Density and Pressure
5 marks · NormalA student is investigating the density of a small irregular-shaped stone. She records the following measurements:
| Measurement | Value |
|---|---|
| Mass of stone | 65 g |
| Initial volume of water in measuring cylinder | 85 cm³ |
| Final volume of water + stone | 107 cm³ |
Calculate the volume of the stone.
Calculate the density of the stone in g/cm³.
If the stone is placed on a sandy surface and exerts a downward force equal to its weight, with a contact area of 1.3 cm², calculate the pressure (in Pa) the stone exerts on the sand. (Take g = 10 N/kg; 1 cm² = 0.0001 m²)
Work this out on paper, then compare with the answer and worked solution below. With a free account you can submit written answers for marking.
Show answer
(a) 22 cm³
(b) 2.95 g/cm³
(c) 50000 Pa · must show Correct conversions, Correct substitution
Common mistakes: Forgetting to convert mass to kg for force; Not converting area to m^2
Show mark scheme and worked solution
Marking points
A1a (a) · 1 mark · Correctly calculates volume by subtraction, includes unit.
M1b (b) · 1 mark · Substitutes values into density formula
A1b (b) · 1 mark · Calculates density with correct value and unit
M1c (c) · 1 mark · Converts all units, finds force correctly (weight = mg)
A1c (c) · 1 mark · Substitutes into pressure = force / area, calculates correct answer in Pa
Worked solution
a) Volume = 107 - 85 = 22 cm³
b) Density = 65 g / 22 cm³ = 2.95 g/cm³
c) Mass = 65 g = 0.065 kg; Force = 0.065 × 10 = 0.65 N Area = 1.3 × 0.0001 = 0.00013 m² Pressure = 0.65 / 0.00013 = 50000 Pa