RAF Airman/Airwoman Selection Test (AST) Mechanical Comprehension Syllabus

Describe the three classes (orders) of levers with the arrangement of fulcrum, load and effort.

Class 1: fulcrum between effort and load (e.g. seesaw, scissors). Class 2: load between fulcrum and effort (e.g. wheelbarrow, nutcracker). Class 3: effort between fulcrum and load (e.g. tweezers, human forearm).

Define mechanical advantage (MA) and give its formula.

Mechanical advantage is how much a machine multiplies the input force. $$\text{MA} = \frac{\text{load (output force)}}{\text{effort (input force)}}$$ It is a ratio with no units.

How is mechanical advantage related to the arm lengths of a lever?

For a lever the mechanical advantage equals the ratio of the effort arm to the load arm: $$\text{MA} = \frac{\text{effort distance from pivot}}{\text{load distance from pivot}}$$ A longer effort arm gives a greater MA.

In a single fixed pulley, what is the mechanical advantage and what is its purpose?

A single fixed pulley has a mechanical advantage of 1 (it does not multiply force). Its purpose is to change the direction of the force, so you can pull down to lift a load up.

In a single movable pulley, what is the mechanical advantage and what is the trade-off?

A single movable pulley has a mechanical advantage of 2 (the load is shared by two rope sections). The trade-off is that you must pull twice the distance (or rope length) to raise the load.

How do you find the mechanical advantage of a block-and-tackle pulley system?

The mechanical advantage (ignoring friction) equals the number of rope segments directly supporting the load (movable block). For example, 4 supporting ropes give an MA of 4, requiring one-quarter of the load force as effort.

What is a gear, and what happens to a gear meshed with another (direction of rotation)?

A gear is a toothed wheel that transmits rotational motion and force. Two meshed gears rotate in opposite directions; adding an idler gear between them makes the driver and driven gears rotate in the same direction.

Give the gear ratio formula in terms of number of teeth.

$$\text{Gear ratio} = \frac{\text{teeth on driven gear}}{\text{teeth on driver gear}}$$ A ratio greater than 1 means the driven gear turns slower with more torque; less than 1 means faster with less torque.

If a driver gear has 10 teeth and the driven gear has 40 teeth, what is the gear ratio and the effect on speed?

Gear ratio $= \frac{40}{10} = 4:1$. The driven gear turns 4 times slower than the driver but provides 4 times the torque (turning force).

How are rotational speed and torque traded off in a gear train?

Gears trade speed for torque. A larger driven gear reduces output speed but increases torque; a smaller driven gear increases speed but reduces torque. The product (power) is conserved, ignoring friction.

Explain the relationship between gear size and rotational speed when two gears mesh.

The smaller gear rotates faster and the larger gear rotates slower. Their speeds are inversely proportional to their numbers of teeth (or radii): $$\frac{N_1}{N_2} = \frac{T_2}{T_1}$$ where $N$ is speed and $T$ is teeth.

What is an inclined plane and why does it make raising a load easier?

An inclined plane is a sloped flat surface (ramp). It reduces the effort force needed to raise a load by increasing the distance over which the force is applied, trading distance for a smaller force.

How is the ideal mechanical advantage of an inclined plane calculated?

$$\text{MA} = \frac{\text{length of slope}}{\text{vertical height}}$$ A longer, more gradual ramp gives a greater mechanical advantage (less effort needed).

How does a wedge work as a simple machine?

A wedge is effectively two inclined planes back to back. It converts a force applied to its blunt end into larger sideways forces at its inclined faces, used to split, cut or lift (e.g. axe, chisel, knife).

How is a screw related to the inclined plane, and what does its pitch determine?

A screw is an inclined plane wrapped around a cylinder. Its pitch is the distance advanced per full turn; a smaller pitch (threads closer together) gives a greater mechanical advantage but requires more turns.

Define work done and give its formula and SI unit.

Work is done when a force moves an object in the direction of the force. $$W = F \times d$$ where $F$ is force (N) and $d$ is distance moved in the force's direction (m). The SI unit is the joule (J), where $1\ \text{J} = 1\ \text{N m}$.

How much work is done lifting a 50 N weight through a height of 3 m?

$W = F \times d = 50 \times 3 = 150\ \text{J}$.

Define energy and state the principle of conservation of energy.

Energy is the capacity to do work, measured in joules (J). The principle of conservation of energy states that energy cannot be created or destroyed, only transferred or transformed from one form to another; the total energy stays constant.

What is the relationship between work done and energy transferred?

The work done on an object equals the energy transferred to it. Doing work is the mechanism by which energy is moved from one form or place to another, so both are measured in joules.

Give the formula for kinetic energy and identify the symbols.

$$E_k = \frac{1}{2} m v^{2}$$ where $E_k$ is kinetic energy (J), $m$ is mass (kg) and $v$ is speed (m/s). Note kinetic energy depends on the square of the speed.

Calculate the kinetic energy of a 2 kg object moving at 3 m/s.

$E_k = \frac{1}{2} m v^{2} = \frac{1}{2} \times 2 \times 3^{2} = \frac{1}{2} \times 2 \times 9 = 9\ \text{J}$.

Give the formula for gravitational potential energy and identify the symbols.

$$E_p = mgh$$ where $E_p$ is gravitational potential energy (J), $m$ is mass (kg), $g$ is gravitational field strength ($\approx 9.81\ \text{N/kg}$) and $h$ is height raised (m).

What energy transfer occurs as an object falls freely, and what equation applies (ignoring air resistance)?

Gravitational potential energy is converted into kinetic energy. Ignoring air resistance, the loss in $E_p$ equals the gain in $E_k$: $$mgh = \frac{1}{2} m v^{2}$$

What is the difference between kinetic energy and potential energy?

Kinetic energy is the energy an object has due to its motion. Potential energy is stored energy due to an object's position (gravitational) or condition (e.g. elastic strain in a stretched spring).

State Hooke's law for a spring, including the formula and what each symbol means.

For an elastic material the extension is proportional to the applied force (up to the limit of proportionality). $$F = kx$$ where $F$ is force (N), $k$ is the spring constant (N/m) and $x$ is the extension (m).

What is the elastic limit of a spring?

The elastic limit is the maximum force or extension beyond which a spring no longer returns to its original length when the load is removed; it becomes permanently (plastically) deformed and Hooke's law no longer applies.

Give the formula for elastic potential energy stored in a stretched spring.

$$E = \frac{1}{2} k x^{2}$$ where $k$ is the spring constant (N/m) and $x$ is the extension (m). This is the area under a force-extension graph.

How do springs combine in series and in parallel regarding stiffness?

In series the springs are softer overall (smaller effective spring constant, larger total extension). In parallel they are stiffer overall (larger effective spring constant, smaller extension) because the load is shared.

How does a hydraulic system multiply force, and why does it work?

A hydraulic system uses an incompressible liquid to transmit pressure equally (Pascal's principle). A small force on a small piston creates a pressure that acts on a larger piston, producing a much larger output force: $$\frac{F_1}{A_1} = \frac{F_2}{A_2}$$

In a hydraulic press, a 10 N force on a piston of area $0.01\ \text{m}^2$ acts on an output piston of area $0.05\ \text{m}^2$. What is the output force?

Pressure $= \frac{10}{0.01} = 1000\ \text{Pa}$. Output force $= P \times A_2 = 1000 \times 0.05 = 50\ \text{N}$.

What is the key difference between hydraulic and pneumatic systems?

Hydraulic systems use an incompressible liquid (e.g. oil), giving precise, powerful force transmission. Pneumatic systems use a compressible gas (e.g. air), which is lighter and cleaner but springy and less precise because the gas can compress.

Define the centre of gravity of an object.

The centre of gravity is the single point at which the entire weight of an object can be considered to act. For a uniform, symmetrical object it lies at its geometric centre.

What two conditions make an object more stable?

An object is more stable when it has a low centre of gravity and a wide base. This means a larger tilt is needed before its centre of gravity passes beyond the edge of its base, so it is less likely to topple.

When does an object topple over, in terms of its centre of gravity and base?

An object topples when its centre of gravity passes (vertically) beyond the edge of its base of support, so that the line of action of its weight falls outside the base, creating an unbalancing turning moment.

Describe stable, unstable and neutral equilibrium.

Stable: when slightly displaced, the object returns to its original position (centre of gravity rises then falls back). Unstable: a small displacement causes it to topple (centre of gravity falls). Neutral: when displaced it stays in the new position (centre of gravity stays at the same height, e.g. a rolling ball).