A pressure calculation with p = F ÷ A needs a force in newtons. If the question gives a mass in kilograms, first find the weight with W = m × g, then divide by the area. Skipping this step is one of the most common ways to lose marks on pressure questions.
This lesson protects every calculation in pressure in solids and fluids. The mass and weight link is explained in mass, weight and density.
Why does it matter?
Mass is how much matter an object has, in kilograms. Weight is the gravitational force on that mass, in newtons. They are different quantities with different units.
With g = 10 N/kg, a 60 kg person has a weight of 600 N. The number is ten times bigger, and using 60 instead of 600 gives a pressure ten times too small.
A routine that prevents the slip
- Underline the quantity given for the load. Is it in N or in kg?
- If it is in kg, write W = mg and calculate the weight first.
- Convert the area to m² if needed.
- Write p = F ÷ A and substitute the force in newtons.
- Check the unit of the answer: N ÷ m² = Pa.
If a question says “force” or “weight”, no conversion is needed. If it says “mass” or gives kilograms, convert.
Worked example
A student of mass 60 kg stands on both feet. Each shoe has a contact area of 0.025 m².
Find the pressure on the floor. Use g = 10 N/kg. (Invented example data.)
Step 1, weight: W = mg = 60 × 10 = 600 N.
Step 2, total area: 2 × 0.025 = 0.050 m².
Step 3, pressure: p = F ÷ A = 600 ÷ 0.050 = 12 000 Pa.
Check: if the student lifts one foot, the area halves to 0.025 m² and the pressure doubles to 24 000 Pa, since 600 ÷ 0.025 = 24 000.
The mistake to watch for
A common slip is to use the mass in place of the force.
Mistaken answer: p = 60 ÷ 0.050 = 1200 Pa.
The student divided kilograms by square metres. The result is 1200 kg/m², not pascals, and it is ten times too small.
The correction is to write the weight first: 600 N ÷ 0.050 m² = 12 000 Pa. The unit check helps here, because kg ÷ m² cannot give Pa.
Check yourself
Use g = 10 N/kg.
1. A book of mass 2.5 kg rests on a table. The contact area is 0.050 m². Find the pressure.
Show answer
W = 2.5 × 10 = 25 N. p = 25 ÷ 0.050 = 500 Pa
2. An elephant has a mass of 4000 kg and each of its four feet has an area of 0.10 m². Find the pressure under the feet when it stands still.
Show answer
W = 4000 × 10 = 40 000 N. Total area = 4 × 0.10 = 0.40 m². p = 40 000 ÷ 0.40 = 100 000 Pa, or 1.0 × 10⁵ Pa.
3. A block exerts a pressure of 8000 Pa on a surface. The contact area is 0.030 m². Find its mass.
Show answer
F = pA = 8000 × 0.030 = 240 N. m = W ÷ g = 240 ÷ 10 = 24 kg
Where this leads next
Put all five skills together in the pressure practice set, and log any repeated slip with the mistake log and retest queue.
Mass and weight are easy to understand and easy to forget under time pressure. A routine that a teacher checks with you on real questions is the core of online one-to-one Physics tuition.