S2 Forces and Pressure
Created by Miss Clarissa Ng | www.clartutors.com
A force can do more than push something along — it can also make an object turn. The size of that turning effect depends on two things at once: how big the force is, and how far from the turning point you apply it.
turning effect = force × perpendicular distance
| Everyday situation | How the turning effect is made larger |
|---|---|
| Spanner on a tight nut | Push further out along the handle — same force, bigger distance |
| Door handle | Placed on the far edge from the hinges, so the same push swings the door with less effort |
| Lever lifting a lid | Long end for your hand, short end under the lid: a small force acts far from the pivot |
| Wheelbarrow | Handles set well back from the wheel, so the load is lifted with a gentler push |
Worked example. A mechanic pushes 200 N on the handle of a spanner, 0.25 m from the nut. The turning effect is 200 N × 0.25 m = 50 N m. If she pushes the same 200 N at 0.50 m instead, the turning effect doubles to 100 N m — the nut comes free with no extra effort.
Why it is called a turning effect and not simply a force. A force applied straight at the pivot turns nothing, however large it is, because the perpendicular distance is zero. Turning effect is therefore a better description of what happens at a spanner, a lever or a door: what matters is the force and where it is applied.
It is a vector, which means it is only fully described when you give both its magnitude (how strong) and its direction (which way it acts).
The SI unit of force is the newton (N).
One newton is the force that gives a one-kilogram mass an acceleration of one metre per second squared. On a bench, that is roughly the pull of gravity on a small apple, so a newton is a modest force — which is why weights and pushes in school problems are usually tens or hundreds of newtons.
- Start it moving, if it was sitting still.
- Bring it to a stop.
- Change the speed it moves at — speeding up (acceleration) or slowing down (deceleration).
- Change the direction it travels in, even if the speed stays the same.
- Turn it about a point, or bend, stretch or squash it.
Nothing on that list happens unless the forces acting on the object are unbalanced. Sorting out whether they balance is therefore the first thing to do in almost every question in this chapter.
Every force you will meet in S2 belongs to one of two families, and the test is simply whether the two objects have to touch.
| Family | What it requires | Members |
|---|---|---|
| Contact forces | The objects must be physically touching for the force to exist. | Friction, normal force, elastic force (tension in a stretched string), air resistance, the push of your hand on a door. |
| Non-contact forces | The force reaches across a gap; no touching needed. | Magnetic force, electrostatic force, gravitational force. |
- Same direction: add the magnitudes. Two people pushing a car forward with 300 N and 250 N give a resultant of 550 N forward.
- Opposite directions: subtract the smaller from the larger, and the resultant points in the direction of the larger force.
Resultant = 0 N → the forces are balanced → the motion does not change. The object stays still, or carries on at a steady speed in a straight line.
Resultant ≠ 0 N → the forces are unbalanced → the object speeds up, slows down, or changes direction.
A delivery trolley is being pushed along a corridor. A worker pushes it forward with 95 N while a second worker, facing the trolley, pushes it back with 62 N. Friction between the wheels and the floor provides a further 9 N acting backwards.
(a) Find the resultant force on the trolley.
Take forward as positive:
(b) Describe the motion of the trolley.
The resultant is not zero, so the forces are unbalanced. The trolley accelerates in the direction of the resultant — that is, it speeds up as it travels forwards.
(c) The two workers stop pushing and the trolley rolls on. What resultant now acts, and what happens?
With no pushes, only the 9 N of friction remains, and it acts opposite to the motion. The trolley decelerates and comes to rest. Note that friction never reverses the motion — it only ever opposes whatever movement is happening — and once the trolley stops, the resultant falls to zero and it stays put.
A swimmer swims across a river at 1.6 m/s while the current carries her downstream. The two velocities are at right angles, so they cannot simply be added or subtracted; they are combined as a triangle, and the size of the combined velocity is given by Pythagoras.
Find her resultant velocity if the current is 1.2 m/s.
Why the direction matters: the swimmer makes good progress across the river and arrives some distance downstream. Both facts come from the same resultant, and both are expected in the answer.
The cause is microscopic. Even a surface that looks and feels polished is covered in tiny ridges, pits and fibres. When two such surfaces are pressed together their high points interlock and partly weld, and sliding one across the other means shearing those contact points apart. The energy needed to do that ends up as thermal energy in the two surfaces, which is why rubbing your hands together warms them.
| Factor | Effect |
|---|---|
| How rough the surfaces are | The rougher the pair, the deeper the interlocking and the larger the friction. Dragging a box over paving needs far more force than dragging it over ice. |
| What the materials are | Rubber on concrete grips far harder than steel on steel. Every pairing of materials has its own grip, all else being equal. |
| How hard the surfaces are pressed together | Press them together harder and more of the high points make contact, so friction rises. Load an identical crate with more boxes and its friction on the same floor increases. |
| The area touching | No effect. A block turned onto its narrow side has the same weight and experiences the same friction as the same block lying on its wide face. The pressure at each contact point rises as the area falls, and the two changes cancel out exactly. |
| To increase friction, designers… | To reduce friction, designers… |
|---|---|
| cut a tread pattern into tyres and a ribbed pattern into shoe soles, so the surfaces interlock | polish the sliding surfaces until the high points are only a few atoms tall |
| add a soft, high-grip layer such as the rubber sleeve on a bicycle handlebar or a goalkeeper's glove | introduce a lubricant — oil, grease, or even water — whose layers slide over one another easily |
| roughen a deliberately slippery floor, for instance with an abrasive strip on a stair edge | replace sliding with rolling, using wheels, ball bearings or rollers |
| raise the load pressing the surfaces together, as a heavier vehicle grips better under braking | streamline the shape, which reduces air resistance rather than surface friction |
The honest answer is both at once, and the mark goes to whoever reasons from the situation they were given rather than quoting a general rule.
| Situation where friction is doing us a favour | Situation where it costs us |
|---|---|
| A cyclist braking on a wet road: the brakes slow the bike by converting motion into thermal energy at the pads and rim, and nothing would slow it without the resulting friction. | The same pads and rim wear away and have to be replaced; the material removed has simply been abraded off. |
| A climber's fingertips holding a rock, and the grip of a shoe on a starting block. | A drill bit or a piston ring wearing against the metal it runs in, so parts must be lubricated and eventually replaced. |
| A pencil leaving a line on paper — graphite is ground off onto the page. | An engine losing useful output because some of the fuel's energy leaves as heat generated by moving parts. |
"Normal" is used here in its mathematical sense of at right angles, not in the sense of "ordinary". A wall pushes back horizontally on your shoulder; the floor pushes up on your feet; a slope pushes at an angle.
- Horizontal surface: the normal force is vertical, and equals the weight whenever no other vertical force acts on the object.
- Slope: the normal force is still perpendicular to the surface, so it now leans. Only part of the weight presses into the slope, so the normal force is smaller than the weight. That is why a block slides down a steep ramp: the part of its weight acting down the slope is no longer cancelled by anything.
Stretch a rubber band and it pulls your fingers together; squeeze a spring and it pushes back at your hand. The force grows with the distortion: over the usable range of a spring, doubling the extension roughly doubles the force. Push past the spring's elastic limit, however, and it is permanently deformed — it will no longer return to its original length, and the neat doubling relationship breaks down.
- A trampoline mat pushing a gymnast back up after she has stretched it downwards.
- A bungee cord slowing a jumper: the cord stretches, and the restoring force grows until it exceeds his weight and brings him to a halt.
- The tension in the rope of a climbing anchor, or in a hammock's fixing.
- A diver's springboard, bent down and then driving the diver upwards as it springs back.
Forces are measured with a spring balance, also called a newton meter. Its working principle is the elastic force you have just met: a spring stretches by an amount proportional to the force pulling on it, and a pointer attached to the spring travels along a numbered scale as the spring extends. Greater force, longer extension, higher reading.
| Part | Purpose |
|---|---|
| Spring | Extends by an amount proportional to the force applied, so its length is the quantity being measured. |
| Pointer | Moves with the spring and marks the reading on the scale. |
| Scale | A graduated strip beside the pointer that turns extension into newtons. |
| Zero adjuster | A small screw or slide that lets you set the pointer to the zero mark before use. |
| Hook | Where the object or weight is hung; the body must hang freely while the reading is taken. |
- Parallax error — the eye is not level with the pointer, so the reading is taken from an angle and the pointer appears against the wrong mark. Always sight straight across, at the same level as the pointer.
- Zero error — the pointer does not sit at 0 N when nothing is hanging on it. Two legitimate fixes: adjust it back with the zero adjuster, or note the starting reading and subtract it from every reading you take.
- Wrong scale division — misreading how much each small gap on the scale stands for. Work out the value of one division before you start, then multiply by the number of divisions the pointer has moved.
Not every force students meet is a hand's push or a hanging weight. Some of the largest forces acting on the planet come from natural events, and they act on a scale that reshapes coastlines and buildings.
| Event | The forces it produces |
|---|---|
| Tropical cyclone | Moving air exerts a huge push on walls, roofs and trees, and the pressure difference across a roof can lift it upwards off the walls it rests on. |
| Earthquake | The ground accelerates sideways and vertically, loading buildings with forces far larger than their own weight, while failing soil can no longer exert enough normal force to support a foundation. |
| Volcanic eruption | Gas at very high pressure blasts rock and ash out of the vent, and falling debris strikes structures with destructive contact forces. |
| Tsunami | A moving wall of water pushes along the whole length of a sea wall; because the water is dense and moving fast, the force is enormous, and the pressure beneath it can scour the sand away from a foundation. |
Push a drawing pin into a noticeboard and it slides in with almost no effort. Push your thumb on the board with the same force and nothing happens. The force is the same — what changes is how tightly that force is packed. That is what pressure measures.
P = F / A where P is pressure in pascals (Pa), F is the force in newtons (N), and A is the area in square metres (m2).
1 Pa = 1 N/m2
The area in the formula is the contact area — only the part of the surface the force actually presses on. A crate on four small feet has a much smaller contact area than the same crate lying flat, even though its weight has not changed.
- Spread it over a larger area → pressure falls
- Squeeze it into a smaller area → pressure rises
Designing for high pressure or low pressure
| Object | Contact area | Pressure it makes | Why it is designed that way |
|---|---|---|---|
| Sharp knife blade | Very small — the edge is ground to a thin line | Very high | Few newtons are enough to part the fibres of the food |
| Drawing pin | Tiny at the point, wide at the head | High at the point, low under the thumb | Enters the board easily without hurting your thumb |
| Snowshoes | Large — wide flat boards | Very low | Keeps the walker on top of soft snow |
| Tractor tyres | Wide and broad | Low | Stops the wheels sinking into wet soil |
| Running spikes | Tiny studs | Very high | Bite into the track for grip |
A hiker has a weight of 600 N. In ordinary boots her two feet press on the snow over a total contact area of 0.04 m2. Wearing snowshoes, the same weight is shared over a total area of 0.40 m2.
(a) Find the pressure under her boots.
P = F / A = 600 N ÷ 0.04 m2 = 15 000 Pa (15 kPa)
(b) Find the pressure under her snowshoes.
P = F / A = 600 N ÷ 0.40 m2 = 1 500 Pa (1.5 kPa)
(c) Compare the two and explain the result.
The snowshoes give a pressure ten times smaller than the boots, because the contact area is ten times larger while the weight stays at 600 N. That is why she sinks in boots but stays on the surface in snowshoes.
Why a sharp knife cuts and a blunt one does not
A sharpened blade meets the food along a line only a fraction of a millimetre wide, so the contact area is minute. A modest push then produces an enormous pressure at the edge, enough to part the material. A blunt blade has a rounded edge and a much larger contact area, so the same push gives a smaller pressure and the knife skids instead of cutting. Sharpening a knife is really a way of shrinking the area.
Why snowshoes work
Soft snow gives way beneath a pressure of only a few kilopascals. In boots the walker's 600 N is concentrated onto a small area and exceeds that limit; on wide snowshoes the same 600 N is spread over ten times the area and the pressure drops below the point where the snow collapses. The weight has not changed — only the area carrying it.
Why a dam wall is thicker at the bottom
Water pressure grows with depth (Topic 10), so the lower part of a dam pushes outwards far harder than the top. Engineers give the wall a wide, heavy base and a narrower crest, so the strongest concrete sits where the pressure is greatest.
A liquid or a gas pushes on anything inside it, and it pushes from every side, not just downwards. Three facts follow:
- A fluid exerts pressure in all directions on an object within it.
- The pressure grows with depth, because a deeper point has more fluid above it pressing down.
- The pressure also depends on the fluid's density — a denser liquid packs more mass into the same depth.
P = pressure due to the fluid (Pa)
ρ (rho) = density of the fluid (kg/m3)
g = gravitational field strength, 10 N/kg
h = depth below the surface (m)
This formula gives only the fluid's own contribution. The air above the surface is also pressing down, and its contribution is the atmospheric pressure, roughly 100 000 Pa (100 kPa) at sea level.
When a question asks for the total pressure on an object under water:
Ptotal = Patm + ρ g h
Going Further. A swimming pool holds fresh water of density 1 000 kg/m3. Take g = 10 N/kg and atmospheric pressure = 100 000 Pa. A diver swims at a depth of 3.0 m.
(a) What pressure does the water exert on the diver?
P = ρ g h = 1 000 × 10 × 3.0 = 30 000 Pa (30 kPa)
(b) What is the total pressure on the diver?
Ptotal = 100 000 + 30 000 = 130 000 Pa (130 kPa)
(c) What is the water pressure at half this depth?
P = 1 000 × 10 × 1.5 = 15 000 Pa (15 kPa)
Halving the depth halves the water pressure, because P is directly proportional to h. The atmospheric term does not change with depth — it is the same at the surface and at the bottom.
The same idea in a dam
Reading down a dam wall is the same calculation with different numbers. Take the same water density and g:
| Depth below the surface, h | Water pressure, ρgh |
|---|---|
| 2.0 m | 20 000 Pa (20 kPa) |
| 4.0 m | 40 000 Pa (40 kPa) |
| 6.0 m | 60 000 Pa (60 kPa) |
Each extra metre of depth adds the same 10 000 Pa, so the load on the wall grows steadily from the waterline to the base. That steady increase is exactly why the concrete is made thickest at the bottom.
Replace the fresh water with seawater of density 1 030 kg/m3 and the pressure at 3.0 m becomes 1 030 × 10 × 3.0 = 30 900 Pa, slightly higher, because each cubic metre of seawater carries a little more mass down onto that point. Density and depth are the two dials that set a fluid's pressure.
Most of the marks lost on this topic are not lost to hard physics. They are lost to three habits: mixing up mass and weight, substituting numbers into a formula that was never written down, and giving an answer with the wrong unit or no unit at all. This section fixes all three.
Mass and weight are linked by one equation, and you already know it:
W = m × g
where W is weight in newtons (N), m is mass in kilograms (kg), and g is the gravitational field strength in newtons per kilogram (N/kg). On Earth, take g = 10 N/kg unless the question says otherwise.
Keeping newtons and kilograms straight
Mass and weight are not two names for the same quantity — they are two different quantities that happen to be linked by g. A mass of 6.0 kg weighs 60 N on Earth, but the same 6.0 kg weighs only about 9.6 N on the Moon. The mass never moves: the same number of kilograms travels with the object. What changes is g, and therefore the weight.
This is why the units matter so much. A spring balance measures weight, so its scale is marked in newtons. A beam balance or an electronic balance compares masses, so those read in kilograms. If a question hands you a reading in newtons, you have a weight; if it hands you a reading in kilograms, you have a mass. Converting between them always means multiplying or dividing by g — never by anything else.
| Quantity | What it measures | SI unit | Instrument |
|---|---|---|---|
| Mass | How much matter the object contains | kilogram (kg) | Beam balance or electronic balance |
| Weight | The gravitational force pulling on that matter | newton (N) | Spring balance (newton meter) |
| Gravitational field strength | Weight per kilogram of mass at that place | newton per kilogram (N/kg) | Calculated from W ÷ m |
Write the formula before you substitute
Examiners award a mark for choosing and stating the correct equation, separately from the mark for the arithmetic. So the working should always appear in the same three steps:
- State the equation. e.g. W = m × g (or g = W ÷ m, or m = W ÷ g).
- Substitute the values with their units. e.g. W = 6.0 kg × 10 N/kg.
- Give the answer with its unit, to the precision the data deserves. e.g. W = 60 N.
Doing the arithmetic in your head and writing down only the final number costs you the method marks even when the number is right. Showing the three steps protects you when the arithmetic goes wrong, because the method marks are still there.
The units examiners expect
| Situation | Unit to write | Common wrong answer |
|---|---|---|
| A calculated weight | N | kg |
| A stated mass | kg | N |
| A calculated value of g | N/kg | N, or kg/N |
| A force measured with a spring balance | N | kg, g |
A hiker packs a rucksack of mass 6.0 kg. The hiker also carries a small spring balance, used to check the load.
Take the gravitational field strength on Earth to be 10 N/kg.
- Calculate the weight of the rucksack on Earth. [2]
- The hiker takes the same filled rucksack to Mars, where the gravitational field strength is 3.8 N/kg. Calculate the weight of the rucksack on Mars. [2]
- State the mass of the rucksack on Mars, and explain why it is the same as on Earth. [2]
- On the Moon, the hiker's spring balance reads 9.6 N for the rucksack. Calculate the gravitational field strength on the Moon. [2]
- A second hiker writes in her notes: “The rucksack has a mass of 60 N and a weight of 6.0 kg.” Identify the two errors in this statement and write the corrected sentence. [2]
Total: 10 marks
Model answers
- W = m × g
W = 6.0 kg × 10 N/kg
W = 60 N - W = m × g
W = 6.0 kg × 3.8 N/kg
W = 22.8 N (accept 23 N to 2 significant figures) - The mass is 6.0 kg. Mass is the amount of matter in the object, and it does not depend on where the object is, so it does not change when the rucksack is taken from Earth to Mars. Only the weight changes, because g is smaller on Mars.
- g = W ÷ m
g = 9.6 N ÷ 6.0 kg
g = 1.6 N/kg - The two errors are that the mass has been given in newtons and the weight has been given in kilograms. The corrected sentence is: “The rucksack has a mass of 6.0 kg and a weight of 60 N.”
That closes the page. Worked through in order, Parts A to D cover describing a force, the contact forces that are easy to mix up, pressure in solids and fluids, and the exam habits that turn understanding into marks. If you can write every model answer above without looking, you are ready.
2 Contact and Non-Contact Forces
3 Adding Forces Up: the Resultant
4 Worked Examples: Resultants in a Straight Line
6 The Normal Force: a Surface Pushing Back
7 Elastic Force: the Spring That Pulls Back
8 Measuring Force: Using a Spring Balance Properly
11 Worked example: walking on soft snow
12 Pressure in everyday life
13 Pressure in fluids
16 Exam-Style Question: Mass, Weight and g