Dynamics: (b) the newton as the unit of force

The idea

The newton is the SI unit of force, defined as the force that gives a mass of one kilogram an acceleration of one metre per second squared. In base units this is written 1 N = 1 kg m s⁻², which follows directly from F = ma. Because the newton is a derived unit, it can always be broken down into kilograms, metres and seconds, which is useful for checking that equations are homogeneous.

For example: A resultant force of 5 N acting on a 2 kg mass produces an acceleration of 2.5 m s⁻², and the unit of that result, m s⁻², matches the base-unit form of the newton divided by the kilogram.

What earns the marks

• The newton is the SI unit of force.
• One newton is the force that gives a mass of one kilogram an acceleration of one metre per second squared.
• In base units, 1 N = 1 kg m s⁻².
• The newton is a derived unit, obtained from the relationship F = ma.
• Base-unit analysis of the newton can be used to check the homogeneity of force equations.

Common mistakes and how to put them right

• Writing the newton as a base unit rather than a derived unit.

  Put it right: It is defined in terms of kilograms, metres and seconds.

• Confusing the newton with the kilogram.

  Put it right: The kilogram measures mass, while the newton measures force.

• Omitting the direction when stating a force in newtons.

  Put it right: Force is a vector quantity, so its direction matters.

• Using the wrong base-unit form, such as kg m s⁻¹, instead of kg m s⁻², when checking an equation.

Exam tips

• Convert all quantities to SI base units before substituting into F = ma so the answer comes out in newtons.
• Use base-unit analysis to check that both sides of an equation have the same units.
• Give the direction of a force as well as its magnitude when the question asks for the force.