Forces and Energy

In Grade 6 you described things as fast or slow. Now you can put a number on it.

Speed is how far something travels in a certain time. The equation is:

$speed = \frac{distance}{time}$

If you walk $200\ m$ in $100\ s$, your speed is $200 \div 100 = 2\ m/s$ — two metres every second.

The standard unit of speed is metres per second ($m/s$), although you also see kilometres per hour ($km/h$) on road signs.

You can rearrange the equation to find any one of the three quantities:

• to find distance: $distance = speed \times time$,
• to find time: $time = distance \div speed$.

Most journeys are not at one steady speed — you speed up and slow down. So we often use average speed: the total distance divided by the total time. A cyclist who covers $6000\ m$ in $600\ s$ has an average speed of $10\ m/s$, even if parts of the ride were faster or slower.

A distance-time graph plots how far an object has travelled (up the side) against time (along the bottom). The shape of the line tells the whole story.

Read the line like this:

• A steep line — distance changes quickly, so the object is moving fast.
• A gentle line — distance changes slowly, so the object is moving slowly.
• A flat (horizontal) line — distance does not change, so the object is stationary.

You can even calculate the speed from the graph. Pick a section of the line, find how far it rose (distance) and how long that took (time), then use $speed = distance \div time$. The slope of the line is the speed.

When the forces on an object are balanced, its motion does not change — it stays still or keeps moving steadily. When the forces are unbalanced, the motion does change.

An unbalanced force can:

• speed an object up — when the force acts in the direction of motion,
• slow an object down — when the force acts against the motion,
• change its direction — when the force acts sideways,
• change its shape — when the force squashes or stretches it.

The bigger the unbalanced force, the greater the change in motion. A small push gives a gentle change of speed; a large push gives a sharp one. The direction of the change always matches the direction of the overall (resultant) force.

Why does a small steel bolt sink, while a huge wooden log floats? The answer is density.

Density tells you how much mass is packed into a given volume:

$density = \frac{mass}{volume}$

Its unit is grams per cubic centimetre ($g/cm^3$) or kilograms per cubic metre ($kg/m^3$).

Floating and sinking come straight from density. Compare an object's density with the liquid's density:

• if the object is less dense than the liquid, it floats,
• if the object is more dense than the liquid, it sinks.

Water has a density of about $1\ g/cm^3$. Wood (around $0.6\ g/cm^3$) floats; steel (around $8\ g/cm^3$) sinks. A steel ship floats because its overall shape contains a lot of air, making its average density less than water.

Press a drawing pin between your fingers. The flat head barely hurts, but the sharp point easily pierces a board — even though your hand pushes with the same force. The difference is pressure.

Pressure tells you how concentrated a force is:

$pressure = \frac{force}{area}$

Its unit is the pascal ($Pa$), where $1\ Pa = 1\ N/m^2$.

The same force gives:

• a high pressure when squeezed onto a small area (the pin point),
• a low pressure when spread over a large area (the pin head).

This explains many everyday things. A sharp knife cuts well because its thin edge concentrates the force into a tiny area. Wide tractor tyres spread the vehicle's weight over a large area, lowering the pressure so it does not sink into soft soil. Snowshoes work the same way — a big area means low pressure on the snow.

To work out a pressure, find the force in newtons, find the area in square metres, and divide. A force of $200\ N$ on an area of $0.5\ m^2$ gives a pressure of $200 \div 0.5 = 400\ Pa$.

Whenever a force moves an object, work is done and energy is transferred. The equation is:

$work\ done = force \times distance$

Work is measured in joules ($J$). Lifting a $20\ N$ box up $2\ m$ does $20 \times 2 = 40\ J$ of work — and that $40\ J$ is transferred into the box's gravitational store.

The amount of work done equals the energy transferred. As you learned in Grade 6, energy is never created or destroyed — it just moves between stores. But some of it usually spreads out as heat, which is hard to use again. That is why machines are never perfectly efficient.

The energy we use at home is generated from energy resources, which fall into two groups:

• Renewable resources will not run out — solar, wind, hydroelectric, geothermal and tidal. They generally cause less pollution.
• Non-renewable resources will run out — coal, oil, natural gas (the fossil fuels) and nuclear fuel. Burning fossil fuels releases carbon dioxide.

Choosing energy resources wisely is one of the biggest scientific challenges of your lifetime.

The calculation skills in this topic run right through later science:

• Motion and graphs — distance-time graphs lead on to speed-time graphs and acceleration.
• Forces in detail — you will combine forces to find the resultant force and link it to motion.
• Floating and pressure — density and pressure explain how submarines, hydraulics and weather work.
• Energy and power — work done leads into power (energy transferred per second).
• Electricity — energy transfer in circuits uses exactly these ideas.

Whenever a physics problem feels hard later, slow down and ask: what is the equation, and what units am I using? Getting comfortable with $speed$, $density$, $pressure$ and $work$ now will make senior physics far smoother.