Changes in energy: mass, m, in kilograms, kg

The idea

Mass measures the amount of matter in an object and is measured in kilograms (kg). In energy calculations, mass must be in kg before substitution into equations such as kinetic energy E_k = ½mv² or gravitational potential energy E_p = mgh. For example, a 2.5 kg ball moving at 4 m/s has E_k = ½ × 2.5 × 4² = 20 J. If a mass is given in grams, convert by dividing by 1000: 500 g = 0.5 kg. Mass is not the same as weight; weight is a force in newtons and depends on gravitational field strength. In the equation E_p = mgh, m is the mass in kg, g is gravitational field strength in N/kg, and h is height in m. Always check units before calculating energy changes.

What earns the marks

• State that mass is measured in kilograms (kg) and is a scalar quantity.
• Convert masses given in grams to kilograms by dividing by 1000 before substitution.
• Use mass in kg in equations for kinetic energy and gravitational potential energy.
• Distinguish mass (kg) from weight (N), noting weight = mass × gravitational field strength.
• Check that all quantities are in consistent SI units before calculating energy changes.

Common mistakes and how to put them right

• Using grams directly in an equation instead of converting to kilograms.

  Put it right by dividing by 1000 first.

• Confusing mass with weight and using newtons in place of kilograms.

  Put it right by identifying mass as kg and weight as N.

• Forgetting to square speed when calculating kinetic energy.

  Put it right by applying v² before multiplying by ½m.

Exam tips

• Always write the unit kg after a mass value in your working to show the correct quantity.
• If a mass is given in grams, convert to kg in a separate step before substitution to avoid arithmetic errors.
• In calculations, show the equation, substitution and answer with unit to gain method marks even if the final answer is wrong.