Force and pressure

01

Forces, mass and weight

A force is a push or pull arising from an interaction between objects. To understand a force, identify what it acts on and what exerts it.

A string pulls on a trolley. A table pushes on a book. Earth attracts both objects. Each description names two interacting bodies, even when only one of them is moving.

Contact and non-contact forces

A contact force involves objects or materials touching. Its direction depends on the interaction.

Normal contact force

A surface pushes on an object in a direction perpendicular to the surface. A table supports a book in this way.

Tension

A stretched string or rope pulls on the object attached to it, along the string and away from the object.

Friction

Surfaces in contact exert a force that opposes their relative sliding, or their tendency to slide.

Air resistance

Air exerts a force on an object moving through it. Air is matter, so this is a contact interaction even though we cannot see the air.

Non-contact forces act without the objects touching. Gravitational attraction acts between masses; electrostatic forces act between electric charges; magnetic forces act between magnets or between a magnet and a suitable magnetic material. A magnet can attract a steel paper clip across a gap.

Forces are vectors, so give both magnitude and direction. For example, 6 N upwards describes a force of magnitude 6 newtons acting upwards. The quantity force may be written F or f; its unit is the newton, N.

Mass describes the object; weight is a force

Mass

A measure of the amount of matter in a body. Mass may be written m or M. It is a scalar, measured in kilograms (kg).

Weight

The gravitational force acting on a body. Weight is a vector, measured in newtons (N). Near Earth it acts downwards, towards Earth's centre.

A gravitational field is a region in which a mass experiences a force due to gravitational attraction. The gravitational field strength, g, is the gravitational force per unit mass at that point.

Near Earth's surface, g is approximately 10 N/kg: each kilogram experiences about 10 N of gravitational force. This corresponds to the approximately 10 m/s² downward acceleration of free fall. Field strength is not 10 N/kg everywhere; use the value supplied in a question.

Measuring mass and weight

Use an electronic balance for a mass reading and a spring balance or newton-meter for a force reading. Choose a suitable range and check the zero. When measuring weight with a spring balance, hang the object freely and wait until it is stationary. The upward tension then has the same magnitude as the downward weight.

For example, an object gives a balance reading of 0.150 kg and a steady spring-balance reading of 1.5 N. These are different quantities. Their ratio gives g = 1.5 / 0.150 = 10 N/kg. Record the quantity and unit for each reading; do not call the force reading a mass.

For a small mass, the unit mg means milligram: 1 mg = 0.001 g = 0.000001 kg. In the equation W = mg, the letters instead mean the product m x g, mass multiplied by gravitational field strength. A unit after a mass reading and two quantities in an equation have different roles.

Convert grams to kilograms before using W = mg with g in N/kg. For example, 150 g = 0.150 kg. The prefix conversion changes the number and unit, not the amount of matter.

02

Density from measurements

Density is mass per unit volume. It tells us how much mass occupies a given amount of space.

Compare two samples that each occupy 10 cm³. If one has a mass of 27 g and the other 80 g, the second is denser: it has more mass in the same volume. A larger total mass alone does not show greater density when the volumes are different.

Mass is measured in g or kg; volume is measured in cubic units such as cm³ or m³. Review prefixes and volume conversions if needed. Density uses mass, not the weight in newtons.

Density is a scalar quantity: it has no spatial direction. For a uniform material under the same conditions, doubling the volume doubles the mass, leaving the ratio m / V unchanged.

An irregular solid: measure the displaced volume

Use a balance to find the solid's mass. To find the volume of a suitable irregular solid, record the water volume in a measuring cylinder before and after fully submerging the solid. The increase is the solid's volume.

The solid must be fully submerged, insoluble and non-absorbing, with no water lost. Remove trapped air bubbles: they displace extra water, making the calculated volume too large and the calculated density too small. A floating object's submerged portion is not automatically its whole volume, so this simple method is unsuitable unless the whole solid can be measured correctly.

Choose a cylinder that fits the object and final level while still having useful divisions. Keep it upright and read the bottom of the water meniscus at eye level. The measurement methods page explains the reading technique.

Convert both parts of a density unit

Changing g/cm³ to kg/m³ changes both the mass unit and the volume unit.

Therefore 2.7 g/cm³ = 2700 kg/m³. Dividing 2.7 by 1000 would convert the grams but leave the cubic centimetres unchanged. That would give kg/cm³, not kg/m³.

A regular solid: calculate volume from its shape

For a cuboid, measure its mass and its three perpendicular dimensions. Its volume is length x width x height. Use an instrument with a suitable range and resolution for each dimension.

V = 4.0 x 3.0 x 2.0 = 24 cm³, so ρ = 64.8 / 24 = 2.7 g/cm³. Here geometry provides the volume that displacement provided for the irregular sample.

Measure the actual solid, not a surrounding container or gaps around it. Repeat dimension readings at different positions to judge small variations. If the shape is substantially irregular, assuming a cuboid can give a misleading volume; choose a suitable displacement method instead.

A liquid: subtract the container's mass

1. Weigh a clean, dry, empty measuring cylinder, or zero the balance with the empty cylinder on it.
2. Add the liquid and record its volume at eye level using the appropriate meniscus reading. Keep the outside of the cylinder dry.
3. Weigh the cylinder and liquid. Subtract the empty cylinder's mass, unless it was correctly tared.
4. Divide the liquid's mass by the volume of that same liquid.

For example, an empty cylinder has a mass of 42.6 g. With 50 cm³ of liquid inside, its mass is 82.6 g. The liquid's mass is 82.6 - 42.6 = 40.0 g, giving a density of 40.0 / 50 = 0.80 g/cm³.

Keep the mass and volume measurements matched. If liquid spills after the volume is recorded but before weighing, the smaller measured mass divided by the old volume gives too small a density. Liquid on the outside adds mass without adding to the measured inside volume, so it can make the density too large.

Keep observations separate from calculations. Record the balance and cylinder readings with their units, then show the calculated liquid or solid volume and density. This makes a mistaken subtraction or unit conversion easier to find.

03

Pressure at a surface

Pressure describes the perpendicular force acting per unit area of a surface. The same force produces a greater pressure when spread over a smaller area.

Force is measured in newtons; area is measured in square units. Review mass and weight and square-unit conversions if needed. Area covers a surface; volume measures the space occupied by an object.

Pressure may also be written P. When P means pressure, its unit is Pa; when P means power, its unit is W. Use the named quantity and unit to identify the meaning.

The formula gives the average pressure over the area. If the force is spread uniformly, the pressure is the same across that area. Identify the surface and the force perpendicular to it before calculating.

The same block resting on two faces

A block weighing 30 N rests on a horizontal floor. Only its weight and the floor's upward support act vertically on the block. In either stationary arrangement below, it presses on the floor with a perpendicular force of 30 N.

Use the area of the face touching the floor, not the sum of all the block's faces. Dividing 30 N directly by 150 cm² gives 0.20 N/cm², which is a valid pressure unit, but it is not 0.20 Pa. Convert the area or the final pressure unit correctly.

Determine pressure from measurements

Use a rigid block resting on its flat rectangular face on a horizontal surface. Assume that only its weight and the surface's upward support act vertically.

1. Measure the block's mass: choose a balance whose range includes the mass and whose resolution is suitable for the reading. Check its zero before adding the block and wait for a steady reading.
2. Measure the actual contact face: use a ruler or calipers with suitable range and resolution for both perpendicular side lengths. Align the instrument with each side; check the caliper zero or subtract the ruler's endpoint readings. Read a ruler with the line of sight perpendicular to its scale.
3. Determine the perpendicular force: use the measured mass and supplied gravitational field strength in F = mg. Because the block is stationary, weight and upward support balance; the block presses on the surface with the same force magnitude.
4. Calculate the pressure: multiply the measured side lengths to obtain the contact area, convert it to m², then divide the force in N by this area.

For the block above, a mass reading of 3.0 kg with supplied g = 10 N/kg gives F = 30 N. A measured 15 cm x 10 cm face gives 0.015 m², so the average pressure is the calculated 2000 Pa.

The chosen area must actually support the block. If it rests only on small feet, use their contact areas instead of the whole rectangular footprint. Overestimating the area makes the calculated pressure too small; repeating the length reading does not fix a wrong choice of contact area.

Compare the force and area together

• Same force, larger area: lower pressure. Snowshoes spread the same person's weight over a larger contact area than ordinary shoes.
• Same area, larger perpendicular force: greater pressure.
• Both force and area change: compare F / A. If both double, the pressure stays the same.

The condition matters. A smaller contact area does not always mean a greater pressure if the force also becomes smaller. Calculate the ratio or compare the factors rather than using area alone.

Pressure is not an extra force. Force is measured in N; pressure describes force per area and is measured in Pa. Do not add a separate "pressure force" alongside the same contact force and count the interaction twice.