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.