Forces

Forces are pushes, pulls, or twists that can affect an object's motion or shape. The SI unit for force is newtons (N). The calculation for force is:

$$ \text{Force} = \text{Mass} \times \text{Acceleration}$$

Force is always expressed in newtons. Just like joules, we can have kilonewtons (kN) and meganewtons (MN), though these do not generally turn up in Unit 1-4 of Systems Engineering.

Mass should always be provided in kilograms. This means you may need to convert between units to calculate an accurate answer.

Acceleration is always given in meters per second squared, or $ \text{m/s}^2 $

Generally, this equation shows up in relation to calculating the force of an object when their mass is given in grams/kilograms. The acceleration in this case is gravity, which is $9.8\text{m/s}^2$. In Systems, we generally assume gravity as $10\text{m/s}^2$.

For example, you might be asked about the force needed to lift a 15kg object up 5m.

Since $\text{Force} = \text{Mass} \times \text{Acceleration}$ or $\text{F} = \text{Ma}$, and assuming gravity as 10, then our equation would be

$$\text{Force} = 15\,\text{kg} \times 10\,\text{m/s}^2$$ $$\therefore \text{Force} = 150\,\text{N}$$

Torque

Torque (τ) is a rotational force. It’s what causes an object to rotate and is calculated as the force multiplied by the perpendicular distance to the pivot point. Torque is often used in the context of motors and engines to indicate how much "twisting power" it has.

The longer the distance from the pivot point, the greater the torque with the same force applied. For example, a longer wrench or spanner will give you more torque.

$$ \text{Torque} = \text{Force} \times \text{Perpendicular Distance to the Pivot} $$ $$ \text{τ} = \text{Fd} $$

Moment

A moment is a measurement of the turning effect a force about an axis. You can think of a moment as the 'turning power' of a force. Moments can be clockwise or counter-clockwise. A moment is measured in Newton metres (Nm).

The turning effect is dependent on two variables:

• The size of the force acting on the lever (F)
• The distance of the force perpendicular from the pivot (d)

$$ \text{Moment} = \text{Force} \times \text{Perpendicular Distance to the Pivot} $$ $$ \text{M} = \text{Fd} $$

You will have also experienced this when using a seesaw, or when trying to open a door close to the hinge, rather than near the handle. The further you are from the pivot, the greater the moment you are creating.

An object is said to be in equilibrium (balanced, equal, not rotating), when the clockwise moment and the counter-clockwise moment are equal.

This is covered more in Levers.