mass dropped from a height, assuming no air resistance, will fall at the same rate ( acceleration) of 9.81 so will hit the ground at the same time.

3rd Law:

An object A exerts a force on object B which means that object B will exert an equal and opposite fore on object A.

Note:

There is always a pair of forces.

The forces must be of the same type and act on different objects or they would cancel out.

Terminal Velocity

This is the maximum, constant velocity achieved by an object, and it occurs when the object has a zero resultant force , that is, no further acceleration

Vectors and Scale Diagrams

Scalar quantities have only magnitude.

Vector quantities have both magnitude and direction.

Vector Addition

Vector Subtraction

Graphs of Motion

Displacement - time

Velocity - time

Acceleration - time

Horizontal line above X-axis = constant acceleration

Horizontal line above y-axis = constant deceleration

Energy, work and mechanical power

The 9 Types of Energy

Gravitational Potential (E_p) = $mg\Delta h$

kinetic energy (E_k) = $\frac12mv^2$

Law of conservation of energy

Energy can neither be created nor destroyed, but can be transferred into different types

Work (W)

$\Delta W=Fs$ (when distance moved is in same direction as force)

$\Delta W=Fs\cos\theta$ (when force is acting at an angle to the displacement)

Force - Displacement Graphs

The area under the graph is the work done / energy

Power

Power is the rate of transfer of energy.

$P=\frac{\Delta W}{\Delta t}=\frac{\Delta E}{\Delta t}$

Explosions

Momentum before the explosion is zero because object is stationary

For momentum to be conserved, momentum after must be equal zero

Forces at an angles

2 or 3 Forces in Equilibrium

No resultant force

Object could be at rest or moving with constant velocity

For 3 forces, we can form a closed loop (triangle) by joining tips to tail

For more complex resolutions:

Ensure the angle is to the horizontal

Resolve vertically or horizontally then find resultant force and direction

SUVAT: the equations of uniform acceleration

$v=u+at$

$s=ut+\frac12at^2$

$v^2=u^2+2as$

$s=\frac{(v+u)t}{2}$

Freefall, a = -g

If an object falls to a lower position, s will be negative.

We assume no air resistance

Projectile Motion

Gravity is the only force acting and it acts in the vertical direction

Acceleration in the vertical direction

No horizontal force so no horizontal acceleration

We assume no air resistance

Separate horizontal and vertical components

Centre of Gravity

The point at which the entire weight of an object appears to act.

Moments

The product of force and perpendicular distance

$M=Fd$

Principle of Moments

The sum of all the clockwise moments is equal to the sum of all the anticlockwise moments